The dispersion relation of pion in nuclear matter

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π-π弱相互作用

es and the nature of aromatic– aromatic interactions
In the arrangement of aromatic rings one can distinguish generally between a stacked arrangement and an edge- or point-to-face, T-shaped conformation (Fig. 1). The T-shaped conformation is a C–H ؒ ؒ ؒ π interaction.20–22 Stacking does not necessarily have to be a perfect face-to-face alignment of the atoms but can also be an oﬀset or slipped packing. Both face-to-face and T-shaped conformations are limiting forms in aromatic interactions. Among these, the stacked (facial) arrangements are of particular interest as π–π interactions. A sizeable number of theoretical and experimental studies have been performed to understand the nature of π–π interactions. While there is considerable experimental evidence on the structure and property inﬂuencing character of these interactions, their true nature is still a matter of some discussion.3,5–7,12 The following electrostatic or van-der-Waals interactions are discussed as intermolecular forces 23 for the stabilization of π–π interactions between closed-shell molecules;5,24 (Fig. 2 gives a pictorial summary of the interactions). (a) Dipole– dipole (electrostatic) interactions: the interactions between the diﬀerent permanent and static molecular charge distributions. (b) Dipole–induced-dipole interactions between the static molecular charge distribution of group A with a proximityinduced change in charge distribution of group B. (c) Induceddipole–induced-dipole (London) dispersion interaction: the instantaneous dipole moment from a ﬂuctuating electron cloud polarizes a neighboring molecule and induces in it also an instantaneous dipole. These van-der-Waals interactions (a)–(c) are inherently attractive and their potentials fall oﬀ rapidly with distance by 1/r 6. (d) Pauli repulsion: at very short distances the ﬁlled electron clouds of the interacting molecules begin to overlap and the (Pauli) repulsion between the electron shells J. Chem. Soc., Dalton Trans., 2000, 3885–3896 3885

Quantum Foam

a rXiv:g r-qc/4115v15Jan24February 7,20082:43WSPC/Trim Size:9.75in x 6.5in for Proceedings quantumfoam QUANTUM FOAM Y.JACK NG Institute of Field Physics,Department of Physics and Astronomy,University of North Carolina,Chapel Hill,NC 27599-3255,USA E-mail:yjng@ Quantum foam,also known as spacetime foam,has its origin in quantum ﬂuctuations of spacetime.Its physics is intimately linked to that of black holes and computation.Arguably it is the source of the holographic principle which severely limits how densely information can be packed in space.Various proposals to detect the foam are brieﬂy discussed.Its detection will provide us with a glimpse of the ultimate structure of space and time.1.Introduction Before last century,spacetime was regarded as nothing more than a passive and static arena in which events took place.Early last century,Einstein’s general rela-tivity changed that viewpoint and promoted spacetime to an active and dynamical entity.Nowadays many physicists also believe that spacetime,like all matter and energy,undergoes quantum ﬂuctuations.These quantum ﬂuctuations make space-time foamy a on small spacetime scales.But how large are the ﬂuctuations?How foamy is spacetime?Is there anytheoretical evidence of quantum foam?And how can we detect quantum foam?In what follows,we address these questions.The outline of this paper is as follows:By analysing a gedanken experiment for spacetime measurement,we show,in sub-section 2.1,that spacetime ﬂuctuations scale as the cube root of distances or time durations.In subsection 2.2,we show that this cube root dependence is consistent with the holographic principle.Subsection 2.3is devoted to a comparison of this peculiar dependence with the well-known random-walk problem and other quantum gravity models.Here we also consider the cumulative eﬀects of individual space-time ﬂuctuations.In section 3,we discuss how quantum foam aﬀects the physics of clocks and computation (subsection 3.1),and show that the physics of space-time foam is intimately connected to that of black holes (subsection 3.2).Just as there are uncertainties in spacetime measurements,there are also uncertainties in energy-momentum measurements.This topic of energy-momentum uncertainties is given a brief treatment in section 4.Some proposals to detect quantum foam areFebruary7,20082:43WSPC/Trim Size:9.75in x6.5in for Proceedings quantumfoam2considered in section5.One particular proposal involving ultra-high energy cosmic ray events is discussed in the Appendix.Before we proceed,we should mention that the approach to the physics of quan-tum foam adopted here is very conservative:the only ingredients we use are quan-tum mechanics and general relativity.Hopefully,by considering only distances(time durations)much larger than the Planck length(time)or energies(momenta)much smaller than Planck energy(momentum),a semi-classical treatment of gravity suf-ﬁces and a bonaﬁde theory of quantum gravity is not needed.We should also make it clear at the outset that we make no assumptions on the high energy regime of the ultimate quantum gravity theory.We refrain from speculating on violations of Lorentz invariance and the consequent systematically modiﬁed dispersion relations, involving a coeﬃcient ofﬁxed magnitude andﬁxed sign,which many people believe are unavoidably induced by quantum gravity.(In the terminology of Ref.2,these quantum gravity eﬀects are called“systematic”eﬀects.)The only quantum grav-ity eﬀects we are concerned with in this paper are those due to quantum fuzziness —uncertainties involvingﬂuctuating magnitudes with both±signs,perhaps like a ﬂuctuation with a Gaussian distribution about zero.(In the terminology of Ref.2, these eﬀects are called“non-systematic”eﬀects.)2.Quantum Fluctuations of SpacetimeIf spacetime indeed undergoes quantumﬂuctuations,theﬂuctuations will show up when we measure a distance(or a time duration),in the form of uncertainties in the measurement.Conversely,if in any distance(or time duration)measurement,we cannot measure the distance(or time duration)precisely,we interpret this intrinsic limitation to spacetime measurements as resulting fromﬂuctuations of spacetime.The question is:does spacetime undergo quantumﬂuctuations?And if so,how large are theﬂuctuations?To quantify the problem,let us consider measuring a distance l.The question now is:how accurately can we measure this distance?Let us denote byδl the accuracy with which we can measure l.We will also refer to δl as the uncertainty orﬂuctuation of the distance l for reasons that will become obvious shortly.We will show thatδl has a lower bound and will use two ways to calculate it.Neither method is rigorous,but the fact that the two very diﬀerent methods yield the same result bodes well for the robustness of the conclusion.2.1.Gedanken ExperimentIn theﬁrst method,we conduct a thought experiment to measure l.The impor-tance of carrying out spacetime measurements toﬁnd the quantumﬂuctuations in the fabric of spacetime cannot be over-emphasized.According to general relativ-ity,coordinates do not have any intrinsic meaning independent of observations;a coordinate system is deﬁned only by explicitly carrying out spacetime distance mea-surements.Let us measure the distance between point A and point B.FollowingFebruary7,20082:43WSPC/Trim Size:9.75in x6.5in for Proceedings quantumfoam3 Wigner3,we put a clock at A and a mirror at B.Then the distance l that we want to measure is given by the distance between the clock and the mirror.By sending a light signal from the clock to the mirror in a timing experiment,we can determine the distance l.However,the quantum uncertainty in the positions of the clock and the mirror introduces an inaccuracyδl in the distance measurement.We expect the clock and the mirror to contribute comparable uncertainties to the measurement.Let us concentrate on the clock and denote its mass by m.Wigner argued that if it has a linear spreadδl when the light signal leaves the clock,then its position spread grows toδl+ l(mcδl)−1when the light signal returns to the clock,with the minimum atδl=( l/mc)1/2.Hence one concludes thatlδl2.(2)c2Thus general relativity alone would suggest using a light clock to do the measure-ment.This result can also be derived in another way.If the clock has a radius d/2(larger than its Schwarzschild radius r S),thenδl,the error in the distance measurement caused by the curvature generated by the mass of the clock,may be estimated by a calculation from the Schwarzschild solution.The result is r S mul-February7,20082:43WSPC/Trim Size:9.75in x6.5in for Proceedings quantumfoam4tiplied by a logarithm involving2r S/d and r S/(l+d/2).For d>>r S,oneﬁndsδl=1d and hence Eq.(2)as an order of magnitude estimate.The product of Eq.(2)with Eq.(1)yieldsδl (ll2P)1/3=l P lb The spacetimeﬂuctuation translates into a metricﬂuctuation over a distance l and a time interval τgiven byδgµνgreater than(l P/l)2/3,(t P/τ)2/3respectively.For a discussion of the related light-coneﬂuctuations,see Ref.5.February 7,20082:43WSPC/Trim Size:9.75in x 6.5in for Proceedings quantumfoam 5llδl δlδlδllFigure 1.Partitioning a big cube into small cubes.The big cube represents a region of space measuring l by l by l .The small cubes represent the smallest physically-allowed cubes measuring δl by δl by δl that can be lined up to measure the length of each side of the big cube.Strangely,the size of a small cube is not universal,but depends on the size of the big cube.A simple argument based on this construction leads to the holographic principle.of degrees of freedom that the region can hold is given by the number of small cubes that can be put inside that region.But how small can such cubes be?A moment’s thought tells us that each side of a small cube cannot be smaller than the accuracy δl with which we can measure each side l of the big cube.This can be easily shown by applying the method of contradiction:assume that we can construct small cubes each of which has sides less than δl .Then by lining up a row of such small cubes along a side of the big cube from end to end,and by counting the number of such small cubes,we would be able to measure that side (of length l )of the big cube to a better accuracy than δl .But,by deﬁnition,δl is the best accuracy with which we can measure l .The ensuing contradiction is evaded by the realization that each of the smallest cubes (that can be put inside the big cube)measures δl by δl by δl .Thus,the number of degrees of freedom in the region (measuring l by l by l )is givenby l 3/δl 3,which,according to the holographic principle,is no more than l 2/l 2p .Itfollows that δl is bounded (from below)by the cube root of ll 2P ,the same result asfound above in the gedanken experiment argument.Thus,to the extent that the holographic principle is correct,spacetime indeed ﬂuctuates,forming foams of size δl on the scale of l .Actually,considering the fundamental nature of spacetime and the ubiquity of quantum ﬂuctuations,we should reverse the argument and then we will come to the conclusion that the “strange”holographic principle has its originFebruary7,20082:43WSPC/Trim Size:9.75in x6.5in for Proceedings quantumfoam6in quantumﬂuctuations of spacetime.c2.3.Quantum Gravity ModelsThe consistency of the uncertainties in distance measurements with the holographic principle is reassuring.But the dependence of theﬂuctuations in distance on the cube root of the distance is still perplexing.To gain further insight into this strange state of aﬀairs,let us compare this peculiar dependence on distance with the well-known one-dimensional random-walk problem.For a random walk of steps of equal size,with each step equally likely to either direction,the root-mean-square deviation from the mean is given by the size of each step multiplied by the square root of the number of steps.It is now simple to concoct a random-walk model10,11for theﬂuctuations of distances in quantum gravity.Consider a distance l,which we partition into l/l P units each of length l P.In the random-walk model of quantum gravity,l P plays the role of the size of each step and l/l P plays the role of the number of steps.Theﬂuctuation in distance l is given by l P times the square root of l/l P,which comes out to the square root of ll P.This is much bigger than the cube root of ll2P,theﬂuctuation in distance measurements found above.The following interpretation of the dependence ofδl on the cube root of l now presents itself.As in the random-walk model,the amount ofﬂuctuations in the dis-tance l can be thought of as an accumulation of the l/l P individualﬂuctuations each by an amount plus or minus l P.But,for this case,the individualﬂuctuations cannot be completely random(as opposed to the random-walk model);actually successive ﬂuctuations must be somewhat anti-correlated(i.e.,a plusﬂuctuation is slightly more likely followed by a minusﬂuctuation and vice versa),in order that together they produce a totalﬂuctuation less than that in the random-walk model.This small amount of anti-correlation between successiveﬂuctuations(corresponding to what statisticians call fractional Brownian motion with self-similarity parameter1c Recently,Scardigli and Casadio9claim that the expected holographic scaling seems to hold onlyin(3+1)dimensions and only for the“generalized uncertainty principle”found above forδl.February 7,20082:43WSPC/Trim Size:9.75in x 6.5in for Proceedings quantumfoam7distance and time duration measurements —we will see below that these models (corresponding to the hatched line to the right of the random-walk model shown in Fig.2)have already been observationally ruled out.correlationl 1/3l 2/3P l 0l 1P l 1/2l 1/2P l 1l 0PFigure 2.Lower bounds on δl for the various quantum gravity models.The ﬂuctuation of the distance l is given by the sum of l/l P ﬂuctuations each by plus or minus l P .Spacetime foam ap-pears to choose a small anti-correlation (i.e.,negative correlation)between successive ﬂuctuations,giving a cube root dependence in the number l/l p of ﬂuctuations for the total ﬂuctuation of l (indicated by the arrow).It falls between the two extreme cases of complete randomness,i.e.,zero (anti-)correlation (corresponding to δl ∼l 1/2l 1/2P )and complete anti-correlation (correspondingto δl ∼l P ).Quantum gravity models corresponding to positive correlations between successive ﬂuctuations (indicated by the hatched portion)are observationally ruled out.Let us now examine the cumulative eﬀects 13of spacetime ﬂuctuations over alarge distance.Consider a distance l ,and divide it into l/λequal parts each of which has length λ.If we start with δλfrom each part,the question is how do the l/λparts add up to δl for the whole distance l .In other words,we want to ﬁnd the cumulative factor C deﬁned byδl =C δλ,(4)For the holography model,since δl ∼l 1/3l 2/3P =l P (l/l P )1/3and δλ∼λ1/3l 2/3P =l P (λ/l P )1/3,the result isC = lδλ=lFebruary7,20082:43WSPC/Trim Size:9.75in x6.5in for Proceedings quantumfoam8Table1.The corresponding quantities in the discussion of distance measure-ments(ﬁrst column),time duration measurements(second column),clocks(third column),and computers(fourth column)appear in the same row inthe following Table.distance time duration running number of bitsdivided by speed(τ)time divided by compu-of light(l/c)(T)tation speed(I/ν)February7,20082:43WSPC/Trim Size:9.75in x6.5in for Proceedings quantumfoam9 T,the linear spread of the clock(of mass m)grows toδl ( T/m)1/2.But the position uncertainty due to the act of time measurement must be smaller than the minimum wavelength of the quanta used to read the clock:δl ct,for the entire period T.It follows that14t2Tc3,(7) the analogue of Eq.(2).One can combine the above two equations to give14T/t3 t−2P =c5G∼1086/sec2.(9)February7,20082:43WSPC/Trim Size:9.75in x6.5in for Proceedings quantumfoam10The latter bound is intriguing:it requires the product of the number of bits and the square of the computation rate for any simple computer to be less than the square of the reciprocal of Planck time,14which depends on relativistic quantum gravity(involving c, ,and G).This relation links together our concepts of informa-tion/computation,relativity,gravity,and quantum uncertainty.Numerically,the computation bound is about seventy-six orders of magnitude above what is avail-able for a current lap-top computer performing ten billion operations per second on ten billion bits,for which Iν2∼1010/s2.3.2.Black HolesNow we can apply what we have learned about clocks and computers to black holes.14,15Let us consider using a black hole to measure time.It is reasonable to use the light travel time around the black hole’s horizon as the resolution time of the clock,i.e.,t∼Gmc4≡T BH.(10) We have just recovered Hawking’s result for black hole lifetime!Finally,let us consider using a black hole to do computations.This may sound like a ridiculous proposition.But if we believe that black holes evolve according to quantum mechanical laws,it is possible,at least in principle,to program black holes to perform computations that can be read out of theﬂuctuations in the Hawking black hole radiation.How large is the memory space of a black hole computer,and how fast can it compute?Applying the results for computation derived above,we readilyﬁnd the number of bits in the memory space of a black hole computer,given by the lifetime of the black hole divided by its resolution time as a clock,to beI=T BHm2P∼r2SFebruary 7,20082:43WSPC/Trim Size:9.75in x 6.5in for Proceedings quantumfoam 11Spacetime foamComputation/InformationBlack hole Iν2∼c 5m P c2/3,(13)where a priori β∼1.The corresponding statement for energy uncertainties isδE =γE EFebruary7,20082:43WSPC/Trim Size:9.75in x6.5in for Proceedings quantumfoam12the energy-momentum uncertainties are very small,suppressed by a fractional(two-thirds)power of the Planck energy-momentum.(For example,the uncertainty in the energy of a particle of ten trillion electron-volts is about a thousand electron-volts.) Energy-momentum uncertainties aﬀect both the energy-momentum conservation laws and the dispersion relations.Energy-momentum is conserved up to energy-momentum uncertainties due to quantum foam eﬀects,i.e.,Σ(pµi+δpµi)is conserved, with pµi being the average values of the various energy-momenta.On the other hand the dispersion relation is now generalized to readE2−p2c2−ǫp2c2 pcE P 2/3.(16)The speed of(massless)photonv=∂E6ǫE2/3February7,20082:43WSPC/Trim Size:9.75in x6.5in for Proceedings quantumfoam13 light from distant galaxies has to travel a distance of many wavelengths.It is pos-sible that over so many wavelengths,theﬂuctuations can cumulatively add up to a detectable level at which point the phase coherence for the light-waves is lost.Loss of phase coherence would mean the loss of interference patterns.Thus the strategy is to look for the blurring of images of distant galaxies in powerful telescopes like the Hubble Space Telescope.This technique to detect spacetime foam was proposed by Lieu and Hillman19,and elaborated by Ragazzoni and his collaborators20.The proposal deals with the phase behavior of radiation with wavelengthλreceived from a celestial source located at a distance l away.Fundamentally,the wavelength deﬁnes the minimum length scale over which physical quantities such as phase and group velocities(and hence dispersion relations)can be deﬁned.Thus, the uncertainty inλintroduced by spacetime foam is the starting point for this analysis.A wave will travel a distance equal to its own wavelengthλin a time t=λ/v g where v g is the group velocity of propagation,and the phase of the wave consequently changes by an amountφ=2πv p tv g,(18)(i.e.,if v p=v g,φ=2π)where v p is the phase velocity of the light wave.Quantum gravityﬂuctuations,however,introduce random uncertainties into this phase which is simplyδφ=2πδ v pv g ∼± Eλ 2/3,(20)where we have used v p=E/p and v g=dE/dp,and E/E P=l P/λ.We emphasize that this may be either an incremental advance or a retardation in the phase.In travelling over the macroscopically large distance,l,from source to observer an electromagnetic wave is continually subjected to random,incoherent spacetime ﬂuctuations.Therefore,by our previous argument given in subsection2.3,the cumulative statistical phase dispersion is∆φ=Cδφwith the cumulative factor C=(l/λ)1/3,that is∆φ=2πa l Pλ 1/3=2πa l2/3P l1/3February7,20082:43WSPC/Trim Size:9.75in x6.5in for Proceedings quantumfoam14Lieu and Hillman,which is more than four billion light years from Earth,is not far enough to make the light wave front noticeably distorted.A simple calculation13 shows that,over four billion light years,the phase of the light wavesﬂuctuates only by one billionth of what is required to lose the sharp ring-like interference pattern around the galaxy which,not surprisingly,is observed21by the Hubble Telescope.This example illustrates the degree of diﬃculty which one has to overcome to de-tect spacetime foam.The origin of the diﬃculty can be traced to the incoherent nature of the spacetimeﬂuctuations(i.e.,the anticorrelations between successive ﬂuctuations).But not all is lost with Lieu and Hillman’s proposal.One can check that the proposal can be used to rule out13,if only marginally,the random-walk model of quantum gravity,which would(incorrectly)predict a large enough phaseﬂuctuation for light from PKS1413+135to lose phase coherence,contradicting evidence of diﬀraction patterns from the Hubble Telescope observation.It follows that models corresponding to correlating successiveﬂuctuations are also ruled out.5.2.High EnergyγRays from Distant GRBFor another idea to detect spacetime foam,let us recall that,due to quantum ﬂuctuations of spacetime,the speed of lightﬂuctuates around c and theﬂuctuations increase with energy.Thus for photons(quanta of light)emitted simultaneously from a distant source coming towards our detector,we expect an energy-dependent spread in their arrival times.To maximize the spread in arrival times,we should look for energetic photons from distant sources.High energy gamma rays from distant gamma ray bursts17ﬁt the bill.So the idea is to look for a noticeable spread in arrival times for such high energy gamma rays from distant gamma ray bursts.This proposal wasﬁrst made by G.Amelino-Camelia et al.17in another context.To underscore the importance of using the correct cumulative factor to estimate the spacetime foam eﬀect,let usﬁrst proceed in a naive manner.Atﬁrst sight,the ﬂuctuating speed of light would seem to yield18an energy-dependent spread in the arrival times of photons of the same energy E given byδt∼|ǫ|t(E/E P)2/3,where t is the average overall time of travel from the photon source.Furthermore,the modiﬁed energy-momentum dispersion relation would seem to predict time-of-ﬂight diﬀerences between simultaneously-emitted photons of diﬀerent energies,E1andE2,given byδt≃ǫt(E2/31−E2/32)/E2/3P.But these results for the spread of arrivaltimes of photons are not correct,because we have inadvertently used l/λ∼Et/ as the cumulative factor instead of the correct factor(l/λ)1/3∼(Et/ )1/ingthe correct cumulative factor,we get a much smallerδt∼t1/3t2/3P for the spreadin arrival time of the photons of the same energy.Thus the result is that the time-of-ﬂight diﬀerences increase only with the cube root of the average overall time of travel from the gamma ray bursts to our detector,leading to a time spread too small to be detectable.1February7,20082:43WSPC/Trim Size:9.75in x6.5in for Proceedings quantumfoam155.3.Interferometry TechniquesSuppressed by the extraordinarily short Planck length,ﬂuctuations in distances, even large distances,are very small.So,to measure suchﬂuctuations,what one needs is an instrument capable of accurately measuringﬂuctuations in length over long distances.Modern gravitational-wave interferometers,having attained extraor-dinary sensitivity,come to mind.The idea of using gravitational-wave interferom-eters to measure the foaminess of spacetime was proposed by Amelino-Camelia10 and elaborated by the author and van Dam6.Modern gravitational-wave inter-ferometers are sensitive to changes in distances to an accuracy better than10−18 meter.To attain such sensitivity,interferometer researchers have to contend with many diﬀerent noises,the enemies of gravitational-wave research,such as thermal noise,seismic noise,and photon shot noise.To this list of noises that infest an inter-ferometer,we now have to add the faint yet ubiquitous noise from spacetime foam.In other words,even after one has subtracted all the well-known noises,there is still the noise from spacetimeﬂuctuations left in the read-out of the interferometer.The secret of this proposal to detect spacetime foam lies in the existence of another length scale10available in this particular technique,in addition to the minuscule Planck length.It is the scale provided by the frequency f of the inter-ferometer bandwidth.What is important is whether the length scale l2/3P (c/f)1/3,characteristic of the noise from spacetime foam at that frequency,is comparable to the sensitivity level of the interferometer.The hope is that,within a certain range of frequencies,the experimental limits will soon be comparable to the theoretical predictions for the noise from quantum foam.The detection of spacetime foam with interferometry techniques is also helped by the fact that the correlation length of the noise from spacetimeﬂuctuations is extremely short,as the characteristic scale is the Planck length.Thus,this faint noise can be easily distinguished from the other sources of noise because of this lack of correlation.In this regard,it will be very useful for the detection of spacetime foam to have two nearby interferometers.To proceed with the analysis,oneﬁrst decomposes the displacement noise in terms of the associated displacement amplitude spectral density22S(f)of fre-quency f.For the displacement noise due to quantum foam,it is given byS(f)∼c1/3l2/3P f−5/6,inversely proportional to(the5/6th power of)frequency.So one can optimize the performance of an interferometer at low frequencies.As lower frequency detection is possible only in space,interferometers like the proposed Laser Interferometer Space Antenna23may enjoy a certain advantage.To be speciﬁc,let us now compare the predicted spectal density from quantum foam noise with the noise level projected for the Laser Interferometer Gravitational-Wave Observatory.The“advanced phase”of LIGO24is expected to achieve a displacement noise level of less than10−20mHz−1/2near100Hz;one can show that this would translate into a probe of l P down to10−31cm,a mere hundred times the physical Planck length.But can we then conclude that LIGO will be within strikingFebruary7,20082:43WSPC/Trim Size:9.75in x6.5in for Proceedings quantumfoam16distance of detecting quantum foam?Alas,the above optimistic estimate is based on the assumption that spacetime foam aﬀects the paths of all the photons in the laser beam coherently.But,in reality,this can hardly be the case.Since the total eﬀect on the interferometer is based on averaging over all photons in the wave front, the incoherent contributions from the diﬀerent photons are expected to cut down the sensitivity of the interferometer by some fractional power of the number of photons in the beam—and there are many photons in the beams used by LIGO.Thus, even with the incredible sensitivity of modern gravitational-wave interferometers like LIGO,theﬂuctuations of spacetime are too small to be detected—unless one knows how to build a small beam interferometer of slightly improved power and phase sensitivity than what is projected for the advanced phase of LIGO!e For completeness,we should mention that the use of atom interferometers7,25 and optical interferometers26to look for eﬀects of spacetimeﬂuctuations has also been suggested.Last but not least,spacetime foam physics has been applied to explain some baﬄing ultra-high energy cosmic ray events27reported by the Akeno Giant Air Shower Array observatory in Japan.But there are uncertainties on both the obser-vational and theoretical sides.We relegate a short discussion on the UHECR events to the Appendix.6.Summary and ConclusionWe summarize by collecting some of the salient points:•On large scales spacetime appears smooth,but on a suﬃciently small scaleit is bubbly and foamy(just as the ocean appears smooth at high altitudesbut shows its roughness at close distances from its surface).•Spacetime is foamy because it undergoes quantumﬂuctuations which giverise to uncertainties in spacetime measurements;spacetimeﬂuctuationsscale as the cube root of distances or time durations.•Quantum foam physics is closely related to black hole physics and com-putation.The“strange”holographic principle,which limits how denselyinformation can be packed in space,is a manifestation of quantum foam.•Because the Planck length/time is so small,the uncertainties in spacetimemeasurements,though much greater than the Planck scale,are still verysmall.•It may be diﬃcult to detect the tiny eﬀects of quantum foam,but it is byno means impossible.Recall that,by analyzing a simple gedanken experiment for spacetime measure-ments,we arrive at the conclusion that spacetimeﬂuctuations scale as the cube root of distances or time durations.This cube root dependence is mysterious,but has。

PragmaticPresupposition英文版

Research value
The results of this study will help deepen our understanding of language, promote the development of linguistics and philosophy, and also provide new ideas and methods for interdisciplinary research.
Research background: With the continuous development of linguistics and philosophy, scholars have begun to pay attention to the phenomenon of presupposition in language use and attempt to conduct in-depth research from different perspectives.
Overview of Pragmatic Presumption Theory
CATALOGUE
02
Pragmatic presupposition, also known as pragmatic presupposition, is a linguistic phenomenon that refers to the implicit and non explicitly stated information conveyed by the speaker to the listener through specific contexts and language usage in verbal communication.

Dispersion relations at finite temperature and density for nucleons and pions

a rXiv:h ep-ph/9911451v123Nov1999FIUN-CP-99/2Dispersion relations at ﬁnite temperature and density for nucleons and pions R.Hurtado 1Department of Physics,University of Wales Singleton Park,Swansea,SA28PP,United Kingdom J.Morales 1and C.Quimbay 1Departamento de F´ısica,Universidad Nacional de Colombia Ciudad Universitaria,Santaf´e de Bogot´a ,D.C.,Colombia November 21,1999To be published in Heavy Ion Physics Abstract We calculate the nucleonic and pionic dispersion relations at ﬁnite tem-perature (T )and non-vanishing chemical potentials (µf )in the context of an eﬀective chiral theory that describes the strong and electromagnetic interac-tions for nucleons and pions.The dispersion relations are calculated in thebroken chiral symmetry phase,where the nucleons are massive and pions are taken as massless.The calculation is performed at lowest order in the energy expansion,working in the framework of the real time formalism of thermal ﬁeld theory in the Feynman gauge.These one-loop dispersion relations are ob-tained at leading order with respect to T and µf .We also evaluate the eﬀective masses of the quasi-nucleon and quasi-pion excitations in thermal and chemical conditions as the ones of a neutron star.Keywords:Chiral Lagrangians,Dispersion Relations,Finite Temperature,Chemical Potentials,Nucleons,Pions.1IntroductionEﬀective chiral theories have become a major conceptual and analytical tool in par-ticle physics driven by the need of a theory to describe the low–energy phenomenology of QCD.The foundations were formulated originally by Weinberg[1]to characterise the most general S-matrix elements for soft pion interactions and later it was further developed by Gasser and Leutwyler[2].Eﬀective chiral theories have shown to be an adequate framework to treat low–energy phenomenology[3]-[6],as they reproduce,at lowest order in the chiral expansion,the most important results from current algebras including the low–energy theorems,and at next-to-leading order,they give precise corrections to these results[3].They have been widely applied to diﬀerent problems as meson–meson,meson–baryon,photon–photon,photon–meson and photon–baryon scattering,photoproduction processes and rare kaon decays[7,18].The propagation properties of relativistic particles in plasmas atﬁnite tempera-ture is also a subject of increasing interest.It is well known that the interaction of a particle with a plasma in thermal equilibrium at temperature T modiﬁes the Disper-sion Relations(DR)with respect to the zero temperature situation.This phenomenon has been extensively investigated for the non-dense plasma case[19]-[30],i.e.when the chemical potential(µf)associated to the fermions of the thermal plasma is equal to zero:µf=0and T=0.In this case the Fermionic Dispersion Relations(FDR) have been studied for massless fermions in[19]-[22]and massive fermions in[23]-[30]. The FDR describe the propagation of the fermionic excitations of the plasma(quasi-fermions and quasi-holes)through the thermal background.These excitations are originated in the collective behaviour of the plasma system at low momentum.On the other hand,DR describing the propagation of the fermionic excitations of a dense plasma atﬁnite temperature can be found in literature[31]-[35].For the dense plasma case atﬁnite temperature,i.e.µf=0and T=0,the FDR have been calculated both for massless fermions in[31]-[34]and for massive fermions in[35]. These FDR have been calculated in the context of realistic physical models,as for instance,the Minimal Standard Model[29,34].In the present work we calculate the DR for quasi–nucleons and quasi–pions prop-agating in a plasma atﬁnite temperature and non–vanishing chemical potentials. The calculation is performed for a SU(2)L×SU(2)R eﬀective chiral Lagrangian with the chiral symmetry broken into SU(2)L+R.This Lagrangian,which we introduce in section2,describe the strong and electromagnetic interactions of massive nucleons and massless pions.The calculation is performed using the real time formalism of the thermalﬁeld theory[36]-[38]in the Feynman gauge.The one–loop DR are calculated at lowest order in the energy expansion and obtained taking the T2andµ2f terms from the self–energy,as shown in section3.As an application of the DR obtained,we evaluate the eﬀective masses of the quasi–nucleon and quasi–pion excitations takingthe following values:T=150MeV,µp=100MeV andµn=2µp,beingµp(µn)the chemical potential for protons(neutrons)[43].This evaluation is shown in section4, as well as the discussion of the main results and conclusions.2Eﬀective chiral Lagrangian at leading order in the energy expansionEﬀective chiral theories are founded in the existence of an energy scaleΛχat which chiral symmetry SU(N f)L×SU(N f)R,with N f the number ofﬂavours,breaks into SU(N f)L+R leading to N2f−1Goldstone bosons associated to the N f broken generators.These Goldstone bosons are identiﬁed with the meson ground state octet for N f=3,and with the triplet of pions[2,6]in the case of N f=2.The chiral symmetry of the Lagrangian is broken through the introduction of an explicit mass term for the nucleons.A general form for a Lagrangian with SU(2)L+R symmetry describing the strong and electromagnetic interactions for massive nucleons and massless pions is[39,40]:L=F2π4FµνFµν,(2.1)whereLπN=¯Niγµ∂µN−ie¯NγµAµ 1+τ32FπN+Mg2A¯N τ·πFπ,(2.4) where the covariant derivative and electromagnetic charge are deﬁned asDµΣ=∂µΣ+ieAµ[Q,Σ],(2.5)Q= 23 .(2.6)Hereπ,N and Aµrepresent the pion,nucleon and electromagneticﬁelds,Fπ=93MeV is the pion decay constant,e is the electromagnetic coupling constant,g A=1.26is the axial coupling constant,and M is the average nucleon mass.3Dispersion relations for nucleons and pionsIn this section we calculate the DR for nucleons and pions in the framework of the Lagrangian given by(2.1).We consider the propagation of the nucleonic and pionic excitations in a dense thermal plasma constituted by protons,neutrons,charged pions,=0,where f i neutral pions and photons,being this plasma characterised byµfirepresents the diﬀerent fermion species.The calculation is performed in the real time formalism of the thermalﬁeld theory in the Feynman gauge.The real part of the nucleonic and pionic self-energies are evaluated at lowest order in the energy expansion and at one-loop order(g A/Fπ)2,considering only the leading contributions in T andµf.The Feynman rules for the vertices atﬁnite temperature and density(Fig.1)are the same as those at T=0andµf=0,while the propagators in the Feynman gauge for photons Dµν(p),pions D(p)and massive nucleons S(p)are[41]:Dµν(p)=−gµν 1−iΓb(p),(3.2)p2+iǫp/S(p)=,(3.6)e(p·u)/T−1n f(p)=θ(p·u)n−f(p)+θ(−p·u)n+f(p),(3.7) being n b(p)the Bose–Einstein distribution function,and the Fermi–Dirac distribution functions for fermions(n−f(p))and anti-fermions(n+f(p))are:1n∓f(p)=3.1Nucleonic Dispersion RelationUsing the Feynman diagrams given in Fig.(2),we calculate the FDR for quasi–protons and quasi–neutrons.In order to apply a similar procedure to that followed in[21,29,34],weﬁrst consider the hypothetical case of massless nucleons.In this case,we obtain two solutions:one describing the propagation of quasi-fermionsw(k)=M p,n+k3M p,n+O(k3),(3.9)and another one describing the propagation of quasi-holesw(k)=M p,n−k3M p,n+O(k3).(3.10)We observe that if k=0,w(k)=M p,n.Then M p(M n)can be interpreted as the eﬀective mass of the quasi-protons(quasi-neutrons),and their expressions are: M2p= 3g2A M28 T2+g2A M22 +e2µ2p64F2πT2+g2A M22+µ2p .(3.12)For the limit k>>M p,n the FDR are:w(k)=k+M2p,n2k3Log(2k2of the chiral phase transition in non–zero hadronic density [42].We observe that m p,n>Mp,n ,where m p (m n )is the rest mass of the proton (neutron)and M p,n aregiven by (3.11)and (3.12).In the limit m 2p,n >>M 2p,n the FDR become [24]:w (k )2=k 2+m 2p,n +M 2p,n .(3.15)Starting from relation (3.15)and equations (3.11),(3.12),we obtain a generalexpression for the nucleon eﬀective mass splitting ∆M 2N :∆M 2N =m 2p −m 2n +e 2T 28π2 g 2A M 2µ2n 8F 2π+e 2µ2p .(3.16)3.2Pionic Dispersion RelationUsing the Feynman rules given in Fig.(1),we obtain the following DR for quasi-pions:w (k )2=k 2+M 2π±,π0,(3.17)where M π±(M π0)is the eﬀective mass for charged (neutral)quasi–pions,and their expressions are:M 2π±=T 2F 2π+e2 +g 2A M 28π2F 2π2π2T 212.(3.20)4Results and conclusionsWe now give the results of the calculation for the eﬀective masses of quasi–nucleons and quasi–pions.We have used the following values m p =938.271MeV,m n =939.566MeV,M =938.919MeV,T =150MeV,µp =100MeV,µn =200MeV,e 2=0.095.The temperature and chemical potential values are of the order of those in a neutron star [43].The results for the eﬀective masses are:M p=1036.5133MeV M n=1033.8394MeV M π±=637.2312MeV M π0=637.0914MeVwhere M p,M n,Mπ±and Mπ0are the eﬀective masses for the proton,neutron,charged pions and the neutral pion,including the strong and electromagnetic interactions.The eﬀective mass splitting for nucleons and pions are:∆(M p−M n)=2.6740MeV∆(Mπ±−Mπ0)=0.1398MeVwhere∆(Mπ±−Mπ0)is due exclusively to the combined electromagnetic interaction and temperature eﬀects,as shown at(3.20).For the nucleons,from the total eﬀective mass splitting∆(M p−M n),the combined electromagnetic and temperature contribute is∆em(M p−M n)=0.0058MeV.In conclusion,temperature eﬀects enter into the eﬀective mass splitting relations (3.16)and(3.20)exclusively in the electromagnetic interaction term,which at T=0vanishes.Also,in the framework of our model we found that,for the chemical potentials and temperature used,the eﬀective mass on the proton is bigger than the one of the neutron.Our results should be improved by considering massive pions and introducing the weak interaction,as well as using a realistic model for neutron stars, to be presented in short.AcknowledgementsThis work was supported by COLCIENCIAS(Colombia),Universidad Nacional de Colombia and Centro Internacional de F´ısica.We want also to thank to Fernando Cristancho by invitation to participate in the Third Latinamerican Workshop on Nuclear and Heavy Ion Physics,San Andr´e s,Colombia.References[1]Weinberg,Physica A96(1979)327.[2]J.Gasser and Leutwyler,Ann.Phys(N.Y)(1984)158;Nucl.Phys.B250(1985)465.[3]J.F.Donoghue,E.Golowich and B.R.Holstein,“Dynamics of the StandardModel”,Cambridge University Press,1992.[4]U.G.Meissner,Rep.Prog.Phys.56(1993)903.[5]A.Pich,Rep.Prog.Phys.58(1995)563.[6]G.Ecker,Prog.Part.Nucl.Phys.35(1995)1;G.Ecker and M.Mojzis,Phys.Lett.B365(1996)312.[7]M.Wise,Phys.Rev.D45(1992)R2188.[8]G.Bardman and J.Donoghue,Phys.Lett.B280(1992)287.[9]T.M.Yan,H.Y.Chang and 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Dispersion games general definitions and some specific learning results

Dispersion Games:General Deﬁnitions and Some Speciﬁc Learning Results Trond Grenager and Rob Powers and Yoav ShohamComputer Science DepartmentStanford UniversityStanford,CA94305grenager,powers,shoham@AbstractDispersion games are the generalization of the anti-coordination game to arbitrary numbers of agents and ac-tions.In these games agents prefer outcomes in which theagents are maximally dispersed over the set of possible ac-tions.This class of games models a large number of natu-ral problems,including load balancing in computer science,niche selection in economics,and division of roles within ateam in robotics.Our work consists of two main contribu-tions.First,we formally deﬁne and characterize some inter-esting classes of dispersion games.Second,we present sev-eral learning strategies that agents can use in these games,including traditional learning rules from game theory and ar-tiﬁcial intelligence,as well as some special purpose strate-gies.We then evaluate analytically and empirically the per-formance of each of these strategies.IntroductionA natural and much studied class of games is the set of so-called coordination games,one-shot games in which bothagents win positive payoffs only when they choose the sameaction(Schelling1960).1A complementary class that hasreceived relatively little attention is the set of games in whichagents win positive payoffs only when they choose distinctactions;these games have sometimes been called the anti-coordination games.Most discussion of these games hasfocused only on the two-agent case(see Figure1),wherethe coordination game and the anti-coordination game dif-fer by only the renaming of one player’s actions.However,with arbitrary numbers of agents and actions,the two gamesdiverge;while the generalization of the coordination gameis quite straightforward,that of the anti-coordination gameis more complex.In this paper we study the latter,whichwe call dispersion games(DGs),since these are games inwhich agents prefer to be more dispersed over actions.2Al-though one can transform a dispersion game into a coordi-discuss theseﬁndings and present ideas for future research.Dispersion Game DeﬁnitionsIn this section we begin by discussing some simple disper-sion games,and work our way gradually to the most general deﬁnitions.All of the DGs we deﬁne in this section are sub-classes of the set of normal form games,which we deﬁne as follows.Deﬁnition1(CA,CP,CACP games)A normal form game is a tuple,whereis aﬁnite set of agents,is aﬁnite set of actions available to agent,andis the preference relation of agent,deﬁned on the set of outcomes,that satisﬁes the von Neumann-Morgenstern axioms.A game is a common action(CA)game if there exists a set of actions such that for all,;we rep-resent a CA game as.Similarly,a game is a common preference(CP)game if there exists a relation such that for all,;we represent a CP game as.We denote a game that is both CA and CP as CACP.We represent a CACP game asNote that we use the notation to denote the outcome in which agent chooses action,agent chooses action,and so on.In a CA game where,there are total outcomes.Common Preference Dispersion GamesPerhaps the simplest DG is that in which agents indepen-dently and simultaneously choose from among actions, and the agents prefer only the outcomes in which they all choose distinct actions.(This game was deﬁned indepen-dently in(Alpern2001).)We call these outcomes the maxi-mal dispersion outcomes(MDOs).This simple DG is highly constrained.It assumes that the number of agents is equal to the number of actions available to each agent.However,there are many prob-lems in which that we may wish to model with DGs. When the game is similar to the game but easier:there is a larger proportion of MDOs.When however,the situation is more complex:there are no out-comes in which all agents choose distinct actions.For this reason,we will need a more general deﬁnition of an MDO. In the deﬁnitions that follow,we use the notation to be the number of agents selecting action in outcome.Deﬁnition2(MDO)Given a CA game,an outcomeof is a maximal dispersion outcome iff for all agents and for all outcomessuch that,it is the case that.In other words,an MDO is an outcome in which no agent can move to an action with fewer other agents.Note that when the number of agents is less than or equal to the num-ber of actions,an MDO allocates exactly one agent to each action,as above.Under this deﬁnition,the number of MDOs in a general CA game with actions is given by3The reader may wonder why our deﬁnitions don’t require thatstate a strong deﬁnition.Before we can state the deﬁnition,however,we will need the following dispersion relation.Deﬁnition6()Given two outcomesand,we have that iff there exists a agent suchthat,and,and for all other agents,.We let the dispersion relation bethe reﬂexive and transitive closure of.In other words,is more dispersed than if it is possibleto transform into by a sequence of steps,each of whichis a change of action by exactly one agent to an action withfewer other agents.It is important to note that the dispersionordering is a structural property of any CACP game.Thedispersion relation over the set of outcomes forms a partiallyordered set(poset).Note that the set of MDOs is just the setof-maximal elements of.There are many other measures that we could use insteadof the qualitative dispersion relation.Entropy is consistentwith,but stronger than our dispersion relation:if thenthe entropy of is higher than that of,but the converse isnot necessarily true.We have chosen to base our deﬁnitionson the weaker dispersion relation because it is the most gen-eral,and because it corresponds directly to a single agent’schange of actions.Using this dispersion relation,we can state the formal def-inition of strong DGs.Deﬁnition7(Strong DG)A CACP gameis a strong dispersion game iff for all outcomes,itis the case that if but not,then but not.Recall that the preference relation forms a total order-ing while the dispersion relation forms a partial ordering.Thus this deﬁnition requires that is strictly preferred towhen is strictly more dispersed than.If the strong deﬁnition has such nice properties,whybother to state the weak deﬁnition at all?There are manysituations which have a dispersion quality but which can-not be modeled by games in the stronger class.Considerthe situation faced by Alice,Bob,and Charlie who are eachchoosing among three possible roles in the founding of acompany:CEO,COO,and CFO.Because they will be com-pensated as a group,the situation can be modeled as a CPgame.However,suppose that Bob would be a terrible CEO.Clearly,the agents would most prefer an outcome in whicheach role isﬁlled and Bob is not CEO;thus the game satis-ﬁes the weak deﬁnition.However,rather than have all rolesﬁlled and Bob alone be CEO,they would prefer an outcomein which Bob shares the CEO position with one of the otheragents(i.e.,both Bob and another agent select the“CEO”action),even though it leaves one of the other roles empty.In other words,the preference relation conﬂicts with the dis-persion ordering,and the game does not satisfy the strongdeﬁnition.4Note that any mixed strategy equilibrium outcome is neces-sarily preference dominated by the pure strategy MDOs.For thisreason,we henceforth disregard mixed strategy equilibria,and fo-cus on the problem ofﬁnding one of the MDOs.agent,each of which is a function mapping observed histo-ries to distributions over actions.Consider the most naive distributed algorithm.In eachround,each agent selects an action randomly from the uni-form distribution,stopping only when the outcome is anMDO.Note that this naive learning rule imposes very min-imal information requirements on the agents:each agentmust be informed only whether the outcome is an MDO.Unfortunately,the expected number of rounds until conver-gence to an MDO is5The reader might be concerned that this approximationchanges the convergence properties of the rule.Although this maybe the case in some settings,in our experiments with small nodifference was observed from those using the full history.randomly until theﬁrst time she is alone,at which point she continues to replay that action indeﬁnitely,regardless of whether other agents choose the same action.It is easy to see that this strategy is guaranteed to converge in the limit, and that if it converges it will converge to an MDO.The freeze strategy also has the beneﬁt of imposing very mini-mal information requirements:it requires an agent to know only how many agents chose the same action as she did in the previous round.An improvement on the freeze strategy is the basic simple strategy,which was originally suggested by Alpern(2001). In this strategy,each agent begins by randomly choosing an action.Then,if no other agent chose the same action,she chooses the same action in the next round.Otherwise,she randomizes over the set of actions that were either unoccu-pied or selected by two or more agents.Note that the basic simple strategy requires that agents know only which actions had a single agent in them after each round.Deﬁnition8(Basic Simple Strategy)Given an outcome ,an agent using the basic simple strategy willIf,select action with probability1, Otherwise,select an action from the uniform distribution over actions for which.We have extended the basic simple strategy to work in the broader class of games for which.Deﬁnition9(Extended Simple Strategy)Given an out-come,an agent using the extended simple strategy willIf,select action with probability1, Otherwise,select action with probabilityrandomize over the actions for which.Unlike the basic strategy,the extended strategy does not assign uniform probabilities to all actions that were not cho-sen by the correct number of agents.Consider agents react-ing to the outcome.In this case each agent is better off staying with probability0.5and jumping to each of the empty slots with probability0.25,than randomizing uniformly over all four slots.The extended simple strategy can actually be further improved by assigning non-uniform probabilities to the actions for which.We have found empirically that the learning rule converges more rapidly when agents place more probability on the actions that have fewer other agents in them.Note that the ex-tended simple strategy requires that agents know the number of agents selecting each action in the round;the identity of these agents is not required,however.Experimental ResultsThe learning rules and strategies described above differ sig-niﬁcantly in the empirical time to converge.In Figure2we plot as a function of the convergence time of the learn-ing rules in repeated symmetric weak DGs,averaged over 1000trials.Table1summarizes the observed performance of each strategy(as well as the information requirements ofFigure2:Log-log plot of the empirical performance of dif-ferent strategies in symmetric CACP dispersion games.Learning Avg.Rounds toRule Converge()Whether MDOFP EXPNum.in Own ActionFreeze LINEARNum.in All Actions6For certain ratios of led consistently to superlog-arithmic performance;slight modiﬁcations of the extended simple strategy were able to achieve logarithmic performance.DiscussionIn this paper we have introduced the class of DGs and de-ﬁned several important subclasses that display interesting properties.We then investigated certain representative learn-ing rules and tested their empirical behavior in DGs.In the future,we intend to continue this research in two primary directions.First,we would like to further investigate some new types of DGs.We gave examples above of two classes of non-CP dispersion games that model common problems,but due to space limitations we were not able to deﬁne and characterize them in this paper.On a different note,we are also interested in a possible generalization of DGs which models the allo-cation of some quantity associated with the agents,such as skill or usage,to the different actions.We would like to de-ﬁne these classes of games formally,and explore learning rules that can solve them efﬁciently.Second,we would like to continue the research on learn-ing in DGs that we have begun in this paper.The learn-ing rules we evaluated above are an initial exploration,and clearly many other learning techniques also deserve consid-eration.Additionally,we would like to complement the em-pirical work presented here with some analytical results.As a preliminary result,we can prove the following loose upper bound on the expected convergence time of the basic simple strategy.Proposition1In a repeated fully symmetric weak disper-sion game with agents and actions,in which all agents use the basic simple strategy,the expected number of rounds until convergence to an MDO is in.Informally,the proof is as follows.The probability that a particular agent chooses an action alone is, and so the expected number of rounds until she is alone is just.Because of the linearity of expectation, the expected number of rounds for all agents toﬁnd them-selves alone must be no more than,which is less than for ing similar techniques it is possible to show a quadratic bound on the expected conver-gence time of the freeze strategy.Unfortunately,our empirical results show that the basic simple strategy converges in time that is logarithmic in, and that the freeze strategy converges in linear time.This gap between our preliminary analysis and our empirical re-sults begs future analytical work.Is it possible to show a tighter upper bound,for these learning rules or for others? Can we show a lower bound?We would also like to better understand the optimality of learning rules.It is possible in principal to derive the opti-mal reactive learning rule for anyﬁnite number of agents us-ing dynamic programming.Note that the optimal strategies obtained using this method are arbitrarily complex,how-ever.For example,even upon reaching the simple out-come,an optimal reactive strategy for each agent chooses the same action with probability0.5118(not0.5,as the extended simple strategy would dictate).Dispersion games clearly play an important role in coop-erative multiagent systems,and deserve much more discus-sion and scrutiny.We view the results of this paper as open-ing the door to substantial additional work on this exciting class of games.ReferencesAlpern,S.2001.Spatial dispersion as a dynamic coordi-nation problem.Technical report,The London School of Economics.Arthur,B.1994.Inductive reasoning and bounded rational-ity.American Economic Association Papers84:406–411. 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Reinforcement learning:A survey.Journal of Artiﬁcial Intelligence Research4:237–285.Kalai,E.,and Lehrer,E.1993.Rational learning leads to nash equilibrium.Econometrica61(5):1019–1045. Littman,M.L.1994.Markov games as a framework for multi-agent reinforcement learning.In Proceedings of the 11th International Conference on Machine Learning(ML-94),157–163.New Brunswick,NJ:Morgan Kaufmann. Osborne,M.,and Rubinstein,A.1994.A Course in Game Theory.Cambridge,Massachusetts:MIT Press. Robinson,J.1951.An iterative method of solving a game. Annals of Mathematics54:298–301.Schelling,T.1960.The Strategy of Conﬂict.Cambridge, Massachusetts:Harvard University Press.。

聚赖氨酸应用

Biochemical Engineering Journal 65 (2012) 70–81Contents lists available at SciVerse ScienceDirectBiochemical EngineeringJournalj o u r n a l h o m e p a g e :w w w.e l s e v i e r.c o m /l o c a t e /b ejReviewReview on production and medical applications of ␧-polylysineSwet Chand Shukla a ,Amit Singh b ,Anand Kumar Pandey c ,Abha Mishra a ,∗aSchool of Biochemical Engineering,Institute of Technology,Banaras Hindu University,Varanasi 221005,India bDepartment of Pharmacology,Institute of Medical Sciences,Banaras Hindu University,Varanasi 221005,India cSchool of Biomedical Engineering,Institute of Technology,Banaras Hindu University,Varanasi 221005,Indiaa r t i c l ei n f oArticle history:Received 3May 2011Received in revised form 28March 2012Accepted 2April 2012Available online 11 April 2012Keywords:␧-PolylysineHomopolyamideS.albulus Lysinopolymerus Conjugate Drug carrier Targetinga b s t r a c t␧-Polylysine (␧-PL)is a homopolyamide linked by the peptide bond between the carboxylic and epsilon amino group of adjacent lysine molecules.It is naturally occurring biodegradable and nontoxic towards human.This review article gives an insight about the various ␧-PL producing strains,their screening procedures,mechanism of synthesis,characterization,and its application in the medical ﬁeld.The poly cationic nature of ␧-PL at physiological pH makes it as one of the potential candidates in the ﬁeld of drug delivery.Most of the biomedical applications till date use synthetic ␣-PLL as a raw material.However,it is believed that naturally occurring ␧-PL would be an ideal substitute.© 2012 Elsevier B.V. All rights reserved.Contents 1.Introduction ..........................................................................................................................................712.Origin and distribution of ␧-PL ......................................................................................................................713.Mechanism of synthesis .............................................................................................................................714.Biosynthesis and molecular genetics ................................................................................................................715.Microbial production of ␧-polylysine ................................................................................................................726.Screening and detection of ␧-PL production in microbial system...................................................................................737.Puriﬁcation and characterization of ␧-PL ............................................................................................................738.Conformation of ␧-PL ................................................................................................................................749.Application of polylysine in medicine ...............................................................................................................749.1.Polylysine as a drug carrier ...................................................................................................................749.2.Polylysine as nanoparticles...................................................................................................................759.3.Polylysine as a gene carrier...................................................................................................................759.4.Polylysine as liposomes ......................................................................................................................769.5.Polylysine as interferon inducer .............................................................................................................769.6.Polylysine as lipase inhibitor .................................................................................................................779.7.Polylysine as hydrogel ........................................................................................................................779.8.Polylysine as coating material................................................................................................................779.9.Other applications ............................................................................................................................7810.Conclusion ..........................................................................................................................................78References ...........................................................................................................................................78Abbreviations:Pls,polylysine synthetase;NaSCN,sodium thiocynate;FTIR,Fourier transform infrared spectroscopy;NMR,nuclear magnetic resonance spectroscopy;MION,monocrystalline iron oxide nanoparticle;NPs,nanoparticles;IgM,immunoglobulin M.∗Corresponding author.Tel.:+919451887940.E-mail address:abham.bce@itbhu.ac.in (A.Mishra).1369-703X/$–see front matter © 2012 Elsevier B.V. All rights reserved./10.1016/j.bej.2012.04.001S.C.Shukla et al./Biochemical Engineering Journal 65 (2012) 70–81711.Introduction␧-Polylysine (␧-PL)is a basic polyamide that consists of 25–30residues of l -lysine with an ␧-amino group-␣-carboxyl group link-age (Fig.1).Polyamide can be grouped into two categories,one in which the polyamide consists of only one type of amino acid linked by amide bonds called homopolyamide and the other which consists of different amino acids in their chain called proteins [1].Furthermore,proteins are biosynthesized under the direction of DNA,while the biosynthesis of homopolyamides is catalyzed by peptide synthetases.Therefore,the antibiotics that are inhibitors of translation such as chloramphenicol,do not affect the biosyn-thesis of polyamides.Proteins in general exhibit exact length,whereas homopolyamides show a remarkable variation in molec-ular weight.Amide linkages in proteins are only formed between ␣-amino and ␣-carboxylic groups (␣-amide linkages),whereas amide bonds in homopolyamide involve other side chain functions such as ␤-and ␥-carboxylic with ␧-amino groups [1].Particularly,chemically synthesized polylysine were found to have linkages between ␣-carboxyl and ␣-amino group.Many workers investi-gated various applications of ␣-PL in the drug delivery system.However,␣-PL was reported to be toxic to human beings,and there-fore,research has now been diverted towards ﬁnding naturally occurring polymers [2,3].␧-PL is an unusual naturally occurring homopolyamide having linkages between the ␧-amino group and ␣-carboxylic group,and it shows high water solubility and sta-bility.No degradation is observed even when the ␧-PL solution is boiled at 100◦C for 30min or autoclaved at 120◦C for 20min [4].␧-PL was discovered as an extracellular material of Streptomyces albulus ssp.Lysinopolymerus strain 346during screening for Dra-gendorff’s positive substances [5–7].Mutation studies were made by nitrosoguanidine treatment on wild type Lysinopolymerus strain 346to enhance the ␧-PL production.As a result of mutation,S-(2-aminoethyl)-l -cysteine and glycine resistant mutant were isolated,with four times higher amounts of ␧-PL than the wild type [8].␧-PL is a cationic surface active agent due to its positively charged amino group in water,and hence they were shown to have a wide antimi-crobial activity against yeast,fungi,Gram positive,Gram negative bacterial species [4,9].The excreted polymer is absorbed to the cell surfaces by its cationic property,leading to the striping of outer membrane and by this mechanism the growth of microbes sensi-tive to ␧-PL is inhibited.␧-PL degrading enzyme plays an important role in self-protection of ␧-PL producing microbes [9].Due to its excellent antimicrobial activity,heat stability and lack of toxicity,it is being used as a food preservative [10,11].Naturally occurring ␧-PL is water soluble,biodegradable,edible and nontoxic toward humans and the environment.Therefore,␧-PL and its derivatives have been of interest in the recent few years in food,medicine and electronics industries.Derivatives of ␧-PL are also available which offers a wide range of unique applications such as emul-sifying agent,dietary agent,biodegradable ﬁbers,highly water absorbable hydrogels,drug carriers,anticancer agent enhancer,biochip coatings,etc.Polylysine exhibits variety of secondary struc-tures such as random coil,␣-helix,or ␤-sheet conformations in aqueous solution.Moreover,transitions between conformations can be easily achieved using,salt concentration,alcohol con-tent,pH or temperature as an environmental stimulus.There is aH NH*CH 2CH 2CH 2CH 2CH NH 2CO*OHnFig.1.Chemical structure of epsilon polylysine.growing interest in using ␧-PL and its derivatives as biomaterials and extensive research has been done leading to a large number of publications [4,12–15].The present review focuses on various pro-cess parameters for maximal yield of polymer by microbial system more speciﬁcally by actinomycetes,probable biosynthetic route and its application,especially in pharmaceutical industries.2.Origin and distribution of ␧-PLNot much is known about the ␧-PL producing microbial species existing in the environment.It is observed that ␧-PL producers mainly belong to two groups of bacteria’s:Streptomycetaceae and Ergot fungi .Besides Streptomyces albulus ,a number of other ␧-PL producing species belonging to Streptomyces,Kitasatospora and an Ergot fungi,Epichole species have been isolated [16].Recently,two Streptomyces species (USE-11and USE-51)have been isolated using two stage culture method [17].3.Mechanism of synthesis␧-Polylysine (␧-PL)is a homopolymer characterized by a pep-tide bond between ␣-carboxyl and ␧-amino groups of l -lysine molecules.Biosynthetic study of ␧-PL was carried out in a cell-free system by using a sensitive radioisotopic ␧-PL assay method,suggested that the biosynthesis of ␧-PL is a non ribosomal peptide synthesis and is catalyzed by membrane bound enzymes.In vitro ,␧-PL synthesis was found to be dependent on ATP and was not affected by ribonuclease,kanamycin or chloramphenicol [18].In a peptide biosynthesis,amino acids are activated either by adeny-lation or phosphorylation of carboxyl group.Adenylation occurs in translation and in the nonribosomal synthesis of a variety of unusual peptides [19,20];Phosphorylation has been suggested for the biosynthesis of glutathione [21].In the former,ATP is con-verted to AMP and pyrophosphate by adenylation,and in the latter,phosphorylation leads to ADP and phosphate as the ﬁnal prod-ucts.The synthesis of ␧-PL,a homopolypeptide of the basic amino acid l -lysine,is similar to that of poly-(␥-d -glutamate)in terms of adenylation of the substrate amino acid [18].Through the exper-imental observations,the probable mechanism of synthesis was suggested by Kawai et al.showed that in the ﬁrst step of ␧-PL biosynthesis l -lysine is adenylated at its own carboxyl groups with an ATP-PPi exchange reaction.The active site of a sulfhydryl group of an enzyme forms active aminoacyl thioester intermediates,lead-ing to condensation of activated l -lysine monomer.This is the characteristic feature of nonribosomal peptide synthetase enzyme [22–24].␧-PL producing strain of Streptomyces albulus was found to pro-duce ␧-PL synthetase (Pls).A gene isolated from the strain was identiﬁed as a membrane protein with adenylation and thiolation domains which are characteristic features of the nonribosomal pep-tide synthetases (NRPSs).␧-PL synthetase has six transmembrane domains surrounding three tandem soluble domains without any thioesterase and condensation domain.This tandem domain itera-tively catalyzes l -lysine polymerization using free l -lysine polymer as an acceptor and Pls-bound l -lysine as a donor,thereby yielding chains of diverse length (Fig.2).Thus,␧-PL synthetase acts as a ligase for peptide bond formation [25].Yamanaka et al.suggested that ␧-PL synthetase function is regulated by intracellular ATP and found that acidic pH conditions are necessary for the accumulation of intracellular ATP,rather than the inhibition of the ␧-PL degrading enzyme [26].4.Biosynthesis and molecular geneticsThe precursor of ␧-PL biosynthesis was identiﬁed to be l -lysine by radiolabeling studies using [14C]-l -lysine in Streptomyces72S.C.Shukla et al./Biochemical Engineering Journal 65 (2012) 70–81Fig.2.Mechanism for synthesis of ␧-polylysine.albulus 346[18].However,a high-molecular-weight plasmid (pNO33;37kbp)was detected in ␧-PL-producing S.albulus ,and the replicon of pNO33was used to construct a cloning vector for S.albu-lus strain [27].The order and number of NRPSs modules determine the chain length of the ␧-PL [24,28].However,the chain length of ␧-PL was shortened by the use of aliphatic hydroxy-compound and ␤-cyclodextrin derivative [29,30].␧-PL with more than nine l -lysine residues severely inhib-ited the microbial growth while the ␧-PL with less than nine l -lysine residues showed negligible antimicrobial activity.All the strains producing ␧-PL from glycerol showed lower number aver-age molecular weight (M n )than those obtained from glucose [31].The ␧-PL-degrading activity was detected in both ␧-PL tolerant and ␧-PL producing bacteria.The presence of ␧-PL-degrading activity in Streptomyces strains is closely related with ␧-PL-producing activ-ity,which indicates that tolerance against ␧-PL is probably required for ␧-PL producers.The presence of ␧-PL degrading enzyme is detri-mental to industrial production of ␧-PL.Therefore,␧-PL degrading enzyme of S.albulus was puriﬁed,characterized and the gene encoding an ␧-PL degrading enzyme of S.albulus was cloned,and analyzed [32].The ␧-PL-degrading enzyme of S.albulus is tightly bound to the cell membrane.The enzyme was solubilized by NaSCN in the presence of Zn 2+and was puriﬁed to homogeneity by phenyl-Sepharose CL-4B column chromatography,with a molecular mass of 54kDa.The enzymatic mode of degradation was exotype mode and released N-terminal l -lysine’s one by one.Streptomyces vir-giniae NBRC 12827and Streptomyces noursei NBRC 15452showed high ␧-PL-degrading aminopeptidase activity and both strains have the ability to produce ␧-PL,indicating a strong correlation between the existence of ␧-PL degrading enzyme and ␧-PL produc-ing activity [33].␧-PL degrading enzymes were also found in ␧-PL tolerant microorganisms,Sphingobacterium multivorum OJ10and Chryseobacterium sp.OJ7,which were isolated through enrichmentof the culture media with various concentrations of ␧-PL.S.mul-tivorum OJ10could grow well,even in the presence of 10mg/ml ␧-PL,without a prolonged lag phase.The ␧-PL-degrading enzyme activity was also detected in the cell-free extract of ␧-PL tolerant S.multivorum OJ10.The enzyme catalyzed an exotype degradation of ␧-PL and was Co 2+or Ca 2+ion activated aminopeptidase.This indicates the contribution of ␧-PL-degrading enzymes to the toler-ance against ␧-PL [34].An ␧-PL degrading enzyme of ␧-PL tolerant Chryseobacterium sp.OJ7,was also characterized and the puriﬁed enzyme catalyzed the endotype degradation of ␧-PL,in contrast to those of Streptomyces albulus and Sphingobacterium multivorum OJ10.Probably,their possession of proteases enables their growth in the presence of a high ␧-PL concentration.␧-PL degradation was also observed by commercially available proteases,such as Pro-tease A,Protease P and Peptidase R [34,35].5.Microbial production of ␧-polylysinePolylysine can be synthesized by chemical polymerization start-ing from l -lysine or its derivatives.Researchers described two different routes to polymerize lysine residues without the use of protection groups.However,linear ␧-PLL can be obtained by applying 1-ethyl-3-(3-dimethylaminopropyl)carbodiimide as an activating agent for the polycondensation of l -lysine in an aqueous medium.In contrast to this,␣-poly(l -lysine)can be obtained by using dicyclohexyl carbodiimide and 18-crown-6ether in chloro-form [36].Dendrimeric ␣,␧-polylysine were synthesized by using solid phase peptide synthesis method and used dendritic ␣,␧-polylysine as a delivery agent for oligonucleotides [37,38].Moccia et al.for the ﬁrst time reported ␣,␧-polylysine by assembling Fmoc and Boc protected l -lysine monomers by solid phase synthesis [39].Guo et al.synthesized ␧-PL-analogous polypeptides with not only similar ␣-amino side groups but also similar main chain throughS.C.Shukla et al./Biochemical Engineering Journal65 (2012) 70–8173microwave assisted click polymerization technique[40].Recently, Roviello et al.synthesized a cationic peptide based on l-lysine and l-diaminobutyric acid for theﬁrst time by solid phase synthesis [41].␧-PL was discovered as an extracellular material produced by ﬁlamentous actinomycetes group of micro-organism Streptomyces albulus ssp.Lysinopolymerus strain346more than35years ago [5].It is synthesized by a nonribosomal peptide synthetase and released extracellularly.In actinomycetes group of organisms l-lysine is synthesized through the diaminopimelic acid pathway. Diaminopimelate is formed via l-aspartate(Asp)produced by com-bining oxaloacetate in the tricarboxylic acid cycle with ammonium as a nitrogen source.Citrate was found to be facilitator for the production much more than other organic acids of TCA cycle[24].Studies revealed that decline in pH during the fermentation pro-cess is an essential condition for the accumulation of␧-PL.Shima et al.carried out two-step cultivation method for S.albulus.Strain wasﬁrst grown for24h in a culture medium containing glycerol as carbon source with yeast extract,then in second step medium was replaced by glucose,citric acid with(NH4)2SO4[42].It was found that the mutant of strain346decreases the culture pH from its initial value of6.8–4.2by36h,and slowly decreased thereafter to 3.2at96h.The accumulation of␧-PL in the broth increased signiﬁ-cantly when the culture pH was about4.0.The fed batch cultivation was adopted to enhance the␧-PL production with two distinct phases.In phase I,cell was grown at pH(6.8)optimum for cul-ture growth then in phase II,the pH was kept around4.0by the addition of glucose.Depletion of glucose causes an increase in pH of the culture broth leading to the degradation of the produced ␧-PL.Thus the pH control strategy in fed batch culture success-fully enhanced the yield of␧-PL to almost9fold[43].The airlift bioreactor(ABR)was also evaluated and compared with jar fer-mentor for␧-PL production.The results showed that the production level of␧-PL in a ABR with a power consumption of0.3kW/m3was similar to that in a5-l jar fermentor with power consumption of 8.0kW/m3.The leakage of intracellular nucleic acid(INA)-related substance into the culture broth in the ABR was70%less than that in the jar fermentor.Thus,ABR system with low intracel-lular nucleic acid-related substances minimize the difﬁculties of downstream processing for recovery and puriﬁcation of the poly-mer products.Furthermore,the use of ABR is promising tool for the low-cost production of␧-PL of high purity[44].In some␧-PL producing strains,the production of␧-PL is unstable and depen-dent on cell density which can cause problem such as high viscosity and low oxygen transfer efﬁciency.Furthermore,increase of agita-tion speeds leads to the rise of shear stresses which might cause undesired effects on mycelial morphology,product formation,and product yields.Bioprocesses using immobilized cells on various inert supports can increase overall productivity and minimize pro-duction costs[45].Bankar et al.reported that aeration and agitation of the fermentation broth markedly affect␧-PL production,cell mass formation,and glycerol utilization.Fermentation kinetics per-formed revealed that␧-PL production is growth-associated,and agitation speed of300rpm and aeration rate at2.0vvm supports higher yields of␧-PL[46].Many efforts have been made to opti-mize the media in order to enhance the productivity of␧-PL.Shih and Shen applied response surface methodology for optimization of␧-PL production by Streptomyces albulus IFO14147[47].It was found that␧-PL production started on agar plated with iron two or three days earlier than that on plates without iron.Manganese and cobalt were also found to have stimulating effect on␧-PL produc-tion.Kitasatospora kifunense strain produces␧-PL of shorter chain length about8–17lysine residues[48].Metabolic precursors such as amino acids,tricarboxylic acid cycle intermediates and cofactors have been investigated for improved production of␧-PL.Addition of citric acid after24h and l-aspartate after36h of fermentation medium had a signiﬁcant effect on␧-PL production[49].Zhang et al.investigated the production of␧-PL on immobilized cells of Kitasatospora sp.MY5-36on bagasse,macroporous silica gel,syn-thetic sponge,loofah sponge and found that loofah sponge gave highest production of␧-PL in shakeﬂask culture[50].6.Screening and detection of␧-PL production in microbial systemNishikawa and Ogawa developed a simple screening method to detect␧-PL producing microbes.Screenings were carried out on agar plates containing either basic or acidic dyes.The dyes used were,Poly R-478,Remazol Brilliant Blue-R(RBBR)and Methylene blue.The screening method was based on the rationale interac-tion that occurs between charged groups of the secreted␧-PL and charged group of the basic or acidic dyes.A synthetic glycerol(SG) medium containing either0.02%of acidic dye Poly R-478/RBBR or0.002%of Methylene blue was used for the primary screen-ing.The SG medium was composed of glycerol10g,ammonium sulfate0.66g,sodium dihydrogen phosphate0.68g,magnesium phosphate heptahydrate0.25g,yeast extract0.1g,and1.0ml of Kirk’s mineral solution in1l of distilled water.The pH was adjusted to7.0with1M NaOH solution,and the medium was solidiﬁed by adding1.5%agar.The plates were incubated at28◦C for about one week;microbes forming speciﬁc colonies interacting with dyes were picked up and puriﬁed after several culture transfers.The acidic dye condensed around the organism’s colonies while basic dye was excluded from the surrounding zone.A zone of at least ﬁve mm in diameter for each colony was needed to visualize the interaction between secreted substances and dyes[16].The concentrations of␧-PL in the culture broth can be deter-mined by using either the spectrophotometric method or HPLC method.The colorimetric method is based on the interaction between␧-PL and methyl orange,which is an anionic dye,and thus the interaction of cationic␧-PL with anionic methyl orange in the reaction mixture led to form a water insoluble complex[51].The HPLC method for␧-PL detection was reported by Kahar et al.in which HPLC column(Tsk gel ODS-120T,4.6mm×250mm)with a mobile phase comprising of0.1%H3PO4was used[43].7.Puriﬁcation and characterization of␧-PL␧-PL a cationic polymer,can be isolated at neutral pH,and puri-ﬁed from the culture broth by ion exchange chromatography using an Amberlite IRC-50(H+form)column[5,52].The culture super-natant can be passed through an Amberlite IRC-50column at pH 8.5with successive washing by0.2N acetic acid and water.The elution can be made with0.1N hydrochloric acid,and the eluate can be neutralized with0.1N sodium hydroxide to pH6.5.Sub-sequent puriﬁcation can be done by using CM-cellulose column chromatography to get␧-PL in homogeneity.The puriﬁcation of the product can be monitored by UV absorption at220nm and fur-ther characterized by amino acid analysis.The molecular weight of␧-PL can be estimated by gelﬁltration on a Sephadex column [16,53].Kobayashi et al.extracted the␧-PL from Kitasatospora kifu-nense.The pH of the cultureﬁltrate wasﬁrst adjusted to7.0,and the aliquot was mixed with Gly-His-Lys acetate salt as an inter-nal peptide standard.The resulting mixture was then applied to Sep-Pak Light CM cartridge.The cartridge was washed with water and␧-PL was eluted with0.1M HCl.The eluate was lyophilized and the residue was dissolved in0.1%pentaﬂuoropropionic acid [46].Recently,ultra-ﬁltration technique for fractionation of␧-PL of different molecular weight has been applied.The␧-PL with molec-ular weight higher than2kDa form a␤-turn conformation whereas molecular weight smaller than2kDa possesses a random coil74S.C.Shukla et al./Biochemical Engineering Journal65 (2012) 70–81conformation.The fraction of␧-PL with molecular weight higher than2kDa was found to have signiﬁcant antibacterial activity, while the fraction with molecular weight smaller than2kDa shows nominal antibacterial activity[54].8.Conformation of␧-PLStructure and conformation studies are prerequisite to under-stand the functional behavior of␧-PL.Numerous workers have investigated the conformation and the molecular structure of microbially produced␧-PL by NMR,IR and CD spectroscopy[55,56]. The thermal property of crystalline␧-PL was determined by Lee et al.[52].The glass transition temperature(T g)and the melting point(T m)was observed to be88◦C and172.8◦C respectively.The results from pH dependent IR and CD spectra,1H and13C NMR chemical shifts together with that of13C spin-lattice relaxation times T1indicated that␧-PL assumes a␤-sheet conformation in aqueous alkaline solution.␧-PL at acidic pH might be in an electro-statically expanded conformation due to repulsion of protonated ␣-amino group,whereas at elevated pH(above p K a of the␣-amino group)the conformation was found to be similar to the antiparallel ␤-sheet.The molecular structure and conformation of microbial␧-PL was studied by FT-IR and Raman spectroscopy.␧-PL was found to assumed a␤-sheet conformation in the solid state and solid state 13C NMR also revealed that␧-PL existed as a mixture of two crys-talline forms.Spin-lattice relaxation times yield two kinds of T1s corresponding to the crystalline and amorphous components,with the degree of crystallinity as63%[57].Solid-state high-resolution13C and15N NMR spectra of micro-bial␧-PL derivatives with azo dyes have been measured.These chemically modiﬁed␧-PL’s Exhibit15N NMR signals characteristic of the binding mode at the␣-amino groups.The spectral analy-sis reveals that the␧-PL/DC sample contains a small amount of ion complexes with methyl orange(MO).It has been shown that side chain␣-amino group of␧-PL does not make a covalent bond with methyl orange(MO)but forms a poly-ion complex,(␧-PL)-NH3+SO3−-(MO).On the other hand,dabsyl chloride(DC)makes covalent bond with␧-PL to form sulfonamide,(␧-PL)-NH-SO2-(DC). However,a few tens percent of DC change to MO by hydrolysis to form a poly-ion complex,(␧-PL)-NH3+SO3−-(MO)[58].Rosenberg and Shoham characterized the secondary structure of polylysine with a new parameter namely,the intensity ratio of the bands of charged side chain amine NH3+and amide NH bands.The enthalpy of the secondary structure transition,which is observed in PLL at the change of pH from11to1amounts to4.7kJ mol−1[59].9.Application of polylysine in medicinePolylysine is available in a large variety of molecular weights. As a polypeptide,polylysine can be degraded by cells effortlessly. Therefore,it has been used as a delivery vehicle for small drugs[60]. The epsilon amino group of lysine is positively charged at phys-iological pH.Thus,the polycationic polylysine ionically interacts with polyanion,such as DNA.This interaction of polylysine with DNA has been compacted it in a different structure that has been characterized in detail by several workers[61–66].In addition,the epsilon amino group is a good nucleophile above pH8.0and there-fore,easily reacts with a variety of reagents to form a stable bond and covalently attached ligands to the molecule.Several coupling methods have been reported for preparation of conjugated of␧-PL [67–70].(a)Modiﬁcation of epsilon amino groups of polylysine with bifunctional linkers containing a reactive esters,usually add a reac-tive thiol group to the polylysine molecule and consequent reaction with a thiol leads to a disulﬁde or thioether bond,respectively.This has been used to couple large molecules,such as proteins to polylysine.(b)Compounds containing a carboxyl group can be acti-vated by carbodiimide,leading to the formation of an amide bond with an epsilon amino group of polylysine.(c)Aldehydes,such as reducing sugars or oxidized glycoprotein,form hydrolysable schiff bases with amino groups of␧-PL,which can be selectively reduced with sodium cyanoborohydride to form a stable secondary amine.(d)Isothiocyanate reacts with epsilon amino groups by forming a thiourea derivative.(e)Antibody coupling can also be done specif-ically to the N-terminal amino group of polylysine[71,72].A variety of molecules such as proteins,sugar molecules and other small molecules have been coupled to polylysine by using these methods.Puriﬁcation of the conjugates are usually being achieved by dialysis or gelﬁltration in conjunction with ion-exchange chromatography or preparative gel electrophoresis. Fractionation of the ligand–polylysine ratio and conjugate size can be done by using acid urea gel electrophoresis in combination with cation-exchange HPLC,ninhydrin assay and ligand analysis (sugar,transferrin,etc.)[73].Galactose terminated saccharides such as galactose,lactose and N-acetylgalactosamine were found to be accumulated exclusively in the liver,probably by their hepatic receptor.These conjugates could therefore be excellent carriers for a drug delivery system to the liver.The other saccharides such as the mannosyl and fucosyl conjugates are preferentially delivered to the reticuloendothelial systems such as those in the liver,spleen and bone marrow.In particular,fucosyl conjugates accumulated more in the bone marrow than in the spleen whereas xylosyl con-jugates accumulated mostly in the liver and lung.Generally,the accumulated amount in the target tissue increased with increasing molecular weight and an increased number of saccharide units on each monomer residues of polymer[74].One of the disadvantages of polylysine from the pharmaceu-tical point of view is its heterogeneity with respect to molecular size.The size distribution of polylysine with degrees of polymer-ization(dp)can be reduced by gel permeation chromatography. Al-Jamal et al.studied sixth generation(G6)dendrimer molecules of␣-poly-l-lysine(␣-PLL)to exhibit systemic antiangiogenic activ-ity that could lead to solid tumor growth arrest.Their work showed that G6PLL dendrimer have an ability to accumulate and persist in solid tumor sites after systemic administration and exhibit antian-giogenic activity[75].Sugao et al.reported6th generation dendritic ␣-PLL as a carrier for NF␬B decoy oligonucleotide to treat hepatitis [76].Han et al.synthesized a new anti-HIV dendrimer which con-sisted of sulfated oligosaccharide cluster consisting with polylysine core scaffold.The anti-HIV activity of polylysine-dendritic sulfated cellobiose was found to have EC50-3.2␮g/ml for viral replication which is as high as that of the currently clinically used AIDs drugs. The results also indicated that biological activities were improved because of dendritic structure in comparison to oligosaccharide cluster which were reported to have low anti-HIV activity[77].9.1.Polylysine as a drug carrierPolylysine can be used as a carrier in the membrane transport of proteins and drugs.Shen and Ryser reported that␣-PLL was found to be easily taken up by cultured cells.In fact,the conju-gation of drug to polylysine markedly increased its cellular uptake and offers a new way to overcome drug resistance related to deﬁ-cient transport[60,78,79].Resistance toward methotrexate has been encountered in the treatment of cancer patients.The poly lysine conjugates of methotrexate(MTX)were taken up by cells at a higher rate than free drugs form.This increased uptake can overcome drug resistance due to deﬁcient MTX transport.Addi-tion of heparin at a high concentration restores growth inhibitory effect of MTX-poly lysine[11,60].Shen and Ryser worked conjuga-tion of␣-PLL to human serum albumin and horseradish-peroxidase。

Acceleration of stable TTI P-wave reverse-time migration with GPUs

Acceleration of stable TTI P-wave reverse-time migration with GPUsYoungseo Kim a,n,Yongchae Cho b,Ugeun Jang b,Changsoo Shin ba Seoul National University,Research Institute of Energy and Resources151-744/Building135,College of Engineering,Seoul National University,Daehak-dong Gwanak-gu,Seoul,Republic of Koreab Seoul National University,Research Institute of Energy and Resources151-744/36-2061College of Engineering,Seoul National University,Daehak-dongGwanak-gu,Seoul,Republic of Koreaa r t i c l e i n f oArticle history:Received7May2012Received in revised form25September2012Accepted19October2012Available online29October2012Keywords:GPUMPIREMRTMTTIa b s t r a c tWhen a pseudo-acoustic TTI(tilted transversely isotropic)coupled wave equation is used to implementreverse-time migration(RTM),shear wave energy is signiﬁcantly included in the migration image.Because anisotropy has intrinsic elastic characteristics,coupling P-wave and S-wave modes in thepseudo-acoustic wave equation is inevitable.In RTM with only primary energy or the P-wave mode inseismic data,the S-wave energy is regarded as noise for the migration image.To solve this problem,we derive a pure P-wave equation for TTI media that excludes the S-wave energy.Additionally,weapply the rapid expansion method(REM)based on a Chebyshev expansion and a pseudo-spectralmethod(PSM)to calculate spatial derivatives in the wave equation.When REM is incorporated with thePSM for the spatial derivatives,waveﬁelds with high numerical accuracy can be obtained without griddispersion when performing numerical wave modeling.Another problem in the implementation of TTIRTM is that waveﬁelds in an area with high gradients of dip or azimuth angles can be blown up in theprogression of the forward and backward algorithms of the RTM.We stabilize the waveﬁelds byapplying a spatial-frequency domain high-cutﬁlter when calculating the spatial derivatives using thePSM.In addition,to increase performance speed,the graphic processing unit(GPU)architecture is usedinstead of traditional CPU architecture.To conﬁrm the degree of acceleration compared to the CPUversion on our RTM,we then analyze the performance measurements according to the number of GPUsemployed.&2012Elsevier Ltd.All rights reserved.1.IntroductionRTM(reverse-time migration)(Baysal et al.,1983)is the mosteffective tool for imaging the sequence structure of strata withdistinct velocity contrasts and geologically complex structures.Although practical implementation requires substantial comput-ing costs,the rapid development of the computer industry andthe improvement of the algorithm have made RTM a leader inhigh-end imaging.As the outcomes have become common ininterpreting geological structures,many studies have focused onenhancing the images obtained by RTM.One factor for improvingRTM is the consideration of anisotropy.Although most rocks havethe characteristics of anisotropy,many geophysicists have notwanted to use elastic wave equation-contained anisotropy para-meters because the S-wave must be inherently included in theequation.To apply the anisotropic characteristics of rocks to RTM andeliminate the S-wave modes in the wave equation,Alkhalifah(2000)derived a simpliﬁed dispersion relation in VTI(verticaltransversely isotropic)media by setting the SV-wave velocity tozero.The dispersion relation was referred to as pseudo-acousticapproximation,and the VTI pseudo-acoustic wave equation wasapplicable to describing the seismic anisotropy of subsurfaceformations.However,because the symmetric axis perpendicularto the bedding is not always vertical,migration images with theVTI approximation cannot always provide the best quality interms of the deﬁnition of layers and salt boundaries.To considervarious geological structures,Zhou et al.(2006)and Fletcher et al.(2009)derived the TTI(tilted transversely isotropic)pseudo-acoustic wave equation based on the Alkhalifah approximation.Three major problems exist in the RTM with the TTI pseudo-acoustic wave equation.First,SV-waves are generated as artifactsin numerical modeling,although it seems that there should beonly P-wave components.Grechka et al.(2004)proved that theartifacts are actually correctly modeled SV-waves of a TI(trans-versely isotropic)medium that has v s¼0.Although we regard v sas zero,this assumption does not mean that the SV-wave phasevelocity is zero for all propagation angles.To solve this problem,Duveneck et al.(2008)set Thomsen’s(1986)parameters,E and d,to be equal in a small region close to a source position,and ZhangContents lists available at SciVerse ScienceDirectjournal homepage:/locate/cageoComputers&Geosciences0098-3004/$-see front matter&2012Elsevier Ltd.All rights reserved./10.1016/j.cageo.2012.10.013n Corresponding author.Tel.:þ821042285568;fax:þ8228756296.E-mail address:kysgood0@snu.ac.kr(Y.Kim).Computers&Geosciences52(2013)204–217et al.(2009)proposed a set of new equations based on the eigenvalue analysis of the original acoustic wave equation.The second problem is that the numerical modeling of the TTI pseudo-acoustic wave equation takes much more time than does the acoustic wave equation in isotropic media.The TTI pseudo-acoustic wave equation is composed of the combination of a pressure waveﬁeld and an auxiliary waveﬁeld and includes many terms of second derivatives and coupled ﬁrst derivatives.The wave equation in isotropic media requires only the P -wave velocity,while ﬁve parameters are required to describe the wave propagation using the TTI pseudo-acoustic wave equation.Third,the waveﬁeld values obtained through numerical modeling with the TTI pseudo-acoustic wave equation may be blown up in areas where the dip or azimuth angles are substantially changed (Crawley et al.,2010).Fletcher et al.(2009)stabilized wave propagation by setting the SV-wave velocity to half of the P -wave vertical velocity;however,this method generates additional energy from the SV-wave,which can produce incorrect reﬂectors or make the image unclear.Recently,Yoon et al.(2010)addressed the instability of wave propagation by making d equal to E around high symmetry axis gradient spots.In this study,we derive a pure P -wave equation in 2D and 3D TTI media to exclude SV-wave energy in RTM.The spatial frequency-domain dispersion relation obtained from the exact dispersion relations for VTI media derived by Tsvankin (1996)is used to derive the pure P -wave equation in the VTI media (Zhan et al.,2011).Then,the TTI version of the wave equation is obtained by rotating wavenumbers.To obtain a stable solution of the wave equation even in large time steps,we employ the rapid expansion method (REM)to propagate waveﬁelds in time (Pestana and Stoffa,2010).To calculate the spatial derivatives in the wave equation,we select a pseudo-spectral method (PSM)(Kosloff and Baysal,1982;Fornberg,1987)because wave propa-gation incorporated with this method does not incur numerical dispersion,and REM combined with this method can generate a highly accurate solution for wave propagation.In the progression of applying the PSM,we multiply the spatial-frequency domain high-cut ﬁlter function with Fourier transformed waveﬁelds at each time step to prevent the waveﬁeld values from being blown up in areas with high gradients of dip or azimuth angles (Zhan et al.,2011).In addition,to accelerate the performance speed of the numerical modeling,we calculate the 2D or 3D Fourier transforms and their inverses using GPUs with CUDA and parallel computing with MPI (Gropp et al.,1999).In addition to the kernel (a function executed in parallel on the GPU device)for FFT,all algorithms required for the RTM are computed on the GPUs.2.Mathematical expression of pure TTI P -wave equation The 3D spatial-frequency domain ðk x ,k y ,k z Þdispersion relation used by Etgen and Brandsberg-Dahl (2009)and Crawley et al.(2010)is expressed as follows:o 2¼v 2p 0ð1þ2e Þðk 2x þk 2y Þþk 2z À2ðe Àd Þðk 2x þk 2y Þk 2z k 2x þk 2y þk 2z !,ð1Þwhere o is the angular frequency,v p 0is the P -wave velocity,and e and d are the Thomsen (1986)parameters.The dispersion relation in Eq.(1)can be applied to the VTI media and can be transformed into the form in TTI media by rotating wavenumber components ðk x ,k y ,k z Þ.The rotated wavenumbers are expressed as follows:^kx ^k y ^k z26643775¼cos y cos j k x þcos y sin j k y þsin y k z Àsin j k x þcos j k y Àsin y cos j k x Àsin y sin j k y þcos y k z 264375,ð2ÞEq.(1)can be rewritten in a rotated coordinate system asÀo 2¼v 2p 0c 1k 2x þc 2k 2y þc 3k 2z þc 4k x k y þc 5k y k z þc 6k z k x þc 7k 4x =k 2r þc 8k 4y =k 2r þc 9k 4z =k 2r þc 10k 2x k 2y =k 2r þc 11k 2y k 2z =k 2r þc 12k 2z k 2x =k 2rþc 13k 3x k z =k 2r þc 14k x k 3z =k 2r þc 15k 3x k y =k 2r þc 16k 3x k y =k 2r þc 17k 3y k z =k 2r þc 18k y k 3z =k 2rþc 19k 2x k y k z =k 2r þc 20k x k 2y k z =k 2r þc 21k x k y k 2z =k 2r 0B B B B B B B B B B B B B B B B B @1C CCC CCC CC C CC C CC C C A ,ð3Þwherec 1¼1þ2e ðsin 2j þcos 2y cos 2j Þ,c 2¼1þ2e ðcos 2j þcos 2y sin 2j Þ,c 3¼1þ2e sin 2y ,c 4¼À2e sin 2y sin 2j ,c 5¼2e sin 2y sin j ,c 6¼2e sin 2y cos j ,c 7¼2ðd Àe Þsin 2y cos 2j ðsin 2j þcos 2y cos 2j Þ,c 8¼2ðd Àe Þsin 2y sin 2j ðcos 2j þcos 2y sin 2j Þ,c 9¼2ðd Àe Þsin 2y cos 2y ,c 10¼0:5ðd Àe Þf sin 2y ðcos 4j þ3Þþ8sin 2y sin 2j cos 2j ð3cos 2y À2Þg ,c 11¼0:5ðd Àe Þf sin 2j ðcos 4y þ3Þþ4cos 2y ðcos 2j À4sin 2y sin 2j Þg ,c 12¼0:5ðd Àe Þf cos 2j ðcos 4y þ3Þþ4cos 2y ðsin 2j À4sin 2y cos 2j Þg ,c 13¼4ðd Àe Þsin y cos y cos j ð2sin 2y cos 2j À1Þ,c 14¼4ðd Àe Þsin y cos y cos 2y cos j ,c 15¼4ðd Àe Þsin 2y sin j cos j ðcos 2j cos 2y þsin 2j Þ,c 16¼4ðd Àe Þsin 2y sin j cos j ðsin 2j cos 2y þcos 2j Þ,c 17¼À4ðd Àe Þsin y cos y sin j ðsin 2j cos 2y þcos 2j Þ,c 18¼4ðd Àe Þsin y cos y cos 2y sin j ,c 19¼4ðd Àe Þsin y cos y sin j ð6sin 2y cos 2j À1Þ,c 20¼4ðd Àe Þsin y cos y cos j ð4sin 2y sin 2j À1Þ,c 21¼4ðd Àe Þsin 2y sin j cos j ð6sin 2y À5Þ:In Eq.(3),y is the dip angle and j is the azimuth ing aFourier transform,we can transform Eq.(3)from the frequency domain to the time domain.When the i o term is substituted by @=@t ,Eq.(3)is changed to the following:@2u ðx ,t Þ@t 2¼v 2p 0c 1k 2x þc 2k 2y þc 3k 2zþc 4k x k y þc 5k y k z þc 6k z k xþc 7k 4x =k 2r þc 8k 4y =k 2r þc 9k 4z =k 2r þc 10k 2x k 2y =k 2r þc 11k 2y k 2z =k 2r þc 12k 2z k 2x =k 2r þc 13k 3x k z =k 2r þc 14k x k 3z =k 2r þc 15k 3x k y =k 2r þc 16k 3x k y =k 2r þc 17k 3y k z =k 2r þc 18k y k 3z =k 2r þc 19k 2x k y k z =k 2r þc 20k x k 2y k z =k 2r þc 21k x k y k 2z =k 2r 0B B B B B B B B B B B B B B B B B @1CC C C C C C C CC C CC C C CC A u ðx ,t Þ,ð4Þwhere u ðx ,t Þis the waveﬁeld at time t .The solution of the 2D TTI pure P -wave equation can be obtained by setting j to 0.In the 2D case,21terms of the spatial derivatives in Eq.(4)can be reduced to 7terms.Y.Kim et al./Computers &Geosciences 52(2013)204–2172053.The solution of the wave equation using REM witha pseudo-spectral methodBy replacing the multiplication of the square of the P-wave velocity and the term of the spatial derivatives in Eq.(4)with the symbolÀF2,the wave equation in Eq.(4)can be written as follows:@2uðx,tÞ@t¼ÀF2uðx,tÞ:ð5ÞThe formal solution to Eq.(5)with two initial conditions ofu0¼uðx,0Þand_u0¼@uðx,tÞ=@t9t¼0is given by the following:uðx,tÞ¼cosðF tÞu0þFÀ1sinðF tÞ_u0:ð6ÞThe waveﬁelds uðx,tþD tÞand uðx,tÀD tÞcan be obtained by setting the t term in Eq.(6)to tþD t and tÀD t,respectively. Adding these two waveﬁelds removes the odd part of the solution,resulting inuðx,tþD tÞþuðx,tÀD tÞ¼2cosðF D tÞuðx,tÞ:ð7ÞBecause the PSM provides optimal spatial accuracy for a given grid size,we select the method to calculate the spatial derivatives with the REM.Based on the PSM,the form of Eq.(7)can be written using the Fourier transform as follows:uðx,tþD tÞ¼2FTÀ1½cosðF D tÞFT½uðx,tÞ Àuðx,tÀD tÞ,ð8Þwhere FT and FTÀ1represent the Fourier transform and its inverse transform,respectively.The cosine operator in Eq.(8)can be expanded by its Cheby-shev expansion for one-step REM as proposed by Kosloff et al. (1989),and the cosine is expanded as follows(Pestana and Stoffa, 2010):cosðF D tÞ¼X Mk¼0C2k J2kðBÞQ2kði xÞ,ð9Þwhere C0¼1and C k¼2for k Z1,9J kðzÞ9¼9z9k=ð2k k!Þ,Q2k is presented asQ0ði xÞ¼1,Q2ði xÞ¼1À2x2,Q4ði xÞ¼1À8x2þ8x4,Q6ði xÞ¼1À18x2þ48x4À32x6,Q8ði xÞ¼1À32x2þ160x4À256x6þ128x8,^Q kþ2ði xÞ¼ðÀ4x2þ2ÞQ kði xÞÀQ kÀ2ði xÞ:ð10ÞIn Eq.(9),J k represents the Bessel function of order k,Q k represents the modiﬁed Chebyshev polynomials that are recur-sively obtained from the initial condition of Q0and Q2,and the characters B,x and m represent R D t,F=R and1=R,respectively. The orthogonal polynomial series expansion for the cosine func-tion was presented by Tal-Ezer et al.(1987).For the3D TTI or VTI modeling,the R value is given by the following:R¼p V maxð1þ29e9maxÞﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ1xþ1yþ1zs,ð11Þwhere V max is the highest P-wave velocity in the direction of the symmetry axis,and D x,D y,and D z are the spatial grid spacing in the x,y,and z directions,respectively.M should satisfy the condition of M4R D t.When we useﬁve Chebyshev polynomial terms,Eq.(9)can be written as follows:cosðF D tÞ¼X Mk¼0C2k J2kðBÞQ2kði xÞ¼C0J0ðBÞQ0ði xÞþC2J2ðBÞQ2ði xÞþC4J4ðBÞQ4ði xÞþC6J6ðBÞQ6ði xÞþC8J8ðBÞQ8ði xÞ¼J0ðBÞþ2J2ðBÞð1À2x2Þþ2J4ðBÞð1À8x2þ8x4Þþ2J6ðBÞð1À18x2þ48x4À32x6Þþ2J8ðBÞÂð1À32x2þ160x4À256x6þ128x8Þð12Þand theﬁnal equation to perform the numerical modeling can beexpressed as follows:uðx,tþD tÞ¼2½J0ðBÞuðx,tÞþ2J2ðBÞf uðx,tÞÀ2m2FðxÞgþ2J4ðBÞf uðx,tÞÀ8m2FðxÞþ8m4F2ðxÞgþ2J6ðBÞf uðx,tÞÀ18m2FðxÞþ48m4F2ðxÞÀ32m6F3ðxÞgþ2J8ðBÞf uðx,tÞÀ32m2FðxÞþ160m4F2ðxÞÀ256m6F3ðxÞþ128m8F4ðxÞg Àuðx,tÀD tÞ,ð13Þwhere FðxÞ¼FTÀ1½F2FT½uðx,tÞ .4.Pseudo-spectral method with CUDA and MPIWhen the model size for RTM is small enough to implementthe numerical modeling with one GPU,massage passing with MPIis not required in the PSM application.However,the devicememory size of the GPUs is not large enough to implement theactual application on wide-azimuth real exploration data.Inaddition,modeled data for the illumination zone should be storedin a global memory in the forward algorithm when RTM isperformed on a cluster without a blade hard disk in each node.To solve these problems,multiple GPUs and CPU processors areemployed to implement the RTM for one shot.Fig.1displays the algorithm structure of a PSM for obtainingFðxÞin Eq.(13)when four GPU devices are employed to imple-ment the modeling for a shot.Let nx,ny and nz denote the numberof grids in the x,y,and z directions and the symbol x representsthe location of the waveﬁeldðx,y,zÞ.k and~k areðk x,k y,k zÞandðk x,k y,zÞ,respectively.#1in Fig.1demonstrates the domainpartition for four GPU devices where the waveﬁelds in time tare partitioned vertically into four parts(divided by colors),andeach color represents the subdomain assigned to a GPU device.AGPU device does not need to store waveﬁelds on the total domain,which can implement the actual application on a large-sizedmodel by using many GPUs.The waveﬁelds in the total domain are larger than nxÂnyÂnzbecause the grids in each axis are padded until the number of gridpoints is suitable for a prime factor length FFT(Fig.2(a)).When NGPUs i¼ð0,1,2,...,NÀ1Þare employed,the array of waveﬁeldsassigned to i-th GPU is expressed as½1:nxfft;1:nyfft;ðnzfft=NÞÃiþ0:5:ðnzfft=NÞÃðiþ1Þþ0:5À1 :Because a GPU has enough waveﬁelds to implement the Fouriertransform in the x and y directions,2D FFT can be performed inevery xy-plane along z directions.In this study,we implement the2D FFT on uðxÞby using complex cuFFT supported by NVIDIA andthen obtain uð~kÞ(shown in#2in Fig.1and Fig.2(b)).To perform the FFT in the z direction,communication amongthe GPU devices is needed to exchange waveﬁelds.The dataexchange between GPUs involves three memory copies:from GPUto CPU,from CPU to CPU,and from CPU to GPU(Micikevicius,2009).In the communication from CPU to CPU(#3-#4)afterthe memory copy is made from GPU to CPU(#2-#3),dataexchange among CPUs is achieved using MPI as follows./*Send waveﬁelds to other processors*/forði¼0;i o N;iþþÞf=Ã‘me’is my rankÃ=buffer[i]¼uk_tilde[1:nxfft,Y.Kim et al./Computers&Geosciences52(2013)204–217206: Communication among nodes: Multiply pseudo-Laplacian to waveﬁelds : Fourier transform: Inverse Fourier transformFig.1.Diagram of the parallel3D pseudo-spectral modeling when four GPU devices are employed to implement numerical modeling for a shot.The symbol x represents the location of the waveﬁeldðx,y,zÞ.k and~k areðk x,k y,k zÞandðk x,k y,zÞ,respectively.(For interpretation of the references to color in thisﬁgure caption,the reader is referred to the web version of this article.)(nyfft/N)*iþ0.5:(nyfft/N)*(iþ1)þ0.5-1,(nzfft/N)*meþ0.5:(nzfft/N)*(meþ1)þ0.5-1]; if(i¼¼me)xzwork[1:nxfft,(nyfft/N)*meþ0.5:(nyfft/N)*(meþ1)þ0.5-1,(nzfft/N)*meþ0.5:(nzfft/N)*(meþ1)þ0.5-1]¼buffer[me];elsesend data in buffer[i]to processor i usingMPI_Bsend;}/*Receive waveﬁelds from other processors*/nrecv¼0;whileðnrecv o NÞfif(nrecv!¼me){receive data from nrecv-th processorusing MPI_Recv and store into buffer[nrecv];xzwork[1:nxfft,(nyfft/N)*meþ0.5:(nyfft/N)*(meþ1)þ0.5-1, (nzfft/N)*nrecvþ0.5:(nzfft/N)*(nrecvþ1)þ0.5-1]¼buffer[nrecv];}Y.Kim et al./Computers&Geosciences52(2013)204–217207nrecv þ¼1;}To facilitate understanding,we also illustrate the manner of data exchange in Fig.2(d).After the memory-copy is made from CPU and GPU (#4-#5),waveﬁelds u ðk Þcan be obtained by performing 1D FFT in the z direction and are then stored in the device memory of each GPU device.The array of waveﬁelds u ðk Þassigned to i -th GPU is expressed as½1:nxfft ;ðnyfft =N ÞÃi þ0:5:ðnyfft =N ÞÃði þ1Þþ0:5À1;nzfft ;and is also displayed in Fig.2(c).The processes from #7to #12are the inverses of the processes that occur from #1to #6.Whereas the processes from #1to #6are for preparing a PSM,the processes from #7to #12constitute the main routines for calculating the derivatives in the spatial directions usingtheFig.2.The structure of the prime numbered grids.(a)and (b)are the structures before and after the memory exchange,respectively,between the CPUs and GPUs in the progressions from #1to #6in Fig.1.(c)presents the manner of exchange.Y.Kim et al./Computers &Geosciences 52(2013)204–217208PSM.To implement the REM,we must calculate FðxÞin Eq.(13), which is expressed in detail as follows:FðxÞ¼v2p0c1FTÀ1½k2xFT½uðx,tÞþc2FTÀ1½k2yFT½uðx,tÞþc3FTÀ1½k2zFT½uðx,tÞþc4FTÀ1½k x k y FT½uðx,tÞ þc5FTÀ1½k y k z FT½uðx,tÞþc6FTÀ1½k z k x FT½uðx,tÞþc7FTÀ1½ðk4x=k2rÞFT½uðx,tÞþc8FTÀ1½ðk4y=k2rÞFT½uðx,tÞþc9FTÀ1½ðk4z=k2rÞFT½uðx,tÞþc10FTÀ1½ðk2xk2y=k2rÞFT½uðx,tÞþc11FTÀ1½ðk2yk2z=k2rÞFT½uðx,tÞþc12FTÀ1½ðk2zk2x=k2rÞFT½uðx,tÞþc13FTÀ1½ðk3xk z=k2rÞFT½uðx,tÞþc14FTÀ1½ðk x k3z=k2rÞFT½uðx,tÞþc15FTÀ1½ðk3xk y=k2rÞFT½uðx,tÞþc16FTÀ1½ðk x k3y=k2rÞFT½uðx,tÞþc17FTÀ1½ðk3yk z=k2rÞFT½uðx,tÞþc18FTÀ1½ðk y k3z=k2rÞFT½uðx,tÞþc19FTÀ1½ðk2xk y k z=k2rÞFT½uðx,tÞþc20FTÀ1½ðk x k2yk z=k2rÞFT½uðx,tÞþc21FTÀ1½ðk x k y k2z=k2rÞFT½uðx,tÞB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB@1C CC CC CC CC CC CC CC CC CC CC CC CC CC CC CC CC CC CC CC CC CC CC CC CC CC CC A¼v2p0X21i¼1c i FTÀ1½L iðkÞÁuðkÞ :ð14ÞBecause Eq.(14)consists of21terms of spatial derivatives,the processes from#7to#12should be repeated21times.Each GPU device calculates HðkÞ¼L iðkÞÁuðkÞin the subdomain assigned to each(#7in Fig.1)and performs the inverse Fourier transform with cuFFT in the z direction to obtain H ið~kÞ.Because data exchange should be required to take the inverse Fourier transform to H ið~kÞin the xy-plane,data communication among CPUs should be performed with the MPI;its computational algorithm can be summarized as follows./*Send waveﬁelds to other processors*/forði¼0;i o N;iþþÞf=Ã’me’is my rankÃ=buffer[i]¼uk_tilde[1:nxfft,(nyfft/N)*meþ0.5:(nyfft/N)*(meþ1)þ0.5-1,(nzfft/N)*iþ0.5:(nzfft/N)*(iþ1)þ0.5-1];if(i¼¼me)xzwork[1:nxfft,(nyfft/N)*meþ0.5:(nyfft/N)*(meþ1)þ0.5-1, (nzfft/N)*iþ0.5:(nzfft/N)*(iþ1)þ0.5-1]¼buffer[me];elsesend data in buffer[i]to processor i using MPI_Bsend;}/*Receive waveﬁelds from other processors*/nrecv¼0;whileðnrecv o NÞfif(nrecv!¼me){receive data from nrecv-th processor using MPI_Recvand store into buffer[nrecv];xzwork[1:nxfft,(nyfft/N)*nrecvþ0.5:(nyfft/N)*(nrecvþ1)þ0.5-1,(nzfft/N)*meþ0.5:(nzfft/N)*(meþ1)þ0.5-1]¼buffer[nrecv];}nrecvþ¼1;}After the completion of data exchange among the CPUs and memory copy from the CPUs to the GPUs,the waveﬁelds on the subdomain assigned to a GPU are taken from the inverse trans-form to each xy-plane along the z direction(shown in#11-#12 in Fig.1).Then,by multiplying the coefﬁcient c i by H iðxÞ,each GPU stores the values of c i FTÀ1ðL iðkÞÁuðkÞÞin Eq.(14)in the device memory.Finally,by repeating steps#7to#1221times, we can calculate FðxÞin Eq.(14)and obtain the waveﬁelds in the next time step uðx,tþD tÞin Eq.(13).Fig.3shows the2D algorithm with the GPUs and the MPI.The 2D algorithm can be obtained by excluding the waveﬁelds in the x direction on the3D algorithm because the data in the x direction are not shared among processors.In addition,when we perform 2D TTI modeling,the processes from#7to#12in Fig.3can be reduced to one-third of the repetitions used in the3D algorithm. To compare waveﬁelds obtained by the TTI P-wave equation based on our proposed algorithm and those obtained by the pseudo-acoustic TTI wave equation suggested by Fletcher et al. (2009),we display2D and3D waveﬁeld snapshots in Fig.4.The P-wave vertical velocity in the medium is constant at2000m=s. The Thomsen parameter E and d are0.24and0.1,respectively. The tilt angle isﬁxed to45J in the2D and3D cases,and the azimuth angle is set to45J in the3D case.The wave snapshots in Fig.4(a)–(d)are obtained using the pseudo-acoustic TTI wave equation based on a second-order time-domain eighth-order space-domainﬁnite difference stencil.The SV-wave velocity is set to zero in Fig4(a)and(b).Fig.4(a)and(b)demonstrates the diamond shape of the SV wavefront.In the P-wave RTM imple-mentation,the SV-waves may act as artifacts that have a harmful effect on the quality on migration images.When we set the SV-wave velocity to0,Fletcher et al.(2009)showed that waveﬁelds in areas with a high gradient of dip angles can be blown up.To stabilize the waveﬁelds,Fletcher et al.(2009)set the SV-wave velocity to half of the P-wave vertical velocity when a high contrast existed in the dipﬁeld.However,as shown in Fig.4(c)and4(d),the drawback of this approach is that additional S-wave noise is generated.Snapshots presented in Fig.4(e)and (f)are generated by our proposed algorithm.Fig.4(e)and(f) indicates that the S-waves are completely removed and that only P-wave wavefronts are clearly observed.5.Algorithm of reverse time migrationWhen the cross-correlation imaging condition is employed in the RTM,the migration image at the k-th node can be expressed as follows:fk¼Xnshoti¼1Z T maxS kðtÞR kðT maxÀtÞd t,ð15Þwhere T max is the maximum recording time,i is the shot number,S k(t)is the source waveﬁeld,R kðT maxÀtÞis the backward-propagated receiver waveﬁeld,and f k is the image at the k-th node.The source waveﬁeld S k(t)can be obtained by propagating a mathematical function,e.g.,a Ricker wavelet,as a source signature forward in time.The receiver waveﬁeld R k(t)Y.Kim et al./Computers&Geosciences52(2013)204–217209。

Flotation of diaspore and aluminosilicate minerals applying novel carboxyl hydroxamic acids as colle

This article appeared in a journal published by Elsevier.The attached copy is furnished to the author for internal non-commercial research and education use,including for instruction at the authors institutionand sharing with colleagues.Other uses,including reproduction and distribution,or selling or licensing copies,or posting to personal,institutional or third partywebsites are prohibited.In most cases authors are permitted to post their version of thearticle(e.g.in Word or Tex form)to their personal website orinstitutional repository.Authors requiring further informationregarding Elsevier’s archiving and manuscript policies areencouraged to visit:/copyrightFlotation of diaspore and aluminosilicate minerals applying novel carboxyl hydroxamic acids as collectorYu-Ren Jiang a ,⁎,Bin-Nan Zhao a ,b ,⁎,Xiao-Hong Zhou a ,Li-Yi Zhou aa College of Chemistry and Chemical Engineering,Central South University,Changsha 410083,People ’s Republic of China bHunan Suntown Technology Group Co.,Ltd,No.109Jinxin Road,Suntown Industrial Park,Changsha,Hunan 410200,Chinaa b s t r a c ta r t i c l e i n f o Article history:Received 10December 2009Received in revised form 3March 2010Accepted 14May 2010Available online 20May 2010Keywords:Flotation reagent DiasporeAluminosilicateCarboxyl hydroxamic acid Adsorption mechanismThree novel carboxyl hydroxamic acids including ortho-carboxyl tetrachlorobenzohydroxamic acid (OCB),ortho-carboxyl hexahydrobenzohydroxamic acid (OHB)and ortho-carboxyl tetrahydrobenzohydroxamic acid (OTB),were synthesized and tested as collectors for ﬂotation of diaspore,kaolinite and illite contained in diasporic bauxite from China.Subsequently,their ﬂotation mechanism to diaspore and aluminosilicate minerals was investigated by zeta potential measurements and FT-IR spectrum checking.The results of ﬂotation experiments show that by using carboxyl hydroxamic acid as collectors,the pulp pH value has signi ﬁcant in ﬂuence on their collecting performance as the ﬂoatability of either diaspore or aluminosilicates varies sharply with their change,and the appropriate pH value for the ﬂotation of diaspore gets close to neutral condition where diaspore presents good ﬂoatability while kaolinite and illite exhibits poor performances.Additionally,the ﬂoatability of diaspore and aluminosilicates is in the descending order of diaspore,kaolinite,and illite in the presence of three collectors,and their collecting capacity to three minerals is in the ascending order of OTB,OHB and OCB.Of three synthesized carboxyl hydroxamic acids,OCB has the strongest collecting capability to diaspore while relatively weak to aluminoscilicate minerals,whose good selectivity for the ﬂotation between diaspore and aluminosilicates is possibly suited for direct ﬂotation desilication of diasporic bauxite.Moreover,the optimum pH value for diaspore ﬂotation associated with FT-IR spectrum and zeta potentials indicate that the adsorption interaction between the synthesized collectors and diaspore is dominantly a kind of chemical bonding one in the form of three cycle chelate rings due to the coordination of carboxyl and hydroxamate to the metal aluminum atoms,where the oxygen atoms contained in carboxyl and hydroxamate of the polar group have the stereo conditions to form ﬁve to seven membered rings.By contrast,the adsorption interactions of the carboxyl hydroxamic acid on the surfaces of aluminosilicate minerals are mainly dominated by means of hydrogen bonds.©2010Elsevier B.V.All rights reserved.1.IntroductionBauxite is the major raw material for alumina production,and Bayer process is widely applied in alumina technology with mass ratio of Al 2O 3to SiO 2(A/S)more than 8(Xu et al.,2004)on account of the advantage of short ﬂow,small investment,stable product quality and low energy consumption.Although there are plenty of bauxite resources in China,most of them (at least 90%)are characteristic of high silica,high alumina and low mass ratio A/S (A/S=4–6)(Huang et al.,2005).High-grade bauxite with mass ratio of A/S greater than 10is necessary to be processed directly by the Bayer process (Ma et al.,1996;Papanastassiou et al.,2002;Zhong et al.,2008).Due to this reason,majority of the bauxites in China cannot meet the requirement of the advanced Bayer process in alumina technology.Therefore,it ishighly desirable to increase the mass ratio of A/S by ﬂotation desilication before Bayer process.Flotation is known to be a highly versatile separation technology and has been widely used for industrial mineral processing (Yoon and Shi,1989).Many researches on direct ﬂotation desilication have been shown to be an ef ﬁcient method for the desilicating of diasporic bauxite (Feng et al.,1998;Liu,1999;Lu et al.,2002).Flotation reagents are the critical technique in the ﬂotation separation process.The use of traditional reagents and their combinations has been reported a lot in the ﬁeld of direct ﬂotation desilication (ﬂotation of diaspore and depression of aluminosilicates)such as oleic acid,tall oil,sodium dodecylbenzene sulfonate,oxidized paraf ﬁn soap,733,styrene phosphate,aliphatic hydroxamic acid,and aromatic hydroxamic acid and their mixtures (Wang et al.,2003;Hu et al.,2004;Hu et al.,2005);Jiang et al.(2001a)synthesized a new type of collector called COBA,which has a strong collecting ability to diaspore,weaker capability to kaolinite,and higher selectivity than salicylhydroxamic acid.The difference of whose collecting perfor-mance was due to the difference of polar group,like electronegativity,Hydrometallurgy 104(2010)112–118⁎Corresponding authors.Tel.:+8673188836834.E-mail addresses:jiangyr@ (Y.-R.Jiang),zhaobinnan2003@ (B.-N.Zhao).0304-386X/$–see front matter ©2010Elsevier B.V.All rights reserved.doi:10.1016/j.hydromet.2010.05.006Contents lists available at ScienceDirectHydrometallurgyj o u r n a l h o me p a g e :w w w.e l s ev i e r.c o m/l o c a t e /hyd ro m e ttopological index,cross-section size and hydrophobicity.Recently,the research on novelﬂotation reagents for reverseﬂotation desilication (ﬂotation of aluminosilicates and depression of diaspore)has been soaring in China.Liu et al.(2003)discovered a kind of cationic polyacrylamide,which had little inﬂuence on kaoliniteﬂotation, possessed the ability to inhibit diaspore at pH range of5.5–8.5.The research work of Li et al.(2001)showed that the modiﬁed starch/ polyacrylamide,absorbed on mineral surfaces through electrostatic force,and chemical/hydrogen bonding,were superior to starch in the inhibition of diaspore.Hu et al.(2003a)synthesized the cationic collector N-dodecyl-1,3-diaminopropane,which excelled over lauryl amine in the collecting ability to kaolinite,pyrophyllite and illite with theﬂotation recoveries over80%.Zhao et al.(2003a,b,2004)also synthesized N-(3-aminopropyl)dodecanamide,N-(2-aminoethyl) dodecanamide and N-(3-diethylaminopropyl)fatty amide forﬂota-tion of aluminosilicates.It was proved that N-(3-aminopropyl) dodecanamide had relatively strong collecting ability to kaolinite, pyrophyllite,and illite.N-(2-aminoethyl)dodecanamide presented very strong collecting ability to pyrophyllite with theﬂotation recovery of97.7%;while relatively weak collecting ability to kaolinite and illite with theﬂotation recoveries no more than82%.N-(3-diethylaminopropyl)fatty amide possessed very high collecting ability to diaspore withﬂotation recovery of99.9%;but the data of ﬂotation of aluminosilicates was not given to understand the selectivity of these collectors.From the aspect of reportedﬂotation reagents for desilication,no matter direct or reverseﬂotation of bauxite,collectors and depres-sants have achieved certain developments.However,due to its short history in research,plenty of difﬁculties and problems still remain. First,the selection ofﬂotation reagents mostly focuses on the traditional ones and their combinations;few studies have reported the designing and synthesis of novel structures.In addition,the present reagents are characteristic of low selectivity,and highly efﬁcient reagents for the separation of bauxite have not been found. For instance,although directﬂotation desilication for diasporic bauxite has been employed for several years in China,the recovery of an acceptable bauxite concentrate was not yet very high in commercial scale(Liu and Liu,2005).Hydroxamic acid is extensively applied in theﬂotation of rare earth minerals as collector(Yang et al.,1992)because it has nitrogen and oxygen atoms which contain lone pair electrons to coordinate with metal atoms.The self-made COBA(Jiang et al.,2001a)containing carboxyl group and hydroxamate group in the same molecule was employed in theﬂotation of diaspore and kaolinite as collector showing that it has much higher selectivity than salicylhydroxamic acid,which indicates that the introduction of carboxyl group has greatly enhanced the selectivity of the collector.The present work is to try to design a type of new compounds for theﬂotation of diaspore against aluminosilicate minerals by putting a carboxyl group and a hydroxamate group into one molecule based on our previous experiment ing chemical approach,three novel carboxyl hydroxamic acids,ortho-carboxyl tetrachlorobenzohydroxa-mic acid(OCB),ortho-carboxyl hexahydrobenzohydroxamic acid (OHB)and ortho-carboxyl tetrahydrobenzohydroxamic acid(OTB), were synthesized as collectors for theﬂotation of diaspore and aluminosilicates.The investigations of theﬂotation experiments and the adsorption mechanism illustrated that the synthesized carboxyl hydroxamic acids was a new type of selective collectors,especially OCB possesses high selectivity for theﬂotation between diaspore and aluminosilicates and possibly suites the directﬂotation desilication of diasporic bauxite.2.Experimental2.1.Mineral samples and reagentsDiaspore,kaolinite,illite were all were obtained from Henan, China,which were handpicked and then crushed and ground in a porcelain mill.The fraction of minus0.076mm was used inﬂotation. The results of mineralogical analysis,chemical analysis and X-ray diffraction showed that the three minerals were all at least90%pure.Three novel carboxyl hydroxamic acid compounds including ortho-carboxyl tetrachlorobenzohydroxamic acid(OCB),ortho-car-boxyl hexahydrobenzohydroxamic acid(OHB)and ortho-carboxyl tetrahydrobenzohydroxamic acid(OTB)were synthesized in our laboratory.The pH modiﬁers employed were analytical grade hydrochloric acid or sodium hydroxide,the frother used was chemical grade1,and3-dimethylbutanol and distilled water made in our laboratory was used in all tests.2.2.Synthesis procedures of carboxyl hydroxamic acidsNovel carboxyl hydroxamic acids used in theﬂotation tests were synthesized by reaction of hydroxylamine hydrochloride with the corresponding dicarboxylic esters referring to the method described for the general synthesis procedures(Fatih and Veysel,2001).The structures of synthesized compounds were identiﬁed and consistent with the data of elemental analysis and the IR spectra.Scheme1 illustrates the general synthetic method of the carboxyl hydroxamic acids.2.2.1.General synthetic procedures for carboxyl hydroxamic acids1Equiv.of respective dicarboxylic acid in ethanol was mixed with 0.4equiv.of98%sulfuric acid,and then the solution was reﬂuxed with stirring for6h.The excess ethanol was eliminated on a rotary evaporator and sulfuric acid was neutralized with an aqueous solution 5%sodium bicarbonate until formation of carbon dioxide ceased.The formed diester was washed with water and separated in a separatory funnel.1Equiv.of hydroxylamine hydrochloride in methanol was added to a methanol solution containing1equiv of potassium hydroxide. Potassium chloride precipitated from the solution was removed by suctionﬁltration,and then a methanol solution with1equiv of potassium hydroxide was added to theﬁltrate.Subsequently,the synthesized diester dissolved in methanol was added to the hydroxylamine solution and stirred for8h at room temperature.A color change to orange red occurred during the reaction.The volume of the resulting solution was reduced by evaporating at40°C and acetone was added to the solution to precipitate potassium salt of carboxyl hydroxamate.The precipitate was recrystallized in water and acidiﬁed to pH5.5by using aqueous solution5%hydrochloride acid to give the desired product carboxyl hydroxamic acid.Ortho-carboxyl tetrachlorobenzohydroxamic acid(OCB).Yield:72.5%. Found(%):C,30.72;H,1.04;N,4.30.Calculated for C8H3Cl4NO4(%):C, Scheme1.General synthetic method of carboxyl hydroxamic acids.113 Y.-R.Jiang et al./Hydrometallurgy104(2010)112–11830.13;H,0.95;N, 4.39.IR(KBr,νmax/cm−1):3175.09vs(NH), 2848.13b(OH),1667.25vs(CO)and1569.53s(CN).Ortho-carboxyl hexahydrobenzohydroxamic acid(OHB).Yield: 68.3%.Found(%):C,52.01;H,7.23;N,7.26.Calculated for C8H13NO4 (%):C,51.33;H,7.00;N,7.48%.IR(KBr,νmax/cm−1):3500.70vs(NH), 2869.30b(OH),1714.74vs(CO)and1562s(CN).Ortho-carboxyl tetrahydrobenzohydroxamic acid(OTB).Yield: 67.8%.Found(%):C,52.01;H,6.03;N,7.32.Calculated for C8H11NO4 (%):C,51.89;H,5.99;N,7.56;IR(KBr,νmax/cm−1):3439.46vs(NH), 2923.67b(OH),1703.42vs(CO)and1538.85s(CN).2.3.Flotation performance of carboxyl hydroxamic acidsFlotation tests were performed with a XFG-35ﬂotation machine having30mL effective cel1volume,where the impeller speed was ﬁxed at l650r/min.In each test,2.0g mineral samples and decent amount of distilled water were used,and the dosage of frother used wasﬁxed at5.0×10−4mol/L.The general procedures for theﬂotation tests were as follows:the mineral sample and distilled water were added in theﬂotation cell,and the suspension was agitated for1min. After the desired pH value was adjusted by mass ratio5%aqueous solution hydrochloric acid or aqueous solution sodium hydroxide,a desired amount of collector and frother were added;and then the ﬂotation was carried out and maintained for5min.Theﬂoated products and the unﬂoated ones were collected,dried,and weighed. Theﬂotation recovery was calculated based on the percentage mass ratio of theﬂoated products in the summation ofﬂoated and unﬂoated products.2.4.FT-IR spectroscopyIn order to characterize the nature of the interaction between the collectors and the minerals,the infrared spectra of collectors as well as samples with or without collectors pretreated are measured by the KBr technique.Model FTIR-750Infrared spectrophotometer from Nicolet CO.in USA was used to obtain the IR spectra.The mineral samples were ground to be less than5μm in an agate mortar before being conditioned with2×10−2mol/L collectors.2.5.Zeta potential measurementZeta potential was measured on a Delsa-440SX zeta potential instrument(Brookhaven Corporation,USA).The mineral sample was further ground to minus5μm in an agate mortar.The mineral suspension containing0.01%(mass fraction)solid was dispersed in a beaker for 15min and the pH value was measured.1×10−3mol/L KNO3solution was used as a supporting electrolyte.The measurement error was found to be within±5mV after at least three measurements in each condition.3.Results and discussion3.1.Flotation behaviors of diaspore and aluminosilicates with carboxyl hydroxamic acids as collectorsTheﬂotation recoveries of diaspore,kaolinite and illite with 2×10−4mol/L of OCB,OHB and OTB as collectors of different carbon types are shown in Fig.1.It can be seen that by using carboxyl hydroxamic acid as collectors,the pulp pH value has signiﬁcantinﬂuence on their collecting performance as theﬂoatability of either diaspore or aluminosilicates varies sharply with its change, especially when below6and above8.The appropriate pH value for theﬂotation of diaspore gets close to neutral condition where diaspore presents goodﬂoatability while kaolinite and illite exhibits poor performances.Additionally,theﬂoatability of the three minerals is in the descending order of diaspore,kaolinite and illite in the presence of three collectors with the same concentration.Their collecting capability to three minerals is in the ascending order of OTB,OHB and OCB in the presence of the same concentration.Theﬂotation responses of the diaspore and aluminosilicates as functions of the concentration of OCB,OHB and OTB at pulp pH7are presented in Fig.2.As it can be concluded from Fig.2,the recoveries of the diaspore and aluminosilicates rise with the increase of collectors' dosages.For diasporeﬂotation,the collecting capacity of OCB remains at a very high level with theﬂotation recoveries above95%.Atthe Fig.1.Effect of pulp pH value onﬂotation of diaspore and aluminosilicates using OCB, OHB and OTB as collectors:(a)diaspore;(b)kaolinite;(c)illite.114Y.-R.Jiang et al./Hydrometallurgy104(2010)112–118concentration of 2×10−4mol/L OCB,the recovery of diaspore is 97.4%,but for OHB and OTB,the collecting abilities are relatively poor,and the ﬂotation recovery of diaspore is 67.6%and 45.5%,respectively.The maximum ﬂotation recoveries of diaspore using OCB,OHB and OTB in the tested dosage are 99.7%,89.2%and 73.0%,respectively.The collecting ability of the three collectors to diaspore is in the descending order of OCB,OHB and OTB,illustrating that with the increase of the nonpolar group in carboxyl hydroxamic acid itscollecting ability grows correspondingly.For aluminosilicates ﬂota-tion,although the recoveries rise with the growth of collectors dosage and there exists difference of recovery between kaolinite and illite,the three carboxyl hydroxamic acids still exhibit poor collecting ability to illite and kaolinite as none of their recoveries can reach up to 40%.Integrated results from Figs.1and 2,the novel synthesized collectors all present better collecting abilities to diaspore than that to illite and kaolinite,the collecting capacity of them to mineral ﬂotation is in the order of diaspore N kaolinite N illite,and the collecting capacity of them is in the order of OCB N OHB N OTB.Of the three synthesized carboxyl hydroxamic acids,OCB has very strong collecting capacity to diaspore while relatively weak to aluminoscilicate minerals,since the ﬂotation recovery of diaspore above 97%while those of kaolinite and illite below 40%with relatively low OCB dosage in a relatively wide pH range,so OCB is possibly suited for the direct ﬂotation desilication of diasporic bauxite.3.2.Zeta potential of diaspore and aluminosilicates with or without carboxyl hydroxamic acidSince it exhibits good selectivity in the ﬂotation between diaspore and aluminosilicate minerals,OCB was selected as a representative compound to investigate its effect on the zeta potential of kaolinite,illite and diaspore.Fig.3shows the relationship between zeta potential of minerals and pH values in the absence and presence of OCB.The results present that isoelectric point (IEP)determined is 4.3,3.4and 6.3for kaolinite,illite and diaspore,respectively,which are generally consistent with the previous reported literatures (Fuerste-nau and Fuerstenau,1982;Saada et al.,1995;Hussain et al.,1996;Jiang et al.,2001b;Qin et al.,2003;Xia et al.,2009).Compared with kaolinite and illite,diaspore has a relatively higher IEP.In the pH region below the isoelectric point,the negative zeta potential increases slightly.When pH N IEP,the zeta potential increases rapidly with the negative growth of pH values,while pH reaching 10for diaspore or 8for kaolinite and illite,it has no signi ﬁcant change and keeps approximate invariance.However,no matter without or with OCB,the zeta potential of diaspore,kaolinite and illite presents almost the same variance trend.Based on the zeta potential of diaspore and aluminosilites without OCB,qualitatively,the higher IEP value of diaspore is related to a greater number of surface Al –O sites,while the lower IEP value of aluminosilicates is attributed to a greater number of surface Si –O sites.The structure of diaspore is signi ﬁcantly different from aluminosili-cates.The comminution destroys ionic/covalent Al –O bonds,resulting in a surface of unsaturated or ionic nature.The aluminosilicates are negatively charged in the pH range 2–10.This is attributable to isomorphic exchange of surface ions and surface ionization of the hydroxyl group.Si 4+can be replaced by Al 3+ions,leading to the formation of negatively charged oxygen surfaces.This permanent negative charge is independent of pH value.Al 3+,K +,Na +ions may be dissolved out of the basal plane of aluminosilicates and contribute to the negative charge of the mineral surfaces.This dissolution processresults in negatively charged SiO 32−and AlO 2−groups left on thesurface.Furthermore,the ionization of the surface hydroxyl group gives rise to the charge on the surface of diaspore and aluminosilicate as:Al –OH ⇌Al –O −+H +and Si –OH ⇌Si –O −+H +.The extent of surface ionization is a function of the pulp pH value.Adsorption or dissociation of H +and OH −accounts for their surface charges.When collector OCB is introduced into the pulp in the pH range around 7,its polar group is mainly in the form of carboxyl anion (–COO −)and neutral hydroxamate group (–COCNHOH)or hydroaxamic anion (–CONHO −)since pKa 1of –COOH around 4.5and pKa 2of –CONHOH around 8.5.Therefore,there will be no electrostatic forces between OCB and mineral surfaces.However,around this pH value,better ﬂoatabilities of mineral are observed than those at otherpHFig. 2.Effect of OTB,OCB and OHB concentration on ﬂotation of diaspore and aluminosilicates (a)diaspore;(b)kaolinite;(c)illite.115Y.-R.Jiang et al./Hydrometallurgy 104(2010)112–118value,especially for diaspore nearly getting to 100%recovery,indicating that OCB around this pH value should be adsorbed on the surfaces of minerals by other force such as chemical bond or hydrogen bond.Analyzed from the polar group of OCB at pH value around 7,on one hand,the N NH and –OH in the –CONHOH group act as donator of hydrogen bond,and ≡Al –O −and (or)≡Si –O −on the mineral surface act as receptor.Accordingly,when OCB contacts with the particles of minerals,hydrogen bond may take place between the above groups ofOCB and minerals (kaolinite,illite and diaspore);On the other hand,as the polar group of OCB,the oxygen atoms of N C O and –OH in –COOH group,the oxygen atoms of N C O and –NHOH in –CONHOH group all have lone-pair electrons.Since the negative value of net charge of these oxygen atoms is relatively high and aluminum atoms on the mineral surface is absent of electrons,those oxygen atoms in OCB act as Lewis base and may form covalent bond with aluminum atom (acting as Lewis acid)on the mineral surface.OCB possessed poor collecting capacity to aluminosilicates and very highcollectingFig. 3.Relationship between zeta potential and pulp pH with or without OCB (a)diaspore;(b)kaolinite;(c)illite.Fig. 4.FT-IR spectra of diaspore and aluminosilicates with and without collector (a)diaspore;(b)kaolinite;(c)illite.116Y.-R.Jiang et al./Hydrometallurgy 104(2010)112–118capacity to diaspore.These evidences indicate that the adsorption of OCB on aluminosilicates (either kaolinite or illite)is hydrogen bond while the adsorption of OCB on diaspore surface is mainly chemical bond (perhaps including hydrogen bond).3.3.FT-IR spectra analysis of diaspore and aluminosilicates with or without carboxyl hydroxamic acidTo further investigate the interaction mechanism of carboxyl hydroxamic acid on minerals,OCB was also chosen for analyzing its in ﬂuence on the FT-IR spectra of diaspore,kaolinite,and illite.Fig.4presents the FT-IR spectra of diaspore,and aluminosilicates treated with or without OCB.For the IR spectra of free OCB,a broad band at center of 3448.13cm −1is assigned to the vibrating absorption of OH in the carboxyl and hydroxamate group with the strong hydrogen bond.The typical N –H stretching band appears at a medium band of 3000–3200cm −1,and a strong absorption at 1667.25cm −1is attributed to the C O vibration of the carboxyl and hydroxamate carboxyl group.For the IR spectra of the three minerals untreated with OCB,a band in 1984–1821cm −1of Al O or Si O stretching absorption were observed due to the relaxation and reconstruction of the planes,which are in great accordance with those reported in previous literatures (Hu et al.,2003b;Xia et al.,2009).When the three minerals treated with OCB,characteristic absorption peaks of OCB were not observed on these minerals surfaces except N C O absorption on diaspore,where such result is possibly caused by the concentration of OCB which is too low to be detected by the FT-IR spectrophotometer.However,it can be observed from Fig.4that OCB led the shift of absorption peaks of the minerals in many aspects.Observed from Fig.4a,diaspore is an amphoteric oxide mineral,so there are a wide stretching and vibrating absorption of OH at 2800and 3000cm −1.The bands of 2117.23cm −1and 1985.32cm −1are the inside and outside swing absorption of OH,962.37cm −1and 1066.72cm −1are the inside and outside bending and vibrating absorption of OH,and 747.01cm −1is the stretching and vibrating absorption of Al –O.When diaspore is treated with OCB,absorption of C O at 1667.25cm −1in OCB redshifts to 1656.90cm −1with thedecreased intensity;the stretching and vibrating peak of Al –O in diaspore at 747.01cm −1blueshifts to 766.24cm −1with the decreased intensity.These results illustrate that probably there are chemical bonds between diaspore and the collector;and such results are con ﬁrmed by and in agreement with the result of zeta potential mentioned above.Seen from Fig.4b,the weak absorption at 1633.80cm −1in the spectrum of kaolinite attributing to the bending mode of H –O –H indicates the existence of little free water (Zhao et al.,2003c;Guan et al.,2009).After conditioned by OCB,spectrum of kaolinite exhibits a peak at 1636.80cm −1.This may be caused by the formation of the N –H ⋯O hydrogen bond between the group of NHOH in OCB and the oxygen of kaolinite surface (Liu et al.,2007);therefore,the N –H bond is enhanced and leads the absorption shift to a higher wavenumber and intensity.In Fig.4c,similar to kaolinite,after treated with OCB the absorption of 1637.72cm −1in illite shifts to a higher wavenumber of 1639.31cm −1with higher intensity,so,the hydrogen bond is also formed for illite.This result is also con ﬁrmed by an agreement with the result of zeta potential mentioned above.To summarize,the adsorption between OCB and diaspore is mainly by means of chemical bonding while for kaolinite and illite is through hydrogen bond.3.4.Interaction mode of carboxyl hydroxamic acid on mineral surface In the polar groups of the synthesized collectors,–OH of the carboxyl group and –NHOH of the hydroxamate group may dissociate to oxygen anions possessing strong coordination capacity for the formation of covalent bonds to aluminum atom on diaspore surface.Additionally,the oxygen atom of N C O in the carboxyl group –COOH,the oxygen atom of N C O in the hydroxamate group all have lone-pair electron whose negative value of net charge is relatively high,which presents that these atoms all have the possibility of bonding with diaspore.Meanwhile,these atoms have the natural conditions to form ﬁve to seven numbered bined with the analysis of zeta potential and IR spectra as well as the facts of ﬂotation experiments,the interaction mechanism of the synthesized collectors anddiasporeFig.5.The suggested interaction mode of carboxyl hydroxamic acid on mineral surface (a)carboxyl hydroxamic acid on diaspore surface through chemical bonding;(b)carboxyl hydroxamic acid on aluminosilicates surface through hydrogen bond.117Y.-R.Jiang et al./Hydrometallurgy 104(2010)112–118。

The Delta(1232) at RHIC

a r X i v :n u c l -t h /0409026v 3 26 J a n 2005The ∆(1232)at RHICHendrik van Hees †and Ralf RappCyclotron Institute and Physics Department,Texas A&M University,CollegeStation,Texas 77843-3366E-mail:hees@,rapp@Abstract.We investigate properties of the ∆(1232)and nucleon spectral functions at ﬁnite temperature and baryon density within a hadronic model.The medium modiﬁcations of the ∆consist of a renormalization of its pion-nucleon cloud and resonant π∆scattering.Underlying coupling constants and form factors are determined by the elastic πN scattering phase shift in the isobar channel,as well as empirical partial decay widths of excited baryon resonances.For cold nuclear matter the model provides reasonable agreement with photoabsorption data on nuclei in the ∆-resonance region.In hot hadronic matter typical for late stages of central Au -Au collisions at RHIC we ﬁnd the ∆-spectral function to be broadened by ∼65MeV together with a slight upward mass shift of 5-10MeV,in qualitative agreement with preliminary data from the STAR collaboration.PACS numbers:25.75.-q,21.65.+f,12.40.-y 1.Introduction At low energies,the main features of Quantum Chromodynamics (QCD)are conﬁnement and the spontaneous breaking of chiral symmetry.The former implies that we onlyobserve hadrons (rather than quarks and gluons),while the latter is believed to govern the (low-lying)hadron-mass ttice-QCD calculations predict a phase transition from nuclear/hadronic matter to a deconﬁned,chirally symmetric state [1]at temperatures T ≃150-200MeV,dictating a major reshaping of the hadronic spectrum in terms of degenerate chiral partners.The observation of such medium modiﬁcations is therefore an important objective in relativistic heavy-ion collision rge theoretical eﬀorts have been devoted to evaluate in-medium properties of vector mesons which are accessible experimentally through dilepton invariant-mass spectra [2].In most of these studies,baryon-driven eﬀects are essential to account for the dilepton enhancement observed in P b -Au collisions at the SPS below the free ρmass [3,4].Thus,changes in the baryon properties themselves deserve further investigation.In addition,recent measurements of πN invariant-mass spectra in nuclear collisions [5,6,7]may open a more direct window on modiﬁcations of the ∆(1232).†presenting authorTo date,in-medium properties of the∆have mostly been assessed in cold nuclear matter[8,9,10,11,12,13],with few exceptions[14,15].In this article we will discuss properties of the nucleon and the∆(1232)in a hot and dense medium[16],employing a ﬁnite-temperatureﬁeld theory framework based on hadronic interactions.Both direct interactions of the∆with thermal pions as well as modiﬁcations of its freeπN self-energy(incuding vertex corrections)will be accounted for.The article is organised as follows.In Sec.2we introduce the hadronic Lagrangian and outline how its parameters are determined using scattering and decay data in vacuum.In Sec.3we compute in-medium self-energies for nucleon and∆.In Sec.4we ﬁrst check our model against photoabsorption cross sections on the nucleon and nuclei, followed by a discussion of the spectral functions under conditions expected to occur in high-energy heavy-ion collisions.We close with a summary and outlook.2.Hadronic Interaction Lagrangians in VacuumThe basic element of our analysis are3-point interaction vertices involving a pion and two baryons,πB1B2.Baryonﬁelds are treated using relativistic kinematics, E2B(p)=m2B+p2,but neglecting anti-particle contributions and restricting Rarita-Schwinger spinors to their non-relativistic spin-3/2components.Pions are treated fully relativisticly(ω2π(k)=m2π+k2).The resulting interaction Lagrangians are thus of the usual nonrelativistic form involving(iso-)spin-1/2Pauli matrices,1/2to3/2transition operators,as well as spin-3/2matrices[9,17,18,19,20],see Ref.[16]for explicit expressions.To simulateﬁnite-size eﬀects we employed hadronic form factors with auniform cutoﬀparameterΛπB1B2=500MeV(except forπNN andπN∆vertices).The imaginary part of the vacuum self-energy for the∆→Nπdecay takes the formImΣ(Nπ)∆(M)=−f2πN∆MF2(k cm)Θ(M−m N−mπ)(1)with k cm the center-of-mass decay momentum(an extra factor m N/E N(k cm)has been introduced in Eq.(1)to restore Lorentz-invariance),and the real part is determined via a dispersion relation.With a bare mass of m(0)∆=1302MeV,a form-factor cutoﬀΛπN∆=290MeV and a coupling constant fπN∆=3.2we obtain a satisfactoryﬁt to the experimentalδ33-phase shift[21,15,22].To account for resonant interactions of the∆with pions we identiﬁed the relevant excited baryons via their decay branchings B→π∆.The pertinent coupling constants have been determined assuming the lowest partial wave to be dominant(unless otherwise speciﬁed)[23],using pole masses and(total)widths of the resonances.The same procedure has been adopted for resonantπN interactions(which are used to evaluate ﬁnite-temperature eﬀects on the nucleon).The resonances included are N(1440), N(1520),N(1535),∆(1600),∆(1620)and∆(1700).The total widthsﬁguring into the resonance propagators have been obtained by scaling up the partialπN andπ∆channels,and vacuum renormalizations of the masses have been neglected.Figure 1.Diagrammatic representation ofπN∆vertex corrections(dashed lines:pion,solid lines:nucleon,double solid lines:∆(1232));a bubble with labelαcorresponds to a Lindhard functionΠα(α∈{1,2})attached to baryon lines withpertinent Migdal parameters,i.e.,g′12forα=1and g′22forα=2.Finally,the evaluation of the photoabsorption cross section requires aγN∆vertex for which we employ the magnetic coupling[10]LγN∆=−fγN∆3m2π d4lE N(l)k2F2π(|k|)(3)×{[Θ(k0)+σ(k0)fπ(|k0|)]Aπ(k)G N(l)−f N(l0)A N(l)Gπ(k)}, where k=p−l is the pion4-momentum.The thermal distributions are deﬁned by f N(l0)=f fermi(l0−µN,T)and fπ(|k0|)=f bose(|k0|,T)exp(µπ/T),with f fermi and f bose the Fermi and Bose functions,respectively.For simplicity,ﬁnite pion-chemical potentials,µπ>0,are treated in the Boltzmann limit to avoid Bose singularities in the presence of broad pion spectral functions(a more detailed discussion of this point will be given elsewhere).In Eq.(3)positive energies k0>0correspond to outgoing pions,i.e.,∆→πN decays,while k0<0accounts for scattering with(incoming)pions from the heat bath.The key quantities in Eq.(3)are the in-medium pion and nucleon propagators, Gπand G N,and pertinent spectral functions A N=−2Im G N and Aπ=−2Im Gπ.The modiﬁcations of the pion propagator are implemetend via a self-energy,arising from two parts:(i)interactions with thermal pions modeled by a four-point interaction in second order(“sunset diagram”)[24],with a coupling constant adjusted to qualitatively reproduce the results of more elaborateππinteractions in s,p,and d-wave[25]; (ii)interactions with baryons via p-wave nucleon-and∆-hole excitations atﬁnite temperature,described by standard Lindhard functions,supplemented by short-range correlations encoded in Migdal parameters[26](our default values are g′NN=0.8, g′N∆=g′∆∆=0.33).These excitations induce a softening of the pion-dispersion relation which can even lead to a(near)vanishing of the pion group velocity atﬁnite momentum, inducing an artiﬁcial threshold enhancement in the∆self-energy[14].This feature isk γ[GeV]σγ/Ak γ[GeV]σγ/A [µb ]Figure 2.Photoabsorption cross sections on nucleons (left panel,data from [29])andnuclei (right panel;data from [30,31,32,33,34,35]).remedied by accounting for appropriate vertex corrections,which in the case of ρ→ππdecays are required to maintain a conserved vector current in the medium [27,28].Here we apply the same technique to the πN ∆vertex,cf.Fig.1.The nucleon self-energy is calculated in terms of resonant interactions with thermal pions,at the same level of approximation as the pion Lindhard functions (i.e.,neglecting oﬀenergy-shell dependencies in the spectral functions of the excited baryons).The second contribution to the in-medium ∆self-energy consists of resonant π∆→B interactions,corresponding to the ﬁnite-temperature part of πB loops.The resulting self-energy expressions are similar to Eq.(3)but with only the scattering part (k 0<0)retained (note that this is consistent with our description of the ∆(1232)in vacuum where πB loops are not included).4.In-medium Spectral Properties of the ∆4.1.Photoabsorption on Nucleons and NucleiValuable constraints on the ∆spectral function in cold nuclear matter can be obtained from photoabsorption cross sections on nuclei.To leading order in αem ,the latter can be related to the photon self-energy (electromagnetic current correlator),Πγ,by [18]σabs γA k 12ImΠγ(k 0=k ),Πγ=1M N [GeV]-I m G N [G e V -1]k 0 [GeV]-I m G π [G e V -2]Figure 3.Left panel:nucleon spectral function at RHIC (solid line T =180MeV,̺N =0.68̺0;dashed line:T =100MeV,̺N =0.12̺0).Right panel:pion spectralfunction for cold nuclear matter (dashed line:T =0,̺N =0.68̺0)and at RHIC (solidline:T =180MeV,̺N =0.68̺0);the dash-dotted line corresponds to switching oﬀbaryonic eﬀects leaving only the 4-point interactions with thermal pions.Migdal parameters or the nuclear density is very moderate.Given our rather simple approach for the cross section,the agreement with data is fair.The discrepancies at low energy (which seem to be present already for the nucleon)could be due to interference with the background,collective eﬀects involving direct NN −1-excitations,or transverse contributions with in-medium ρmesons in the vertex corrections of the ∆decay.At higher energies,further resonances in the photon self-energy need to be included.4.2.Hot Hadronic MatterLet us ﬁnally turn to the results for hot hadronic matter.In heavy-ion collisions one expects a hierarchy of chemical freeze-out (determining the ratios of stable hadrons)and thermal freeze-out (where elastic rescattering ceases).The former is characterized by a temperature T chem and a common baryon chemical potential µB .Thermal freezeout occurs at lower T fo ≃100MeV,which requires the build-up of additional chemical potentials for pions,kaons,etc.[36],to conserve the observed hadron ratios,including relative chemical equilibrium for elastic processes,e.g.πN ↔∆implying µ∆=µN +µπ.Under RHIC conditions the nucleon spectral function exhibits an appreciable broadening and a moderate downward mass shift (left panel of Fig.3)due to resonant scattering oﬀthermal pions.The pion spectral function (right panel of Fig.3)is strongly broadened mostly due to scattering oﬀbaryons,with little mass shift.Thermal motion completely washes out the multi-level structure visible at zero temperature (dashed line).Also for the ∆spectral function (left panel in Fig.4)the main eﬀect is a broadening with a slight repulsive mass shift.Half of the increase of the in-medium width is due to baryon-resonance excitations (slightly enhanced due to in-medium pion propagators),adding to the contribution of the πN loop.In the real part,however,the predominantly repulsive contributions from baryon resonances are counterbalanced by net attraction in the πN loop (mostly due to the pion-Bose factor).At thermal freeze-out we ﬁnd1 1.1 1.2 1.3 1.4 1.5 1.6M ∆ [GeV]0510152025-I m G ∆ [G e V -1]vacuum T=100 MeV T=180 MeV 1 1.1 1.2 1.3 1.4 1.5 1.6M ∆ [GeV]0510152025-I m G ∆ [G e V -1]vacuum T=70 MeV T=160 MeV Figure 4.In-medium ∆(1232)spectral functions in heavy-ion collisions compared tofree space (dash-dotted lines);left panel:RHIC;dashed line:T =100MeV,̺N =0.12̺0(µN =531MeV),µπ=96MeV;solid line:T =180MeV,̺N =0.68̺0(µN =333MeV),µπ=0.Right:future GSI facility;dashed line:T =70MeV,̺N =0.19̺0(µN =727MeV),µπ=105MeV;solid line:T =160MeV,̺N =1.80̺0(µN =593MeV),µπ=0.a peak position at about M ≃1.226GeV and a width Γ≃177MeV,to be compared to the corresponding vacuum values of M ≃1.219GeV and Γ≃110MeV,in qualitative agreement with preliminary data from STAR [7].For more conclusive comparison a detailed treatment of the freeze-out dynamics is mandatory.In the vicinity of T c ,the ∆width increases substantially.We expect this trend to be further magniﬁed when including transverse parts in the vertex corrections,especially in combination with in-medium ρ-mesons [2].In the right panel of Fig.4we show the ∆-spectral function in a net-baryon rich medium,representative for the future GSI facility.Whereas in dilute matter the line shape is only little aﬀected,the resonance structure has essentially melted close to T c ,mostly due to a strong renormalization of the pion propagator at high density.5.Conclusions and outlookBased on hadronic interaction Lagrangians employed within a ﬁnite-temperature many-body approach we have evaluated medium eﬀects on pions,nucleons and deltas.The resulting ∆-spectral functions in cold nuclear matter provide fair agreement with photoabsorption data on nuclei.In hot hadronic matter,we found a signiﬁcant broadening and a slight upward peak shift of the ∆resonance,qualitatively in line with preliminary measurements of πN invariant-mass spectra at RHIC.Future improvements of the πN ∆system in vacuum include u -channel exchange diagrams as well as spin-3/2-∆∗excitations which we expect to increase the rather low form-factor cut-oﬀused so far.We further plan to implement in-medium baryon propagators into the description of axial-/vector mesons within a chiral framework to arrive at a more consistent picture of the equation of state of hadronic matter under extreme conditions [37]and the chiralphase transition.Another interesting ramiﬁcation[38]concerns the role of the medium-modiﬁed∆spectral functions in the soft photon enhancement as recently observed at the SPS[39].AcknowledgmentsOne of us(HvH)acknowledges support from the Alexander-von-Humboldt Foundation as a Feodor-Lynen Fellow.References[1]Karsch F2002Lect.Notes Phys.583209[2]Rapp R and Wambach J2000Adv.Nucl.Phys.251[3]Agakishiev G et al.(CERES/NA45)1998Phys.Lett.B422405[4]Adamova D et al.(CERES/NA45)2003Phys.Rev.Lett.91042301[5]Hjort E L et al.1997Phys.Rev.Lett.794345[6]Pelte D et al.(FOPI)1997Z.Phys.A35955[7]Fachini P2004J.Phys.G30S735[8]Horikawa Y,Thies M and Lenz F1980Nucl.Phys.A345386[9]Oset E and Salcedo L L1987Nucl.Phys.A468631[10]Ericson T and Weise W1988Pions and Nuclei(Clarendon Press,Oxford)[11]Migdal A B,Saperstein E E,Troitsky M A et al.1990Phys.Rept.192179[12]Xia L H,Siemens P J and Soyeur M1994Nucl.Phys.A578493[13]Korpa C L and Lutz M F M2004Nucl.Phys.A742305[14]Ko C M,Xia L H and Siemens P J1989Phys.Lett.B23116[15]Korpa C L and Malﬂiet R1995Phys.Rev.C522756[16]van Hees H and Rapp R2004Preprint nucl-th/0407050[17]Cubero M1990Ph.D.thesis TH Darmstadt[18]Rapp R,Urban M,Buballa M et al.1998Phys.Lett.B4171[19]Urban M,Buballa M,Rapp R et al.2000Nucl.Phys.A673357[20]Nacher J C,Oset E,Vicente M J et al.2001Nucl.Phys.A695295[21]Moniz E J1981Nucl.Phys.A354535c[22]Weinhold W,Friman B and N¨o renberg W1998Phys.Lett.B433236[23]Hagiwara K et al.2002Phys.Rev.D6601001[24]van Hees H and Knoll J2002Phys.Rev.D6*******[25]Rapp R and Wambach J1995Phys.Lett.B35150[26]Migdal A B1978Rev.Mod.Phys.50107[27]Chanfray G and Schuck P1993Nucl.Phys.A555329[28]Herrmann M,Friman B L and N¨o renberg W1993Nucl.Phys.A560411[29]Lepretre A et al.1978Phys.Lett.B7943[30]Ahrens J et al.1984Phys.Lett.B146303[31]Ahrens J1985Nucl.Phys.A446229c[32]Frommhold T et al.1992Phys.Lett.B29528[33]Frommhold T et al.1994Z.Phys.A350249[34]Bianchi N et al.1993Phys.Lett.B299219[35]Bianchi N et al.1996Phys.Rev.C541688[36]Rapp R2002Phys.Rev.C66017901[37]Voskresensky D N2004Preprint hep-ph/0402020[38]Rapp R2004Mod.Phys.Lett.A191717[39]Aggarwal M M et al.(WA98)2004Phys.Rev.Lett.93022301。

英语作文respect

Respect is a fundamental aspect of human interaction,signifying the acknowledgment of the intrinsic worth of individuals and their rights.It is a multifaceted concept that encompasses various dimensions,including respect for oneself,for others, and for societal norms and values.SelfRespect:Selfrespect is the cornerstone of personal integrity.It involves recognizing ones own worth and maintaining a positive selfimage.People with high selfrespect are confident in their abilities and decisions,and they are less likely to be swayed by the opinions of others.They understand the importance of selfcare and selfimprovement,striving to be the best version of themselves.Respect for Others:Respecting others involves treating people with dignity,regardless of their background, beliefs,or social status.It means listening to their opinions,valuing their contributions, and acknowledging their feelings.In a respectful environment,individuals feel valued and appreciated,which fosters a sense of belonging and encourages open communication.Cultural Respect:Cultural respect is essential in our increasingly globalized world.It entails understanding and appreciating the diversity of cultures,traditions,and customs that exist around the globe.By respecting cultural differences,we can promote tolerance and reduce misunderstandings that may arise from ignorance or prejudice.Respect for the Environment:The environment is another aspect that requires our respect.This includes being mindful of our consumption habits,reducing waste,and supporting sustainable practices. Respecting the environment is crucial for preserving the planet for future generations.Professional Respect:In the workplace,respect is vital for maintaining a healthy and productive atmosphere.It involves recognizing the expertise and contributions of colleagues,providing constructive feedback,and promoting a culture of collaboration and mutual support.Respecting Boundaries:Understanding and respecting personal boundaries is an important part of any relationship.This means being aware of the emotional and physical space that others need and not infringing upon it without consent.Teaching Respect:Teaching respect starts from a young age.Parents and educators play a crucial role in instilling the values of respect in children.This can be done through modeling respectful behavior,teaching empathy,and encouraging open discussions about the importance of respect.Consequences of Disrespect:Disrespect can lead to various negative consequences,including damaged relationships, social isolation,and a toxic environment.It can also result in a loss of trust and respect from others.Promoting Respect:Promoting respect is a collective responsibility.It requires individuals,communities,and institutions to actively work towards creating a culture of respect.This can be achieved through education,awareness campaigns,and by setting and enforcing standards of respectful behavior.In conclusion,respect is a vital component of a harmonious society.It is not just about politeness or good manners it is about recognizing the inherent value in every individual and treating them accordingly.By fostering a culture of respect,we can build stronger relationships,create more inclusive communities,and contribute to a more peaceful and understanding world.。

Dispersion relation of the $rho$ meson in hotdense nuclear matter

a r X i v :n u c l -t h /0209043v 4 31 J u l 2003Dispersion relation of the ρmeson in hot and dense nuclear matterJi-sheng Chen a Jia-rong Li b Peng-fei Zhuang aaPhysics Department,Tsinghua University,Beijing 100084,People’s Republic of ChinabInstitute of Particle Physics,Hua-Zhong Normal University,Wuhan 430079,People’s Republic of China The dispersion relation of ρmeson in both timelike and spacelike regimes in hot and dense nuclear medium is analyzed and compared with σmeson based on the quantum hadrodynamics model.The pole and screening masses of ρand σare discussed.The behavior of screening mass of ρis diﬀerent from that of σdue to diﬀerent Dirac-and Fermi-sea contributions at ﬁnite temperature and density.PACS numbers:14.40.Cs,11.55.Fv,11.10.WxHeavy-ion collision physics has stimulated intense in-vestigations of the properties of strongly interacting,hot and dense nuclear matter[1].Among the proposed sig-nals for detecting quark-hadron phase transition,dilep-tons and photons are considered to be the clearest ones because they can penetrate the medium almost undis-turbed and reﬂect the property of the ﬁreball formed in the initial stage of collisions[2].Furthermore,the dilep-tons from the decay of light vector mesons can be con-sidered as possible signals of the partial chiral symme-try restoration.Especially,the property of ρin hot and dense environment has attracted much attention in the literature due to its relatively larger decay width com-pared with ωand φ[3,4,5].It is interesting that the ρmass decreasing mechanism can be used to explain the low invariant mass dilepton enhancement in central A −A collisions observed by CERES-NA45[6,7,8].From the point of view of many-body theory,the col-lective eﬀect of medium on a meson is reﬂected by its full propagator,which determines its dispersion relation as well as the response to the external source[9,10,11].Due to the broken Lorentz symmetry,the dispersion relations for longitudinal and transverse modes of vector mesons are diﬀerent.However,the timelike and spacelike regimes are related to each other through the dispersion relation as in the case of QED[12].With vector meson dominance model,the ρmeson screening mass is an important quan-tity related to the EM (electromagnetic)Debye mass and to the emissivity of dileptons and photons produced in heavy-ion collisions.For example,the screening mass in spacelike limit is associated with the isospin ﬂuctua-tions which can be used as a potential signature of QGP (quark-gluon plasma)formation[13].Furthermore,the scalar quark density ﬂuctuation of QCD is related to the spacelike limit of in-medium self-energy of σas pointed out in Ref.[14],where the contribution of free nucleons at T =0is analyzed through one-loop NN −1excitation.In Refs.[15,16],it was found that the Dirac-sea contri-bution to the pole mass of ρdominates over Fermi sea’s.In this paper,we discuss the dispersion relations of ρand σin both spacelike and timelike regimes determined by the pole positions of their in-medium propagators.The medium eﬀects on ρand σat ﬁnite temperature T and baryon density ρB are taken into account in the frame-work of quantum hadrodynamics model(QHD)throughthe in-medium nucleon excitation.We start from QHD-I to obtain the eﬀective nucleonmass M ∗N and eﬀective chemical potential µ∗for dis-cussing the in-medium meson property.In the relativistic Hartree approximation,the self-consistent equations for M ∗N and µ∗can be written as [16,17]M ∗N −M N =−g 2σ(2π)3d 3pM ∗Nm 2σ1M N−M 2N (M ∗N −M N )−56(M ∗N −M N )3,(1)µ∗−µ=−g 2ωρB /m 2ω,(2)where ω=(2π)3d 3p [n B −¯n B ],(3)with n B (¯n B )being the Fermi-Dirac distribution func-tions for (anti-)baryons,respectively.The coupled equa-tions can be solved numerically with the parameters de-termined by ﬁtting the binding energy at normal nucleardensity ρ0given in Table.I.The M ∗N decreases with in-creasing density ρB at ﬁxed temperature(see Fig.1),anal-ogously to the result of mean ﬁeld theory neglecting the vacuum ﬂuctuations[16].The eﬀective chemical potential µ∗will aﬀect the properties of mesons indirectly through the distribution functions.In Minkowski space,the polarization tensor Πµν(k )of ρcan be divided into two parts with the standard pro-jection tensors P µνL and P µνT according toΠµν(k )=ΠL (k )P µνL +ΠT (k )P µνT(4)withΠL (k )=k 22P ijT Πij (k ).(5)With the eﬀective Lagrangian for ρNN interactions[18]L ρNN =g ρNN¯Ψγµτa ΨV µa −κρ2where V µa is the ρmeson ﬁeld and Ψthe nucleon ﬁeld,the polarization tensor is given in random phase approx-imation (RPA)byΠµν(k )=2g 2ρNN Tp 0d 3pp /−M ∗NΓν(−k )1(2π)3Tr1(p /−k /)−M ∗N,0.511.522.5ΡB Ρo0.40.60.811.21.4m mT 100MeVLN ΡTΣΣsFIG.1:Eﬀective masses as functions of scaled density attemperature T =100MeV.The solid line represents the ef-fective nucleon mass(labeled as N ).The dotted lines are for pole masses(ρand σ,respectively),dot-dashed for transverse screening mass (T ).The dashed lines indicate the longitu-dinal screening mass(L )of ρand screening mass(σs )of σ,respectively.which can be reduced toΠσ(k )=3g 2σM 2Ndx−1(M 2N −x (1−x )k 2)lnM ∗2N −x (1−x )k 2π2p 2dp4p |k |(a +b ),(9)where a =lnk 2−2p |k |−2k 0ωk 2+2p |k |+2k 0ωwith k 2=k 20−k 2.It is neccesary to note again that here we discuss the full propagator D σwith the in-medium nucleons.The eﬀective masses of σmeson deﬁned anal-ogously to those of ρare also displayed in Fig.1.The pole masses m ∗ρ,M ∗N and m ∗σvenus ρB at ﬁxed T behave very diﬀerently.The eﬀective nucleon mass de-creases monotonously with increasing density,while the eﬀective pole mass of ρdecreases at ﬁrst and then be-comes saturated.The pole mass m ∗σalso decreases in the low density region.As for the screening mass behavior,the longitudinal and transverse Debye ones of ρdecrease,but the one of σincreases with increasing density.The corresponding dispersion relation curves calcu-lated from the pole position of the full propagator D µνin both timelike and spacelike regions for ρare shown in the upper panel of Fig.2.Due to the tensor(magnetic)cou-pling and the relatively smaller coupling constant g ρNN compared with ωmeson,the invariant in-medium mass M ρ=3-0.4-0.20.20.40.60.81i K GeV Screening Propagation K GeV0.20.40.60.81k 0 G e VT 100MeV,ΡB Ρ0 1.0aM Ρ00.10.20.30.40.50.60.7K GeV-0.20.20.40.60.80,k G e V 2T 100MeV,ΡB Ρ0 1.0bLTΣFIG.2:(a)Dispersion relation curves for ρ.The solid line corresponds to L mode,dot-dashed to T mode and long-dashed to invariant mass M ρ=54.289102.770458783 2.63 6.1770939Acknowledgments This work was supported by the NSFC under Grant Nos 10135030,10175026,19925519and the China Postdoc Research Fund.APPENDIX AThe ingredients of ΠµνD with the similar expressions of a and b in (9)areΠ00D (k )=Π001D +Π002D +Π003D ,Π001D=−2g ρNNω(n B +¯n B )4+k 2−4ωk 0+4ω22π2kρω(n B +¯n B )(a +b ),Π003D=2gρNN2M N2p 2dp2p |k |a +(ω→−ω);Π0iD (k )=k 0k ik 2,A 1=gρNNω(n B +¯n B )4(k 2+k 20)2p |k |3a −(ω→−ω),A 2=k 22π 2 kρω(n B +¯n B )4k 22p |k |3a +(ω→−ω) ,B 1=gρNNω(n B +¯n B )−4(k 2+3k 20)2p |k |3a+(ω→−ω)],B 2=Π002D ,4 B3= gρNN2M N 2 p2dp k2k2(2k40+k4)+4k0k2(2k20+k2)ω−4(2k2+k2)k2p2+4(2k40−k20k2+2k4)ω2+。

高二英语哲学观点探讨单选题30题

高二英语哲学观点探讨单选题30题1. Which of the following statements best represents the idea of Plato's Theory of Forms?A. The physical world is the ultimate reality.B. Ideas are mere copies of the real world.C. Forms exist independently of the material world.D. Sensory experiences are the source of true knowledge.答案：C。

解析：柏拉图的理念论认为形式是独立于物质世界存在的，A 选项认为物质世界是终极现实，与柏拉图理念论不符；B 选项说理念是现实世界的副本不准确；D 选项认为感官经验是真正知识的来源，这不是柏拉图的观点。

2. According to Aristotle, what is the source of knowledge?A. IntuitionB. ExperienceC. Reason aloneD. Divine inspiration答案：B。

解析：亚里士多德认为知识的来源是经验，A 选项直觉不是亚里士多德强调的知识来源；C 选项仅靠理性不符合亚里士多德的观点；D 选项神的启示也不是亚里士多德的主张。

3. Which philosopher believed that "Cogito, ergo sum" (I think, therefore I am)?A. DescartesB. KantC. HegelD. Nietzsche答案：A。

解析：“我思故我在”是笛卡尔的观点，康德、黑格尔和尼采都没有提出这一观点。

4. What is the main idea of Hume's philosophy regarding cause and effect?A. There is a necessary connection between cause and effect.B. Cause and effect are based on human understanding.C. Cause and effect are determined by divine intervention.D. We can never truly know the cause of an event.答案：B。

水相识别分子印迹技术

收稿:2006年7月,收修改稿:2006年8月　3通讯联系人　e 2mail :chemxuzl @水相识别分子印迹技术王学军　许振良3　杨座国　邴乃慈(华东理工大学化学工程研究所膜科学与工程研发中心　上海200237)摘　要　在各种基于超分子方法的仿生识别体系中,分子印迹聚合物已经证明是一种有潜力的合成受体,受到了广泛的关注。

传统的分子印迹技术通常是在有机溶剂中制备对小分子具有选择性的印迹聚合物,而在水相中制备及识别生物大分子的研究仍具有相当的挑战性。

从小分子到生物大分子、从有机相到水相,反映了分子印迹技术的发展趋势。

本文对最近几年分子印迹在水相制备与识别方面的最新进展进行了总结与评述,探讨了水相识别印迹聚合物的设计策略与制备方法;着重介绍了水相识别技术在固相萃取、色谱固定相、药物控释、中药有效成分提取以及生物分子识别等方面的应用;指出了提高水相识别选择性的途径并对其将来的发展进行了建议与展望。

关键词　分子印迹　水相识别　分子印迹聚合物　分子印迹膜中图分类号:O65812　文献标识码:A 文章编号:10052281X (2007)0520805208Molecular R ecognition in Aqueous Media with Molecular Imprinting TechniqueWang Xuejun Xu 3　Yang Zuoguo Bing Naici(Membr hane Science and Engineering R&D Center ,Chemical Engineering Research Center ,East China University of Science and T echnology ,Shanghai 200237,China )Abstract Am ong the variety of biomimetic recognition systems based on supram olecular approaches ,m olecularly im printed polymers (MIPs )have proved potential as synthetic receptors and received m ore and m ore attention.C onventional m olecular im printing technology allows the synthesis in organic s olvents of m olecularly im printed polymers selective toward relatively low m olecular weight com pounds.H owever ,synthesis in aqueous media of chemically and mechanically stable MIPs that can recognize biom olecules still is a great challenge.From small m olecules to biomacrom olecules,from organic phase to aqueous media ,the application field expands with the development of m olecular im printing technique.The recent progress in preparation and recognition of m olecularly im printed polymers in aqueous phase are overviewed and discussed.The design strategy and preparation methods of aqueous MIPs are investigated.The em phasis is put on the applications of aqueous recognition in the fields of s olid phase extraction ,chromatographic stationary phases ,drug delivery and controlled release ,separation of active ingredients from herbs and recognition of biom olecules.The methods to im prove the selectivities of MIPs in aqueous recognition are presented ,and the challenges ,as well as the suggestions to the development of m olecular im printing technique are outlined.K ey w ords m olecular im printing ;recognition in aqueous media ;m olecularly im printed polymers ;m olecularly im printed membrane1　引言分子印迹技术是将材料科学、生物化学和化学工程等学科有机结合在一起,为获得在空间结构和结合位点上与模板分子完美匹配的聚合物(分子印迹聚合物,MIP )的一种新型功能材料制备技术。

Peierls Distortion in Two-Dimensional Tight-Binding Model

a rX iv:c ond-ma t/14423v1[c ond-m at.m trl-sci ]23A pr 21typeset using JPSJ.sty <ver.0.7e >Peierls Distortion in Two-Dimensional Tight-Binding Model Yoshiyuki Ono ∗and Tetsuya Hamano ∗∗Department of Physics,Toho University,Miyama 2-2-1,Funabashi,Chiba 274-8510(Received January 26,2000)The Peierls distortions in a two-dimensional electron-lattice system described by a Su-Schrieﬀer-Heeger type model extended to two-dimensions are numerically studied for a square lattice.The electronic band is just half-ﬁlled and the nesting vector is (π/a ,π/a )with a the lattice constant.In contrast to the previous understanding on the Peierls transition in two dimensions,the distortions which are determined so as to minimize the total energy of the system involve not only the Fourier component with the nesting wave vector but also many other components with wave vectors parallel to the nesting vector.It is found that such unusual distortions contribute to the formation of gap in the electronic energy spectrum by indirectly (in the sense of second order perturbation)connecting two states having wave vectors diﬀering by the nesting vector from each other.Analyses for diﬀerent system sizes and for diﬀerent electron-lattice coupling constants indicate that the existence of such distortions is not a numerical artifact.It is shown that the gap of the electronic energy spectrum is ﬁnite everywhere over the Fermi surface.KEYWORDS:Peierls transition,two-dimensional electron-lattice systems,nesting,Peierls gap,Peierls distortion,second order perturbation §1.Introduction The Peierls transition is caused by the freezing of a lattice distortion mode which can connect degenerate electronic states at the Fermi level.1)The presence of such a distortion induces an energy gap at the Fermi level of the electronic spectrum.This gap which iscalled Peierls gap lowers the electronic energy.In some cases,this reduction of energy overcomes the increase of the lattice energy due to the frozen mode.In one-dimensionalsystems,particularly,the lowering of the electronic energy is proportional to the square times logarithm of the frozen mode amplitude and therefore can overcome the lattice energy increase which is proportional to the square of the amplitude.Because of the competition between the decrease of the electronic energy and the increase of the lattice energy,there exists a value of the frozen mode amplitude minimizing the total energy of the electron-lattice system.In dimensions higher than one,the situation is not so simple.This is because the number of states at the Fermi level is only two in the case of a one-dimensional system,whereas those in two-or three-dimensional systems form equi-energy line or surface,respectively.In general,a single mode of the lattice distortion can connect only two points in the Fermi surface(or line). In this situation,the gain in the electronic energy is too small to overcome the increase of the lattice energy.However,in some special situation where a single lattice distortion mode can connect many states at the Fermi level,the electronic energy is lowered substantially and the Peierls transition becomes possible.This situation is known as“nesting”.The simplest case can be seen in the two-dimensional square lattice tight-binding model with a half-ﬁlled electronic band.In this case,the Fermi line is a square within theﬁrst Brillouin zone combining four points,(π/a,0),(0,π/a),(−π/a,0)and(0,−π/a),with a the lattice constant.The nesting vector of this system is Q=(π/a,π/a);Fig.1.The asymmetric lines represent shorter bonds,and the other in the perpendicular direction in thiswill propose in§4a new method toﬁnd the lowest energy state,which can reduce a single 2D problem essentially to many1D problems.The last section is devoted to summary and discussion.§2.Model and Basic FormulationThe model Hamiltonian treated in this paper is the following SSH-type Hamiltonian ex-tended to two dimensions,H=− i,j,s[(t0−αx i,j)(c†i+1,j,s c i,j,s+h.c.)+(t0−αy i,j)(c†i,j+1,s c i,j,s+h.c.)]+Kpaper.If we assume the Peierls distortion having the nesting vector Q=(Q x,Q y)=(π/a,π/a) as done by Tang and Hirsch,3)the bond variables x i,j and y i,j can be expressed in the following form,x i,j=x0e i(Q x i+Q y j)a=(−1)i+j x0,(2.2)y i,j=y0e i(Q x i+Q y j)a=(−1)i+j y0,(2.3)where x0and y0are the amplitudes of the distortion to be determined to minimize the total energy of the system.In this situation the electronic part of the above Hamiltonian can be easily diagonalized by introducing the Fourier expansion of the electronicﬁeld operators as follows,c i,j=12(x20+y20),(2.5) where the sum over the wave vector k is restricted to the region satisfying the following two conditions,−πa(2.6)−πa(2.7)and E k is given byE k=directions can have lower energy than the symmetric dimerization realized when x0=y0=/0 (or equivalently x0=−y0).It is not diﬃcult to understand the reason if we see the expression of∆k for each case;in the asymmetric case,∆asymk=2αx0sin k x a,and in the symmetric case,∆sym k =4αx0sin[12(k x−k y)a].The gap on the Fermi surface does not vanishexcept for the points(0,π/a)and(π/a,0)in the case of the asymmetric dimerization.On the other hand the gap vanishes on the line k x−k y=π/a in the case of symmetric dimerization. We have conﬁrmed numerically that if weﬁx the ratio r=y0/x0(0≤r≤1)and minimize the total energy with respect to x0,then the minimum value of the energy is a monotonically increasing function of r and becomes the smallest at r=0.It is clear that the dimerization pattern shown in Fig.1can yield the lowest energy state as far as we consider only the distortion with the basic nesting vector Q.However,we should note that even in this asymmetric dimerization the gap vanishes at some special points on the Fermi surface.In general the Peierls gap is proportional to the matrix element of the electron-lattice coupling term in H between two electronic states with wave vectors k and k±Q.In the case of the SSH-type Hamiltonian as used in this paper,this matrix element is given by a linear combination of sin k x a and sin k y a.It vanishes at(π/a,0)and(0,π/a) irrespectively of the lattice dimerization pattern.This means that the degeneracy between (π/a,0)and(0,−π/a)[or between(0,π/a)and(−π/a,0)]cannot be removed within the ﬁrst order perturbation due to the lattice distortion with Q.We shall come back to this problem in§4.§3.Numerical StudyIn order to check whether the asymmetric dimerization pattern shown in Fig.1can yield the lowest energy state or whether there exist any diﬀerent dimerization patterns giving still lower energy,we have studied numerically the lowest energy state of the Hamiltonian eq.(2.1).Once we know the local values of x i,j’s and y i,j’s,the electronic wave functions {φν(i,j)}are calculated along with corresponding eigenenergies{εν}from the following Schr¨o dinger equation,ενφν(i,j)=−(t0−αx i,j)φν(i+1,j)−(t0−αx i−1,j)φν(i−1,j)−(t0−αy i,j)φν(i,j+1)−(t0−αy i,j−1)φν(i,j−1)].(3.1)Since the number of electrons isﬁxed,it is straightforward to obtain the electronic ground state energy for the given conﬁgurations of x i,j’s and y i,j’s.The bond length variables x i,j’s and y i,j’s are also involved in the lattice potential energy,and they are determined so as tominimize the total energy of the system.This condition yields the following self-consistent equations for these variables similarly as in one-dimensional cases,7,8)x i,j=−2αNK i′ ν′φν(i′+1,j)φν(i′,j),(3.2)y i,j=−2αNK j′ ν′φν(i,j′+1)φν(i,j′),(3.3)where the summation over the one particle statesνis restricted to the occupied ones in the electronic ground state;note that the spin degeneracy factor should be included.The second terms on the right hand sides are due to the periodic boundary conditions,which requireNi=1x i,j=0for arbitrary j andNj=1y i,j=0for arbitrary i.In most of the practical calculations we use typically the following values of parameters; t0=2.5eV,K=21.0eV/˚A2andα=4.0eV/˚A.These values are near to those for poly-acetylene.As is well known what is important in this type of electron-lattice systems is the dimensionless coupling constant deﬁned byλ=α2/Kt0.Aforementioned values of param-eters giveλ≃0.30.When we want to study the coupling constant dependence of various properties,only the value ofαis changed for simplicity.The set of self-consistent equations(3.1)to(3.3)can be solved numerically by iteration. First we give initial values for x i,j’s and y i,j’s,and then calculateφν(i,j)’s by a matrix diagonalization subroutine,the results of which are substituted into the right hand sides of eqs.(3.2)and(3.3).The resulting values of x i,j’s and y i,j’s are compared with the previous values.If the diﬀerence is not small,we proceed by replacing the initial values of x i,j’s and y i,j’s by new ones.This procedure is continued until the diﬀerence becomes negligibly small. We try three diﬀerent initial conﬁgurations.First one is the asymmetrically dimerized pattern as shown in Fig.1.If we start the iteration with the uniform dimerization as expressed by eqs.(2.2)and(2.3)by setting y0=0and giving an appropriate value of the order of10−2a for x0,we end up with the same pattern with a value of x0which minimizes the total energy of the system within that pattern.The second choice is the symmetrically dimerized pattern as given by eqs(2.2)and(2.3)with x0=y0=0.The third one is a random distortion;we give random values for the lattice displacement vectors{u(i,j)}with a relatively small amplitude of the order of10−2×a;many samples are studied in this treatment.The last two choices yield essentially the same result.The resulting distortion pattern is not described by eqs.(2.2)and(2.3).An example of Fourier analysis of thispattern is shown in Fig.2,where X(q x,q y)and Y(q x,q y)are deﬁned by1X(q x,q y)=N2 i,j y i,j exp[−i(q x i+q y j)a].(3.5) We have found that all the Fourier components with q x=q y vanish.9)d 5H >X(q d,q d)/a]× ,P >X(q d,q d)/a]L 5H >Y(q d,q d)/a]b ,P >Y(q d,q d)/a]Fig.2.The numerical minimization of the total energy.As for the vanish when q x=q y.The abscissa indicates q electron-lattice coupling constantαis equal to4.0eV/What is characteristic in these Fourier spectra is that the amplitudes[=In order to check whether this complicated state has a lower energy than the asymmetri-cally dimerized state as shown in Fig.1,we study the size dependence of the energy diﬀerence between the asymmetrically dimerized state(Fig.1)and the lowest energy state obtained by solving the self-consistent equations(3.1)to(3.3);the total energy of the former state is denoted by E A and the latter by E G,both of them being negative.The result is summarized in Fig.3,where the energy diﬀerence scaled by|E A|is plotted as a function of N−2,the in-verse of the total number of the lattice points,for two diﬀerent values ofα,other parameters beingﬁxed as mentioned before.Fig.3.The dimerized state and the lowest energy state abscissa is the inverse of the total number of the with the corresponding value of the0=2.5eV and K=21.0eV/˚A2). The continuous lines areﬁtting to quadratic polynomials.From Fig.3,we may safely conclude that the energy diﬀerence remainsﬁnite in the ther-modynamic limit,and that the lowest energy state obtained from the self-consistent equation has certainly a smaller energy than the asymmetrically dimerized state shown in Fig.1.§4.Peierls Gap due to Second Order ProcessIn this section we discuss why the single mode dimerization(Fig.1)is not the lowest energy state.The lowest energy state obtained numerically in the previous section involvesmulti-mode distortions.The Fourier analysis of the distortions indicates that the gap in the electronic spectrum is induced not only by theﬁrst order perturbation but also by the second order process.As discussed in§1,the Peierls gap in the electronic spectrum is formed usually by theﬁrst order process in which a state|k on the Fermi surface is coupled to another state|k±Q on the Fermi surface by the lattice distortion with a wave vector Q (the nesting vector).The consideration developed in§2indicates that the gap vanishes at special points on the Fermi surface,(π/a,0)and(0,π/a),by thisﬁrst order process because of the peculiar wave number dependence of the electron-lattice coupling term.This fact means that in order to get aﬁnite gap at those point we have to consider the second order process where at least two lattice distortion modes should be relevant.If two distortion modes with wave vectors q1and q2satisfying q1+q2=Q are involved in the second order process,there should appear matrix elements connecting one of the states |k or|k+Q and one of|k+q1 or|k+q2 ,where the former states are on the Fermi surface.This indicates in turn that the two states|k+q1 and|k+q2 which are not on the Fermi surface are mixed with the states|k and|k+Q on the Fermi surface and contribute to the formation of the gap at the Fermi surface.In such a situation it is natural to expect the creation of lattice distortions with wave vectors q1−q2,q2−q1,q1−q2+Q(=2q1) and q2−q1+Q(=2q2).In this way,many lattice distortion modes can be involved in the second order process.Based on the numerical results discussed in the previous section,we assume that,in the lowest energy state,only the lattice distortions with wave vectors parallel to Q are existing. Namely the bond variables x i,j and y i,j are assumed to be expressed in the form,x i,j=x0(−1)i+j+ 0<q<π/a[x q e i qa(i+j)+c.c.],(4.1)y i,j=y0(−1)i+j+ 0<q<π/a[y q e i qa(i+j)+c.c.].(4.2) By this assumption the lattice degree of freedom is reduced from N2to N−1;the uniform mode with q=0is excluded trivially.Then the original Hamiltonian can be written in the wave number representation as follows,H= k,sεk c†k,s c k,s+α k,s2i(x0sin k x a+y0sin k y a)c†k+Q,s c k,s+α 0<q<π/a k,s2 e−i qa/2 x q cos k x+qa c†k+q,s c k,s2+e i qa/2 x∗q cos k x−qa c†k−q,s c k,s2K+N2a2 +y q cos k y−qa2+y∗q cos k y+qconsistent equations for these variables are written in the following form,x0=−2iαKN2 ν′ksin k y aψ∗ν(k x+π/a,k y+π/a)×ψν(k x,k y),(4.6)x q=−2e i qa/2α2a×ψ∗ν(k x−q,k y−q)ψν(k x,k y),(4.7)y q=−2e i qa/2α2a×ψ∗ν(k x−q,k y−q)ψν(k x,k y),(4.8)where the sum overνis restricted to the occupied states.We have omitted complex conjugate forms of eqs.(4.7)and(4.8).It should be noted that for eachνthe corresponding wave function isﬁnite only when k x−k y=const.,though this constant depends onν.In the present calculation scheme,we have only to diagonalize N diﬀerent N×N matrices instead of a single N2×N2.This makes the computational load much lighter,and therefore we can treat far larger system than in the case where we deal with two dimensional problems directly.In Figs.4and5we show the wave number dependences of the amplitudes and the phases of x q’s and y q’s which have been obtained by solving the self-consistent equations for the system size N=128(the total number of lattice points=128×128)and the coupling constantα=4.0eV/˚A(λ=0.30).The initial condition used in this iterative calculation is Re x q=Im x q=x in(some constant of the order of10−2a)for q=2π/Na,x q=0for other q and y q=0for all q,where q is restricted in the region0<q<π/a,and x0=y0=x in.The ﬁnal results does not depend on the values of x in.The results for diﬀerent types of initial conditions will be discussed later.The amplitudes of x q and y q are completely equal to each other and are found to vanish at q values which are even integer times2π/Na,though,as a matter of course,q=π/a isexceptional.As for the phases,weﬁnd the relation arg(x q1)+arg(x q2)=arg(y q1)+arg(y q2)=0mod(π)for q1and q2satisfying q1+q2=π/a.This will be reasonable if we remind us the second order perturbation mechanism of the Peierls gap formation.Once we know the values of{x q},{y q},x0and y0,we can obtain N eigenenergies for each set of N electronic wave vectors.Assuming that the energy of the lower(higher)band is an increasing(decreasing)function of the distance from the line k x+k y=0,we can assign theFig.4.The q0|and|y0|are also plotted.The system size is N=.30).energy versus k relation.The dispersion relation obtained in this way is shown in Fig.6for the case withα=6.0eV/˚A(λ=0.69).10)Only the lower band which is fully occupied in the ground state is shown along the lines depicted in the sub-ﬁgure.Because of the electron-hole symmetry of the system the dispersions of the unoccupied levels are the same as those shown in Fig.6except for the sign of energy.Thus by assigning the dispersion relation for all the points in the k-space,we can now see the gap structure on the Fermi surface.As will be clear from Fig.6,the gap is constant along the line(−π/a,0)−(0,π/a).On the other hand the gap structure along the line (0,π/a)−(π/a,0)is not so simple as will be found from Fig.7,where the dispersion curves of upper and lower bands along the line(0,π/a)−(π/a,0)are shown for the cases with a couple of diﬀerent values of the electron-lattice coupling constant.In contrast to the asymmetrically dimerized case(Fig1),the gap does not vanish at any point,taking almost the same value as that at(π/2a,π/2a).It will be noteworthy that the gap is not minimum at k=(0,π/a)or(π/a,0)and that the multi-mode eﬀect is almost negligible around the point k=(π/2a,π/2a).The position of the gap minimum depends on the coupling constant.In the sameﬁgure,the dispersions in the asymmetrically dimerezed case for each coupling constant are shown for comparison.In order to see the size dependence of the gap∆,we plot in Fig.8the gap at three diﬀerent@ arg(x q)× arg(y q)Fig.5.The q of arg(x0)and arg(y0),which are zero in this N=128,and the coupling constant isα=4.0eV/˚A(λpoints on the line(0,π/a)−(π/a,0),as indicated in the inset,for a coupling constantλ=0.69 (α=6.0eV/˚A).From thisﬁgure weﬁnd that N=128belongs to the large size limit as far as the behavior of the gap concerns and that in the large size limit the gaps∆1and∆2at (π/2a,π/2a)and(0,π/a)are indistinguishable though the value of∆3remains smaller than ∆1and∆2.For smaller values of the coupling constant,a similar tendency is found,but the large size limit is seen only at larger system sizes,although N=128is suﬃciently large even forα=4.0eV/˚A.As indicated by the results shown above,the lowest energy state obtained here is not completely symmetric with respect to x and y directions.This fact means that there exist at least two degenerate states where the roles of x ant y are interchanged.In order to check other degeneracy of the lowest energy states,we have studied what kind of distortion patterns could be obtained when we change the initial distortions in the iterative calculation.As a result,we got many diﬀerent distortion patterns with the same energy as that of the distortion pattern shown in Figs.4and5.Some are diﬀerent only in the phases of the Fourier components of the distortion.Some show completely diﬀerent behaviors.Among them there is a pattern where the nonvanishing Fourier components are xπ/2a,yπ/2a,x0and y0and other components are zero.In these degenerate states,not only the total energy butFig.6.The system size128×128. The wave numbersalso the electronic part and the lattice potential part are also the same,respectively.At the moment we cannot say how many states are degenerate.Detailed analysis of the degeneracy problem is left for a future work.§5.Summary and DiscussionThe lowest energy state of a two dimensional electron-lattice system with a half-ﬁlled electronic band and with a square lattice structure is studied within the SSH-type model extended to two dimensions.On the contrary to the previous common understanding that only the lattice distortion with the nesting vector Q=(π/a,π/a)is frozen in the lowest energy state,3)many modes are found to be frozen in the real lowest energy state.The state discussed by Tang and Hirsch3)might be a local minimum but it is not the absolute minimum of energy.This is because the Peierls gap vanishes at(π/a,0)and(0,π/a)due to the wave number dependence of the electron-lattice coupling term.We have pointed out that the second order perturbation mechanism of the Peierls gap formation is important. Numerical minimization of the total energy leads to the conclusion that many modes having the wave number parallel to Q contribute to the formation of the gap.Assuming this is the case,we can reduce the two-dimensional problem into one-dimensional problems by using the wave number representation of the Hamiltonian as discussed in§4.In this formulation it is,0)Fig.7.The levels along the line(0,π/a)−(π/a,0).Threeα[eV/˚A]=4.0(λ=0.30); continuous thick line.The similar dispersions for the asymmetric thinner lines.possible to treat far larger system sizes than in the case where we search a minimum energy state of the two-dimensional system directly.The electronic energy dispersion and the gap structure on the Fermi surface have been analyzed.Although the wave number dependences of the amplitudes and phases of condensed modes look to show a certain symmetry in the x and y directions,the electronic structures are not necessarily symmetric.What we have shown in this paper is not the unique lowest energy state.A preliminary study indicates there might be inﬁnite number of degenerate ground states.The degree of degeneracy is not known at the moment.It is not clear also what kind of symmetry is relevant to this degeneracy.Detailed study of the degeneracy problem is left for the future work.Nevertheless it will be worthwhile to mention that this type of degeneracy of the ground state yields the possibility of the formation of domain walls like the solitons in the one-dimensional systems where the number of degenerate ground state is only two.6,11,12) This kind of domain walls connecting two diﬀerent ground states may supply interesting properties of the two-dimensional electron-lattice systems just as the charged and neutral solitons in polyacetylene did.Fig.8.The system at diﬀerent points on the line (0,π/a)−(π/a,0).AcknowledgmentsThe authors are grateful to Professor Y.Wada for useful comment on existing references.。

applied physics reviews-focused review

APPLIED PHYSICS REVIEWS–FOCUSED REVIEWPlasmonics:Localization and guiding of electromagnetic energy in metal/dielectric structuresStefan A.Maier a ͒and Harry A.AtwaterThomas J.Watson Laboratories of Applied Physics,California Institute of Technology,Pasadena,California 91125͑Received 17September 2004;accepted 23March 2005;published online 11July 2005͒We review the basic physics of surface-plasmon excitations occurring at metal/dielectric interfaces with special emphasis on the possibility of using such excitations for the localization of electromagnetic energy in one,two,and three dimensions,in a context of applications in sensing and waveguiding for functional photonic devices.Localized plasmon resonances occurring in metallic nanoparticles are discussed both for single particles and particle ensembles,focusing on the generation of conﬁned light ﬁelds enabling enhancement of Raman-scattering and nonlinear processes.We then survey the basic properties of interface plasmons propagating along ﬂat boundaries of thin metallic ﬁlms,with applications for waveguiding along patterned ﬁlms,stripes,and nanowires.Interactions between plasmonic structures and optically active media are also discussed.©2005American Institute of Physics .͓DOI:10.1063/1.1951057͔TABLE OF CONTENTSI.INTRODUCTION............................1II.LOCALIZED PLASMON RESONANCES IN METAL NANOPARTICLES...................2A.Optical properties of single metalnanoparticles (2)B.Interacting particle ensembles as a basis for applications of metal nanoparticles inoptical devices (4)C.Local ﬁeld enhancement around metal nanoparticle structures for sensing andnonlinear applications ....................5III.INTERFACE PLASMON POLARITONS ATMETAL/DIELECTRIC BOUNDARIES.........6A.Surface-plasmon polaritons at metalinterfaces ..............................6B.Metal stripes and nanowires:Two-dimensional conﬁnement .............8C.Apertures in a metallic screen .............8D.Interactions with optically active media .....9IV .OUTLOOK.. (9)I.INTRODUCTIONThe electromagnetic properties of metal/dielectric inter-faces have attracted a vast amount of research effort ever since the work of Mie 1and Ritchie 2for small particles and ﬂat interfaces,respectively.The ability of such structures tosustain coherent electron oscillations known as surface-plasmon polaritons ͑SPPs ͒leading to electromagnetic ﬁelds conﬁned to the metallic surface has been intensively investigated 3,4both in light of the fundamental physics in-volved and for applications such as surface-enhanced spec-troscopy and enhancement of nonlinear light generation.Af-ter initial studies of the physics of these excitations,in the 1980s SPPs started to attract the attention of chemists,as the electric-ﬁeld enhancement around metal nanostructures was found to be crucial for surface-enhanced Raman spectros-copy.More recently,the development of nanofabrication tech-niques such as electron-beam lithography,ion-beam milling,and self-assembly,together with modern nanocharacteriza-tion techniques such as dark-ﬁeld and near-ﬁeld optical mi-croscopies and the emergence of quantitative electromag-netic simulation tools,has lead to a resurgence of interest in this ﬁeld,5partly due to potential applications for creating subwavelength optical devices enabling the miniaturization of optical components to size dimensions of their electronic counterparts,i.e,to the sub-100-nm-size regime.The unify-ing physical processes enabling light localization and guid-ing in such structures are the above-mentioned SPP excita-tions,and the name “plasmonics”for the subﬁeld of modern optics studying such processes has been proposed.6Due to the vast amount of research in this exploding ﬁeld,5we naturally had to select a rather small amount of topics for this review,leading to the omission of important applications of SPPs,for example,their use in integrated biological sensors based on multilayer structures,7investiga-tions from a more chemical viewpoint,8as well as an in-depth treatment of fabrication techniques.9Here,we limit ourselves to a discussion of the fundamental physics ofa ͒Present address:Department of Physics,University of Bath,Bath BA27AY ,U.K.;electronic mail:s.maier@JOURNAL OF APPLIED PHYSICS 98,011101͑2005͒0021-8979/2005/98͑1͒/011101/10/$22.50©2005American Institute of Physics98,011101-1surface-plasmon excitations both for localized plasmons in metallic nanoparticles and for interface plasmons at metall-odielectric ﬁlm boundaries.A special focus has been put on the localization and guiding properties for electromagnetic radiation in light of applications of plasmon excitations for surface-enhanced spectroscopy such as sensing and higher harmonic generation and for the creation of a planar wave-guide technology that can beat the diffraction limit.II.LOCALIZED PLASMON RESONANCES IN METAL NANOPARTICLESA.Optical properties of single metal nanoparticlesThe strong interaction of microscopic metal particles of dimensions below 1␮m with visible light has been em-ployed for beautiful applications long before Gustav Mie’s seminal 1908paper Beiträge zur Optik trüber Medien,spez-iell kolloidaler Metallösungen ͑contributions to the optics of turbid media,particularly solution of colloidal metals ͒.1His-torically,one prominent use of metal nanoparticles has been the staining of glass windows and ceramic pottery as seen in Fig.1͑a ͒by example of the Lycurgus cup ͑Byzantine empire,4th century A.D.͒.The glass cup,on display in the British Museum,shows a striking red color when viewed in trans-mitted light,while appearing green in reﬂection.This pecu-liar behavior is due to small Au nanoparticles embedded in the glass ͓Fig.1͑b ͔͒,which show a strong optical absorption of light in the green part of the visible spectrum ͓Fig.1͑c ͔͒.Indeed,the optical properties of metal nanoparticles,es-pecially those of the noble metals Au,Ag,and Cu,show striking differences relative to their bulk or thin-ﬁlm optical responses.As an example,Fig.1͑c ͒shows the calculated absorption of a thin Au ﬁlm ͑blue dots ͒,as well as that of 30-nm Au spheres immersed in water ͑red dots ͒,where the dispersion properties of Au have been modeled using mea-sured dielectric data for bulk Au.10For the nanoparticles,the optical-absorption spectrum has been obtained by directlysolving Maxwell’s equations for the scattering of electro-magnetic waves by spherical objects as carried out by Mie,1and retaining only the dipolar term,which is suitable for nanoparticles with a diameter d Ӷ␭,where ␭is the wave-length of light in the surrounding medium.As shown,this quasistatic approximation is in good agreement with mea-surements ͑black dots ͒,which has been conﬁrmed via a plethora of studies of the optical response of metallic nano-particles with a diameter well below ␭in solid,liquid,and gaseous environments.4Figure 1͑c ͒further demonstrates a striking difference between the optical response of the thin ﬁlm and the nanoparticles.Whereas the ﬁlm absorbs light throughout the near-infrared and visible regions due to free-electron absorption,for the nanoparticles this process is strongly quenched for energies lower than 2eV ͑correspond-ing to wavelengths larger than 620nm ͒.Indeed,all the free-electron oscillator strength for absorption is pulled into a dipolar absorption peak around 2.25eV,the dipolar surface-plasmon particle resonance.This modiﬁed optical response leads to the bright colors of noble-metal nanoparticles,a nice discussion of which can be found in Ref.11.For higher energies above the dipole resonance,the optical absorption of particles and ﬁlms is similar,due to the dominance of d –sp electronic interband transitions,which are prominent for Au and Cu in the vicinity of the dipole plasmon reso-nance,but less so for Ag.The resonant electromagnetic behavior of noble-metal nanoparticles is due to the conﬁnement of the conduction electrons to the small particle volume.For particles with a diameter d Ӷ␭,the conduction electrons inside the particle move all in phase upon plane-wave excitation with radiation of wavelength ␭,leading to the buildup of polarization charges on the particle surface.These charges act as an ef-fective restoring force,allowing for a resonance to occur at a speciﬁc frequency—the particle dipole plasmon frequency-,where the response of the electrons shows a ␲/2phase lag with respect to the driving ﬁeld.Thus,a resonantly enhanced ﬁeld builds up inside the particle,which in the small particle limit is homogeneous throughout its volume,producing a dipolar ﬁeld outside the particle.This leads to enhanced ab-sorption and scattering cross sections for electromagnetic waves,as well as to a strongly enhanced near ﬁeld in the immediate vicinity of the particle surface.It is this reso-nantly enhanced near ﬁeld from which most of the promising applications of metal nanoparticles stem.For larger particles,the spectral response is modiﬁed due to retardation effects and the excitation of higher-order ͑quadrupole and higher ͒modes,the spectral signature of which can be calculated by retaining higher orders of the Mie theory scattering coefﬁcients.1In general,the spectral position,damping,and strength of the dipole as well as of the higher-order plasmon reso-nances of single metal nanoparticles depend on the particle material,size,geometry,and the dielectric function of the surrounding host.4For theoretical considerations,the large variety of naturally occurring or synthesized shapes of nano-particles is often approximated via spheres or spheroids,for which analytically exact solvable solutions exist to all orders.1,4,12,13The analysis is further facilitated forparticlesFIG.1.͑Color online ͒͑a ͒The Lycurgus glass cup,demonstrating the bright red color of gold nanocrystals in transmitted light.͑b ͒scanning electron microscopy ͑SEM ͒image of a typical nanocrystal embedded in the glass ͑courtesy of the British museum ͒.͑c ͒Calculated absorption spectrum of a thin gold ﬁlm ͑blue dots ͒and of 30-nm Au nanoparticles in water ͑red dots ͒using classical electromagnetic theory.A measured absorption spectrum of an aqueous solution of 30-nm Au colloids ͑black dots ͒shows good agree-ment with the theory.much smaller than the wavelength of light,where only the lowest ͑dipolar ͒order of the modal expansion of the scat-tered ﬁelds has to be retained.In this case,a quasistatic ap-proach serves well to describe the spectral position,width,and strength of the dipolar plasmon resonance,as pointed out in the discussion of Fig.1.For a spherical metal nanoparticle of radius a Ӷ␭embedded in a nonabsorbing surrounding me-dium of dielectric constant ␧m ,the quasistatic analysis gives the following expression for the particle polarizability ␣:␣=4␲a 3␧−␧m␧+2␧m,͑1͒with the complex ␧=␧͑␻͒describing the dispersive dielectric response of the metal.The polarizability and thus the in-duced homogeneous polarization inside the particle are reso-nantly enhanced at the Fröhlich frequency where the de-nominator shows a minimum,limited by the imaginary part of ␧describing Ohmic heating losses within the particle.These losses are due to the creation of electron-hole pairs,the energy of which is subsequently coupled to the phonon bath.14The spectral position of this resonance is seen to red-shift with increasing dielectric constant of the surrounding host due to the buildup of polarization charges on the dielec-tric side of the interface,thus weakening the total restoring force.For ellipsoidal particles with principal axes a ,b ,and c ,an analogous expression can be found in the quasistatic ap-proximation via introducing geometrical depolarization fac-tors L i along these axes,4,12leading to␣=43␲abc␧−␧m ␧m +L i ͑␧−␧m ͒,͚L i =1.͑2͒For spherical particles,L 1=L 2=L 3=1/3.For spheroidal par-ticles ͑L 1=L 2͒,the plasmon resonance thus splits into astrongly redshifted long-axis mode ͑polarization parallel to the long axis ͒and a slightly blueshifted short axis mode ͑polarization perpendicular to the long axis ͒.12For larger particles beyond the Rayleigh approximation,the dipolar resonance redshifts while at the same time suffer-ing substantial broadening.The redshift is due to a reduction of the depolarization ﬁeld due to retardation effects 15—the conduction electrons do not all move in phase anymore,leading to a reduced depolarization ﬁeld at the particle centergenerated by the surrounding polarized matter.Additionally,radiative losses 16begin to signiﬁcantly contribute to the plas-mon damping,dominating the total damping of Au and Ag nanoparticles for particle sizes in excess of 100nm.The de-polarization ﬁeld and radiation damping effect can be seen as lowest-order corrections to the quasistatic theory,leading to additional real and imaginary parts of the denominator of the polarizability.A generalization of the quasistatic approach to particles of arbitrary shape has been suggested,with surpris-ingly good results 17͓see Fig.2͑a ͔͒.For particles with a di-ameter smaller than the free-electron scattering length,scat-tering processes at the particle surface are thought to begin to contribute to the total damping.4These additional damping mechanisms for large and small particles lead to respective decreases in the total enhancement of the exciting ﬁeld via a decrease of the plasmon dephasing time T 2.4Generally,numerical methods such as the T -matrix method,18the discrete dipole approximation 19͓Fig.2͑b ͔͒,or ﬁnite-difference time-domain simulations 20have to be used to calculate the resonance frequencies and mode proﬁles of more complex shapes.Such simulations have especially been employed to determine the local-ﬁeld enhancement at the particle surface,in conjunction with discussions of enhance-ments of nonlinear processes and surface-enhanced Raman scattering ͑SERS ͒as discussed below.Experimentally,sophisticated modern fabrication meth-ods allow for the fabrication of metal nanoparticles and other nanostructures of a variety of shapes using both colloidal synthesis methods 21and top-down nanofabrication tech-niques such as electron-beam lithography,22and a wide vari-ety of methods for the fabrication of metallic nanoparticles and ensembles thereof have recently been described in a dif-ferent review article.9The good control over the size and shape of the particles provided by these methods method allows one generally to observe homogeneously broadened line shapes of dipolar 23and multipolar 24plasmon modes in particle ensembles using conventional far-ﬁeld spectroscopy.The direct examination of single particles has been demon-strated using both dark-ﬁeld 25and near-ﬁeld optical microscopies.26The former method allows for a dramatic visualization of the spectral properties of single particles,as can be seen by the example in Fig.2͑a ͒.FIG.2.͑Color online ͒͑a ͒Dark-ﬁeld microcopy image ͑top ͒and light-scattering spectra ͑bottom ͒of Au nanocrystals of different shapes ͑adapted from Ref.17͒.The measured spectra ͑black curves ͒show good agreement with predictions from a simple analytical extension of quasi-static Mie theory ͑open circles ͒.͑b ͒Electric near-ﬁeld proﬁle of the lowest-order modes of Ag nanoprisms calculated using the discrete dipole ap-proximation formalism ͑adapted from Ref.54͒.B.Interacting particle ensembles as a basis forapplications of metal nanoparticles in optical devicesAdvances in particle synthesis and fabrication tech-niques ͑for example,Refs.22,27,and 28͒have recently allowed for studies of ordered arrays of noble-metal nano-particles.In such arrays,each nanoparticle with a diameter much smaller than the wavelength ␭of the exciting light acts as an electric dipole.Thus,two types of electromagnetic in-teractions between the particles can be distinguished,de-pending on the spacing d between adjacent nanoparticles.For particle spacings on the order of the exciting wavelength ␭,far-ﬁeld dipolar interactions with a d −1dependence domi-nate.Work on regular two-dimensional arrays of Au nano-particles has indeed conﬁrmed the existence of such interac-tions,and quantiﬁed their inﬂuence on both the spectral position of the collective dipolar extinction peak and the plasmon damping characteristics.29Figures 3͑a ͒and 3͑b ͒show an example of the dependence of both extinction peak and plasmon decay time on the grating constant d for a regu-lar square array of 150-nm-diameter Au nanoparticles.Both the variation of the spectral position and width of the reso-nances can be explained by assuming far-ﬁeld dipolar interactions—the ensemble acts effectively as a grating,lead-ing to increased radiation damping of the collective reso-nances for grating constants where grating orders change from evanescent to radiative in character.29Applications of such ordered arrays lie,for example,in the possibility of maximizing surface-enhanced Raman scattering of adsorbed molecules by careful spectral tuning of the plasmon resonance.30For particle spacings much smaller than the wavelength of light,near-ﬁeld dipolar interactions between adjacent par-ticles with a distance dependence of d −3dominate.23,31These strongly distance-dependent interactions lead to a splitting of the plasmon dipolar peak for regular one-dimensional arrays of metal nanoparticles as seen in Fig.3͑c ͒for ordered arrays of 50-nm Au particles.The spectral position of the extinction peak for far-ﬁeld excitation shows a blueshift for polarization perpendicular to the chain axis ͑T ͒,and a redshift for longi-tudinal polarization ͑L ͒,which can easily be understood by analyzing Coulombic force interactions between the elec-trons in neighboring particles.The near-ﬁeld interactions be-tween such particles have been directly visualized using near-ﬁeld optical microscopy,32conﬁrming a strongly en-hanced ﬁeld between the particles ͓Fig.3͑d ͔͒,indicative of near-ﬁeld coupling.One application of near-ﬁeld coupling between particles in ordered arrays is the use of such structures as waveguides for electromagnetic energies at optical frequencies with a lateral mode proﬁle below the diffraction limit of light.6,33Indeed,it has been shown both theoretically 34and experimentally 35that such arrays can guide electromagnetic energy over distances of several hundred nanometers via near-ﬁeld particle interactions.Such structures could poten-tially be used in nanoscale all-optical networks,contributing to a class of functional optical devices below the diffraction limit of light.5,6,36Localized plasmon excitations mediated by particle in-teractions also occur in randomly nanostructured metallic surfaces.37In this case,multiple-scattering processes can lead to “hot spots”of extremely large ﬁeld enhancement ͑on the order of 1000͒,which has enabled the use of such struc-tures for single-molecule spectroscopy.38FIG.3.͑Color online ͒͑a,b ͒Measured extinction spectrum ͑a ͒and plasmon decay time ͑b ͒for regular two-dimensional ͑2D ͒square arrays of Au nanoparticles ͑adapted from Ref.29,copyright by the American Physical Society ͒.Both the spectral position and the decay time of the collective dipolar plasmon mode show a marked variation with grating constant due to far-ﬁeld dipolar interactions.͑c ͒Mea-sured spectral position of the collec-tive plasmon resonances of one-dimensional arrays of closely spaced Au nanoparticles for longitudinal ͑L ͒and transverse polarizations ͑T ͒.Also shown are results of a simple near-ﬁeld point-dipolar coupling model ͑solid lines ͒and ﬁnite-difference time-domain simulations ͑stars ͒.͑d ͒Optical near-ﬁeld around such a chain ob-tained using collection mode near-ﬁeld optical microscopy ͑left ͒and numeri-cal simulations ͑right ͒,adapted from Ref.32.C.Localﬁeld enhancement around metal nanoparticle structures for sensing and nonlinear applications The enhanced nearﬁelds around metallic nanostructures induced by illumination at visible and near-infrared frequen-cies allow for a variety of intriguing applications apart from energy guiding in ordered particle arrays discussed above. Since the enhancedﬁelds are localized to the surface of the nanostructures,they serve as a local probe of the dielectric environment within a few nanometers of the particle surface. This fact has,for example,been employed in studying varia-tions of the local refractive index in light of biological ͑mass͒sensing applications.39–41Also,the local response of metallic nanostructures can serve so as to enhance the in-coming and generatedﬁelds for nonlinear processes and de-cay rate enhancements of emissive species.For nonlinear applications and surface-enhanced Raman sensing,the local-ﬁeld E Local close to the metal surface should be maximized so as to maximize the respective higher-order processes,neglecting the possibility of absorption-induced damage of the optically active medium. The local-ﬁeld enhancement factor L=E Local/E0,with E0be-ing the amplitude of the incomingﬁeld,can for a single nanoparticle be written as the product of two factors L =L SP͑␻͒L LR,highlighting two possible enhancement processes—the surface-plasmon resonance of the whole par-ticle͑L SP͒and the lightning rod effect͑L LR͒.For larger par-ticles,surface roughness and crevices can lead to additional localized resonances forming hot spots on the particle sur-face.For a perfectly spherical particle in the Rayleigh limit, only the dipole surface-plasmon resonance contributes to the enhancement process,with L SPϰQϰT2in the absorption-dominated regime,where T2and Q are the dephasing time, limited by the decay of the particle plasmon into electron-hole pairs and photons and by phase-destroying elastic scat-tering processes,and the quality factor of the resonance,re-spectively.The origins of plasmon decay and dephasing have been extensively discussed in the literature,14,42and T2has been determined both using time-resolved pump-probe measurements43–46and higher harmonic generation.47For small Au nanospheres in air and low-index matrixes,plas-mon excitation competes with interband transitions,leading to low Q factorsϳ10,while radiation damping dominates for larger spheres with diameters of about100nm.16Higher Q factorsϳ20have been reported for spheroidal Au par-ticles,due to a redshift of the long-axis dipolar resonance away from the interband transition edge.42For Ag nanopar-ticles,the respectiveﬁeld enhancements at visible frequen-cies are higher,partly due to a larger spectral separation of the plasmon resonance from the interband transition edge. Another promising route to larger quality factors are metallic nanoshells,where Q factors up to150have been estimated for Ag.48For nonspherical shapes,the geometric and only weakly frequency-dependent lightning rod effect L LR of the electric ﬁeld at sharp surface protrusions,leading to an increased surface charge and thus a crowding of the electric-ﬁeld lines, serves as an additional enhancement process.49–51This way,highly localizedﬁelds can be generated at the tips of elon-gated spheroids or rough surfaces.For very rough or veryhigh-aspect ratio particles,additionally local-plasmon reso-nances at speciﬁc parts on the particle surface can be excited,leading to an additional enhancement.For the case of sphe-roids with aspect ratiosϾ10:1,the overall particle resonancecan be interpreted as an antenna effect,where theﬁeld isfurther enhanced at the tip due to lightning rod and localplasmon resonances.13,52Fully analytical53and a variety ofnumerical models54have been used to quantify theﬁeld en-hancement at sharp points on a variety of single-metal par-ticles,predicting highest-ﬁeld enhancement factors of about100for Ag particles.The heightened opticalﬁelds near metal nanostructuresmanifest themselves in the enhancement of higher harmonicgeneration and local spectroscopy.For example,the total en-hancement of second-harmonic generation on a rough silversurface is expected to scale as L͑␻͒4L͑2␻͒2upon resonance, whereas for Raman spectroscopy the enhancement scales asL͑␻exc͒2L͑␻RS͒2.Note that due to the small Stokes shift in Raman scattering,usually theﬁelds at both the excitationfrequency and the Stokes frequency are enhanced.Forsecond-harmonic generation on the other hand,usually onlyone of the two processes shows enhancement due to the largespectral separation between the two lines.Also,due to thesigniﬁcant absolute value of͉␧͑␻͉͒at visible frequencies,the ﬁeld inside the particle͑where second harmonic generation from the particle itself occurs͒is smaller than theﬁeld out-side͑where SERS occurs͒.Thus,the observed SERS en-hancements are usually signiﬁcantly larger than those of second-and higher harmonic processes.Note that for calcu-lations ofﬁeld enhancement with metallic nanoparticles,the enhancement is usually evaluated for the peak power at a speciﬁc Stokes or higher harmonic output frequency,i.e.,not integrated over the total resonance line shape.Experimentally,the enhancement of second-harmonicgeneration at rough metal surfaces has been observed usingboth far-ﬁeld55–58and near-ﬁeld59,60spectroscopic tech-niques,with measured enhancements of second-harmonicgeneration on Au and Ag islandﬁlms up to1000.58While themagnitude of the reported enhancement varies considerably,recently direct observations of localized second-harmonicenhancements of order1000have been reported on Au sur-faces coated with random scatterers using laser scanningmicroscopy.61,62The highest enhancement of an optical process on arough metal surface so far reported is that of Raman Stokesscattering͑surface-enhanced Raman scattering͒,where emis-sion from single molecules63,64with an enhancement factorof the Raman cross section up to1014has been observed,although the interpretation of these experiments is somewhatcontroversial.At this point,it is believed that this huge in-crease in the cross section is due to both local-ﬁeld enhance-ments up to a factor of1000on roughened Ag surfaces,leading to a Raman enhancement of1012,and to chemicaleffects due to adsorbate binding at the metal surface,65mak-ing up for the additional factor of100in the total enhance-ment.Sinceﬁeld enhancements of a factor of1000canhardly be achieved for single particles,with the possible ex-ception of gap modes in surface crevices,it is believed that ﬁeld localization in small gaps between metal particles due to geometric effects and multiple photon scattering on rough surfaces contributes to this high-ﬁeld enhancement in nanometer-sized volumes,so-called hot spots,53,54,62and re-cently a detailed analytical description of the enhancement using a simple resonator model has been given.66These lo-calized resonances tend to show very different strengths,po-larization,and localization characteristics.The importance of multiple scattering for the creation of hot spots for ﬁeld en-hancement has been highlighted via many studies showing the signiﬁcance of fractal-like character of the silver surface.37,67III.INTERFACE PLASMON POLARITONS AT METAL/DIELECTRIC BOUNDARIESA.Surface-plasmon polaritons at metal interfacesCoherent electron oscillations leading to enhanced local ﬁelds at the surface of metallic structures cannot only be excited in metallic nanoparticles,but also at ﬂat interfaces such as metallic ﬁlms.As is well known,the interface be-tween a metallic ﬁlm and a dielectric can sustain SPPs in the form of coherent longitudinal charge oscillations of the con-duction electrons,thus leading to a surface wave conﬁned within one dimension perpendicular to the surface.3At ﬂat interfaces,these charge oscillations were observed in energy loss spectra obtained via bombardment of the ﬁlm with fast electrons,revealing “low-lying plasma losses”at energies lower than the characteristic bulk-plasmon energy ␻p of the respective metal.2,68At a metal/air boundary,these low-lying plasma losses for electrons occur at a frequency ␻p /ͱ2.This lowering of the plasmon resonance is due to the depolarizing effect of the ﬂat surface,analogous to the case of localizedplasmons in metallic nanoparticles.However,while for exci-tation with fast electrons plasma waves at ﬂat interfaces do not propagate ͑group-velocity ␯g =0͒,SPPs at lower energies exhibit a signiﬁcant dispersion with wave vector k due to retardation effects.Figure 4͑a ͒shows the dispersion relation for surface-plasmon polaritons propagating at a ﬂat interface between Ag and air,glass,and silicon,respectively,calcu-lated using a simple boundary condition analysis for electro-magnetic surface waves,3yieldingk x =␻c ͫ␧͑␻͒␧2␧͑␻͒+␧2ͪ,͑3͒where ␧͑␻͒are the ͑complex ͒dielectric function of the metal and ␧2the dielectric constant of the adjacent dielectric half-space.As can be seen,the dispersion relations of the SPPs al-ways lie to the right of the respective light line,approaching ␻sp =␻p /ͱ1+␧2for large wave vectors,the magnitude of the wave vector at ␻sp being limited by dissipation.While ex-periments with fast electrons mainly probe this high wave-vector regime where dispersion is absent,3for lower wave vectors surface-plasmon polaritons can be excited by TM-polarized light,providing that the retardation-induced mo-mentum mismatch is compensated.The main techniques for achieving this momentum matching are prism coupling,cou-pling via surface grating or roughness ͑defects ͒,and using highly focused optical excitation.3Recently,excitation of surface plasmons using regular hole arrays created via shad-owed metal evaporation has been achieved.69This work has provided a beautiful demonstration of the transition between localized surface plasmons of nontouching particles to dis-persive surface-plasmon polaritons propagating along the hole ﬁlm ͓Figs.4͑b ͒–4͑d ͔͒.FIG.4.͑a ͒Calculated dispersion of surface plasmon-polaritons propagating at a Ag/air,Ag/glass,and Ag/Si interface,respectively.͑b ͒–͑d ͒Measured transmittance as a function of in-plane wave vector and frequency for p -polarized light incident upon an array of nontouching nanoparticles ͑b ͒,an intermediate array of bigger particles with some coalescence ͑c ͒,and a periodic array of holes formed by touching nanoparticles ͑d ͒,showing the transition from localized to dispersive behavior ͑adapted from Ref.69͒.。

Facebook_1310.6753v1

Romantic Partnerships and the Dispersion of Social Ties:A Network Analysis of Relationship Status on FacebookLars Backstrom Facebook Inc.Jon Kleinberg Cornell UniversityABSTRACTA crucial task in the analysis of on-line social-networking systems is to identify important people —those linked by strong social ties —within an individual’s network neighbor-hood.Here we investigate this question for a particular cate-gory of strong ties,those involving spouses or romantic part-ners.We organize our analysis around a basic question:given all the connections among a person’s friends,can you recog-nize his or her romantic partner from the network structure alone?Using data from a large sample of Facebook users,we ﬁnd that this task can be accomplished with high accuracy,but doing so requires the development of a new measure of tie strength that we term ‘dispersion’—the extent to which two people’s mutual friends are not themselves well-connected.The results offer methods for identifying types of structurally signiﬁcant people in on-line applications,and suggest a po-tential expansion of existing theories of tie strength.Categories and Subject Descriptors:H.2.8[Database Management ]:Database applications—Data mining Keywords:Social Networks;Romantic Relationships.INTRODUCTIONIn a social network,an individual’s network neighborhood —the set of people to whom he or she is linked —has been shown to have important consequences in a wide range of settings,including social support [12,24]and professional op-portunities [5,15].As people use on-line social networks to manage increasingly rich aspects of their lives,the structures of their on-line network neighborhoods have come to reﬂect these functions,and the complexity that goes with them.A person’s network neighbors,taken as a whole,encompass a profoundly diverse set of relationships —they typically in-clude family members,co-workers,friends of long duration,distant acquaintances,potentially a spouse or romantic part-ner,and a variety of other categories.An important and very broad issue for the analysis of on-line social networks is to use features in the available data to recognize this variation across types of relationships.Methods to do this effectively can play an important role for many applications at the in-terface between an individual and the rest of the network —managing their on-line interactions [9],prioritizing contentPermission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for proﬁt or commercial advantage and that copies bear this notice and the full cita-tion on the ﬁrst page.Copyrights for components of this work owned by others than ACM must be honored.Abstracting with credit is permitted.To copy otherwise,or re-publish,to post on servers or to redistribute to lists,requires prior speciﬁc permission and/or a fee.Request permissions from permissions@.CSCW’14,February 15–19,2014,Baltimore,Maryland,USA.Copyright c2014ACM 978-1-4503-2540-0/14/02...$15.00./10.1145/2531602.2531642they see from friends [1],and organizing their neighborhood into conceptually coherent groups [23,25].Tie Strength.Tie strength forms an important dimension along which to characterize a person’s links to their network neighbors.Tie strength informally refers to the ‘closeness’of a friendship;it captures a spectrum that ranges from strong ties with close friends to weak ties with more distant acquaintances.An ac-tive line of research reaching back to foundational work in so-ciology has studied the relationship between the strengths of ties and their structural role in the underlying social network [15].Strong ties are typically ‘embedded’in the network,sur-rounded by a large number of mutual friends [6,16],and often involving large amounts of shared time together [22]and ex-tensive interaction [17].Weak ties,in contrast,often involve few mutual friends and can serve as ‘bridges’to diverse parts of the network,providing access to novel information [5,15].A fundamental question connected to our understanding of strong ties is to identify the most important individuals in a person’s social network neighborhood using the underlying network structure.What are the deﬁning structural signatures of a person’s strongest ties,and how do we recognize them?Techniques for this problem have potential importance both for organizing a person’s network neighborhood in on-line applications,and also for providing basic insights into the ef-fect of close relationships on network structure more broadly.Recent work has developed methods of analyzing and esti-mating tie strength in on-line domains,drawing on data from e-mail [19],phone calls [27],and social media [14].The key structural feature used in these analyses is the notion of embeddedness —the number of mutual friends two people share [22],a quantity that typically increases with tie strength.Indeed,embeddedness has been so tightly associated with tie strength that it has remained largely an open question to de-termine whether there are other structural measures,distinct from embeddedness,that may be more appropriate for char-acterizing particular types of strong ties.Romantic Relationships.In this work we propose a new network-based characteriza-tion for intimate relationships,those involving spouses or ro-mantic partners.Such relationships are important to study for several reasons.From a substantive point of view,romantic relationships are of course singular types of social ties that play powerful roles in social processes over a person’s whole life course [4],from adolescence [2]to older age [7].They also form an important aspect of the everyday practices and uses of social media [28].a r X i v :1310.6753v 1 [c s .S I ] 24 O c t 2013And they are an important challenge from a methodological point of view;they are evidently among the very strongest ties,but it has not been clear whether standard structural the-ories based on embeddedness are sufﬁcient to characterize them,or whether they possess singular structural properties of their own[11,18].Our centralﬁnding is that embeddedness is in fact a compar-atively weak means of characterizing romantic relationships, and that an alternate network measure that we term dispersion is signiﬁcantly more effective.Our measure of dispersion looks not just at the number of mutual friends of two peo-ple,but also at the network structure on these mutual friends; roughly,a link between two people has high dispersion when their mutual friends are not well connected to one another. On a large random sample of Facebook users who have de-clared a relationship partner in their proﬁle,weﬁnd that our dispersion measure has roughly twice the accuracy of em-beddedness in identifying this partner from among the user’s full set of friends.Indeed,for married Facebook users,our measure of dispersion applied to the pure,unannotated net-work structure is more effective at identifying a user’s spouse than a complex classiﬁer trained using machine learning on an array of interaction measures including messaging,com-menting,proﬁle-viewing,and co-presence at events and in photos.Further,using dispersion in conjunction with these interaction features produces signiﬁcantly higher accuracy. The main contributions of our work are thus the following.•We propose a new network measure,dispersion,for esti-mating tie strength.Given the ubiquity of embeddedness in existing analyses of tie strength,the availability of this new measure broadens the range of tools available for rea-soning about tie strength,and about mechanisms for tie-strength classiﬁcation in on-line domains.•We provide a new substantive characterization of romantic relationships in terms of network structure,with potential consequences for our understanding of the effect that such relationships have on the underlying social network.•Given this characterization,we examine its variation across different conditions and populations.Weﬁnd,for example, that there are signiﬁcant gender differences in the extent to which relationship partners are recognizable from network structure,and that relationships are more likely to persist when they score highly under our dispersion measure.It is also important to delineate the scope of our results.Our approach to analyzing romantic partnerships in on-line so-cial settings is through their effect on the network structure, and the ways in which such relationships can be recognized through their structural signatures.As such,there is potential for it to be combined with other perspectives on how these relationships are expressed on-line,and the conventions that develop around their on-line expression;a complete picture will necessarily involve a synthesis of all these perspectives. DATA AND PROBLEM DESCRIPTIONWe analyze romantic relationships in social networks using a dataset of randomly sampled Facebook users who declared a relationship partner in their proﬁle;this includes users who listed their status as‘married,’‘engaged,’or‘in a relation-ship’.To evaluate different structural theories on a common footing,we begin with a simply stated prediction task de-signed to capture the basic issues.We take a Facebook user with a declared relationship partner,and we hide the identity of this partner.Then we ask:given the user’s network neigh-borhood—the set of all friends and the links among them—how accurately can we identify the relationship partner using this structural information alone?Figure1gives an example of such a Facebook user’s network neighborhood[21],drawn so that the user is depicted at the center;such diagrams are the‘input’from which we wish to identify the user’s partner. By phrasing the question this starkly,we are able to assess the extent to which structural information on its own conveys information about the relationships of interest.We note that our question has an important contingent nature: given that a user has declared a relationship partner,we want to understand how effectively we canﬁnd the partner.There are different questions that could be asked in a related vein—for example,inferring from a user’s network neighborhood whether he or she is in a relationship.We brieﬂy discuss the connections among these questions in a subsequent section, but the problem of identifying partners is our main focus here. As data for our analyses,we principally use two collections of network neighborhoods from Facebook.Theﬁrst consists of the network neighborhoods of approximately1.3million Facebook users,selected uniformly at random from among all users of age at least20,with between50and2000friends, who list a spouse or relationship partner in their proﬁle.These neighborhoods have an average of291nodes and6652links, for an overall dataset containing roughly379million nodes and8.6billion links.We also employ a smaller dataset—a sample of approxi-mately73000neighborhoods from thisﬁrst collection,se-lected uniformly at random from among all neighborhoods with at most25000links.We refer to this sample as the pri-mary dataset,and the larger dataset in the preceding para-graph as the extended dataset.We compute our main struc-tural and interaction measures on both the primary and ex-tended datasets,and these measures exhibit nearly identical performance on the two datasets.As we discuss further be-low,we evaluate additional network measures,as well as more complex combinations of measures based on machine learning algorithms,only on the primary dataset.All Facebook data in these analyses was used anonymously, and all analysis was done in aggregate. EMBEDDEDNESS AND DISPERSIONTo evaluate approaches for our task of recognizing relation-ship partners from network structure,we start with a fun-damental baseline—the standard characterization of a tie’s strength in terms of its embeddedness,the number of mutual friends shared by its endpoints[22].Embeddedness has also served as the key deﬁnition in structural analyses for the spe-cial case of relationship partners,since it captures how much the two partners’social circles‘overlap’[11,18].This sug-Figure1.A network neighborhood,contributed by a Facebook em-ployee(drawn as the circled nodeat the center),and displayed as an example in the work of Marlow et al[21].Two clear clusters with highly embedded links are visible at the top and right of the diagram;in the lower left of the diagram are smaller,sparser clusters together with a node that bridges between these clusters.gests a natural predictor for identifying a user u’s partner:se-lect the link from u of maximum embeddedness,and propose the other end v of this link as u’s partner.We will evaluate this embeddedness-based predictor,and oth-ers,according to their performance:the fraction of instances on which they correctly identify the partner.Under this mea-sure,embeddedness achieves a performance of24.7%—which both provides evidence about the power of structural information for this task,but also offers a baseline that other approaches can potentially exceed.Next,we show that it is possible to achieve more than twice the performance of this embeddedness baseline using our new network measure,dispersion.In addition to this relative im-provement,the performance of our dispersion measure is very high in an absolute sense—for example,on married users in our sample,the friend who scores highest under this disper-sion measure is the user’s spouse over60%of the time.Since each user in our sample has at least50friends,this perfor-mance is more than30times higher than random guessing, which would produce a performance of at most2%. Theoretical Basis for Dispersion.We motivate the dispersion measure byﬁrst highlighting a basic limitation of embeddedness as a predictor,drawing on the theory of social foci[10].Many individuals have large clusters of friends corresponding to well-deﬁned foci of in-teraction in their lives,such as their cluster of co-workers or the cluster of people with whom they attended college.Since many people within these clusters know each other,the clus-ters contain links of very high embeddedness,even though they do not necessarily correspond to particularly strong ties. In contrast,the links to a person’s relationship partner or other closest friends may have lower embeddedness,but they will often involve mutual neighbors from several different foci,re-ﬂecting the fact that the social orbits of these close friends are Figure a user u;the links value in this embeddedness of4.of interme-diaries u-h link has greaternot bounded within any one focus—consider,for example,a husband who knows several of his wife’s co-workers,family members,and former classmates,even though these people belong to different foci and do not know each other. Thus,instead of embeddedness,we propose that the link be-tween an individual u and his or her partner v should display a ‘dispersed’structure:the mutual neighbors of u and v are not well-connected to one another,and hence u and v act jointly as the only intermediaries between these different parts of the network.(See Figure2for an illustration.)We now formulate a sequence of deﬁnitions that captures this idea of dispersion.To begin,we take the subgraph G u in-duced on u and all neighbors of u,and for a node v in G u we deﬁne C uv to be the set of common neighbors of u and v.To express the idea that pairs of nodes in C uv should be far apart in G u when we do not consider the two-step paths through u and v themselves,we deﬁne the absolute dispersion of the u-v link,disp(u,v),to be the sum of all pairwise distances between nodes in C uv,as measured in G u−{u,v};that is,disp(u,v)=s,t∈C uvd v(s,t),where d v is a distance function on the nodes of C uv.The function d v need not be the standard graph-theoretic distance; different choices of d v will give rise to different measures of absolute dispersion.As we discuss in more detail below, among a large class of possible distance functions,we ulti-matelyﬁnd the best performance when we deﬁne d v(s,t)to be the function equal to1when s and t are not directly linked and also have no common neighbors in G u other than u and v,and equal to0otherwise.For the present discussion,we will use this distance function as the basis for our measures of dispersion;below we consider the effect of alternative dis-tance functions.For example,in Figure2,disp(u,h)=4un-der this deﬁnition and distance function,since there are four pairs of nodes in C uh that are not directly linked and also have no neighbors in common in G u−{u,h}.In contrast, disp(u,b)=1in Figure2,since a and e form the only pair0.4550.46 0.465 0.47 0.475 0.48 0.485 0.49 0.495 0.5 0.505 0.51 00.20.40.60.811.21.4 1.6 1.8 2P r e c i s i o n a t f i r s t p o s i t i o nExponent alphaPerformance of (Dispersion + b)^a/(Embededness + c)Precision@1Figure 3.Performance of (disp (u,v )+b )α/(emb (u,v )+c )as a func-tion of α,when choosing optimal values of b and c .type embed rec.disp.photo prof.view.all0.2470.5060.4150.301married0.3210.6070.4490.210married (fem)0.2960.5510.3910.202married (male)0.3470.6670.5110.220engaged0.1790.4460.4420.391engaged (fem)0.1710.3990.3860.401engaged (male)0.1850.4900.4950.381relationship0.1320.3440.3470.441relationship (fem)0.1390.3160.2900.467relationship (male)0.1250.3690.3990.418Figure 4.The performance of different measures for identifying spouses and romantic partners:the numbers in the table give the precision at the ﬁrst position —the fraction of instances in which the user ranked ﬁrst by the measure is in fact the true partner.Averaged over all instances,re-cursive dispersion performs approximately twice as well as the standard notion of embeddedness,and also better overall than measures based on proﬁle viewing and presence in the same photo.of non-neighboring nodes in C ub that have no neighbors in common in G u −{u,b }.Strengthenings of Dispersion.We can learn a function that predicts whether or not v is the partner of u in terms of the two variables disp (u,v )and emb (u,v ),where the latter denotes the embeddedness of the u -v link.We ﬁnd that performance is highest for functions that are monotonically increasing in disp (u,v )and monotonically decreasing in emb (u,v ):for a ﬁxed value of disp (u,v ),increased embeddedness is in fact a negative pre-dictor of whether v is the partner of u .A simple combina-tion of these two quantities that comes within a few percent of more complicated functional forms can be obtained by the expression disp (u,v )/emb (u,v ),which we term the normal-ized dispersion norm (u,v )since it normalizes the absolute dispersion by the embeddedness.Predicting u ’s partner to be the individual v maximizing norm (u,v )gives the correct answer in 48.0%of all instances.There are two strengthenings of the normalized dispersion that lead to increased performance.The ﬁrst is to rank nodes by a function of the form (disp (u,v )+b )α/(emb (u,v )+c ).Searching over choices of α,b ,and c leads to maximum per-formance of 50.5%at α=0.61,b =0,and c =5;see Figure 3.Alternately,one can strengthen performance by ap-type embed rec.disp.photo prof.view.all0.3910.6880.5280.389married0.4620.7580.5610.319married (fem)0.4880.7640.5380.350married (male)0.4350.7510.5860.287engaged0.3350.6520.5530.457engaged (fem)0.3750.6740.5360.492engaged (male)0.2960.6300.5680.424relationship0.2770.5720.4600.498relationship (fem)0.3180.6000.4400.545relationship (male)0.2390.5460.4790.455Figure 5.The performance of the four measures from Figure 4when the goal is to identify the partner or a family member in the ﬁrst position of the ranked list.The difference in performance between the genders has largely vanished,and in some cases is inverted relative to Figure 4.plying the idea of dispersion recursively —identifying nodes v for which the u -v link achieves a high normalized disper-sion based on a set of common neighbors C uv who,in turn,also have high normalized dispersion in their links with u .To carry out this recursive idea,we assign values to the nodes reﬂecting the dispersion of their links with u ,and then update these values in terms of the dispersion values associated with other nodes.Speciﬁcally,we initially deﬁne x v =1for all neighbors v of u ,and then iteratively update each x v to bew ∈C uv x 2w +2 s,t ∈C uv d v (s,t )x s x temb (u,v ).Note that after the ﬁrst iteration,x v is 1+2·norm (u,v ),and hence ranking nodes by x v after the ﬁrst iteration is equiv-alent to ranking nodes by norm (u,v ).We ﬁnd the highest performance when we rank nodes by the values of x v after the third iteration.For purposes of later discussion,we will call this value x v in the third iteration the recursive disper-sion rec (u,v ),and will focus on this as the main examplar from our family of related dispersion-based measures.(See the Appendix for further mathematical properties of the re-cursive dispersion.)PERFORMANCE OF STRUCTURAL AND INTERACTION MEASURESWe summarize the performance of our methods in Figure 4.Looking initially at just the ﬁrst two columns in the top row of numbers (‘all’),we have the overall performance of embed-dedness and recursive dispersion —the fraction of instances on which the highest-ranked node under these measures is in fact the partner.As we will see below in the discussion around Figure 6,recursive dispersion also has higher perfor-mance than a wide range of other basic structural measures.We can also compare these structural measures to features de-rived from a variety of different forms of real-time interaction between users —including the viewing of proﬁles,sending of messages,and co-presence at events.The use of such ‘inter-action features’as a comparison baseline is motivated by the way in which tie strength can be estimated from the volume of interaction between two people [8,17].Within this category of interaction features,the two that consistently display the best performance are to rank neighbors of u by the number ofphotos in which they appear with u,and to rank neighbors of u by the total number of times that u has viewed their proﬁle page in the previous90days.The last two columns of Fig-ure4show the performance of these two measures;on the set of instances as a whole,recursive dispersion performs better than these features.The remaining rows of Figure4show the performance of these measures on different subsets of the data.Most users who report a relationship partner on Facebook list themselves as either‘married’or‘in a relationship,’with a smaller num-ber who are‘engaged.’The performance of the structural measures is much higher for married users(60.7%)than for users in a relationship(34.4%);the opposite is true for pro-ﬁle viewing,which in fact achieves higher performance than recursive dispersion for users in a relationship.The perfor-mance for users who are engaged is positioned between the extremes of‘married’and‘in a relationship.’In addition,we see important differences based on gen-der.The performance of structural measures is signiﬁcantly higher for males than for females,suggesting some of the ways in which relationship partners produce more visible structural effects—at least according to these measures—on the network neighborhoods of men.And for certain more focused subsets of the data,the performance is even stronger; for example,on the subset corresponding to married male Facebook users in the United States,the friend with the high-est recursive dispersion is the user’s spouse76.9%of the time. We can also evaluate performance on the subset of users in same-sex relationships.Here we focus on users whose status is‘in a relationship.’1The relative performance of our struc-tural measures is exactly the same for same-sex relationships as for the set of all relationships,with recursive dispersion achieving close to twice the performance of embeddedness, and slightly higher performance than absolute and normal-ized dispersion.For female users,the absolute level of per-formance is almost identical regardless of whether their listed partner is female or male;for male users,the performance is signiﬁcantly higher for relationships in which the partner is male.(For a same-sex relationship listed by a male user,re-cursive dispersion identiﬁes the partner with a performance of .450,in contrast with the performance of.369for all partners of male users shown in Figure4.)Finally,returning to the set of all relationships,when the user v who scores highest under one of these measures is not the partner of u,what role does v play among u’s network neigh-bors?Weﬁnd that v is often a family member of u;for mar-ried users(Figure5),the friend v that maximizes rec(u,v)is the partner or a family member over75%of the time.We also see that when we ask for the top-ranked friend to be either the 1There is signiﬁcant informal evidence that the‘married’relation-ship status is employed by younger users of the same gender for a range of purposes even when they are not,in fact,married.While we only include users of age at least20in our sample,the effectis present in that age range.Listing a relationship status that does not correspond to one’s off-line relationship is of course a concern across all categories of users,but from investigation of this issue,the ‘married’status for users of the same gender is the only category for which we see evidence that this is a signiﬁcant factor.distance type all marr.eng.rel. threshold2absolute0.2790.3610.2050.152normalized0.3050.3940.2270.168recursive0.2100.2790.1410.105 threshold3absolute0.4300.5300.3590.270normalized0.4860.5880.4250.322recursive0.5060.6070.4460.344 threshold4absolute0.4730.5680.4140.321normalized0.4830.5700.4340.342recursive0.4550.5390.4050.319 diff component absolute0.3800.4610.3170.253normalized0.3640.4330.3080.258recursive0.3230.3840.2760.228 diff community absolute0.2860.3680.2120.160normalized0.2960.3790.2210.167recursive0.2160.2830.1560.115 spring length absolute0.3790.4740.3070.229normalized0.4540.5530.3870.296recursive0.3960.4800.3410.261 Figure6.Performance of variants of the dispersion measure using dif-ferent underlying distance functions.measure all married engaged relationship betweenness0.4410.5350.3740.293 network constraint0.3070.3940.2320.171 Figure7.Performance of betweenness and network constraint as alter-nate measures of bridging.partner or a family member,rather than just the partner,the performance gap between the genders essentially vanishes in the case of married users,and becomes inverted in the case of users in a relationship—in this latter case,female users are more likely to have their partner or a family member at the top of the ranking by recursive dispersion.A Broader Set of Measures.Since measures of dispersion are based on an underlying dis-tance function d v,it is interesting to investigate how the per-formance depends on the choice of d v.In Figure6,we con-sider dispersion measures based on a range of natural choices for d v.as follows.•First,we can set a distance threshold r,and declare thatd v(s,t)=1when s and t are at least r hops apart inG u−{u,v},and d v(s,t)=0otherwise.The measure of dispersion we use above corresponds to the choice r=3; setting the threshold r=2simply requires that s and t are not directly connected,while setting r=4imposes a stricter requirement.•In a related vein,we could declare d v(s,t)=1if s and t belong to different connected components of G u−{u,v}, and d v(s,t)=0otherwise.This in effect follows the pre-ceding approach,but with the distance threshold r concep-tually set to be inﬁnite.•Since the idea of dispersion at a more general level is based on the notion that the common neighbors of u and v should belong to different‘parts’of the network,it is also natural。

花药开裂方式英文

花药开裂方式英文
English:
When it comes to the dehiscence or the opening of the anthers in a flower, there are two primary mechanisms through which this can occur. The first is longitudinal dehiscence, where the anther splits open along its length, usually through a line of weakness. The second is transverse dehiscence, in which the anther opens horizontally at the top, allowing the pollen to be released. These two methods of dehiscence ensure that the pollen is effectively dispersed from the anther to pollinate other flowers.
Chinese:
当谈到花药在花朵中开裂或敞开的方式时，存在两种主要的机制。

第一种是纵裂开裂，花药沿其长度裂开，通常是通过一条薄弱的线。

第二种是横裂开裂，花药在顶部水平开放，允许花粉释放。

这两种开裂方式确保花粉有效地从花药传播到其他花朵上进行授粉。

小学上册B卷英语第三单元期末试卷(含答案)

小学上册英语第三单元期末试卷(含答案)英语试题一、综合题(本题有50小题，每小题1分，共100分.每小题不选、错误，均不给分)1 The _______ (小豹) is very fast when it hunts.2 Chemical changes are usually _____ (irreversible).3 My favorite _____ is a dinosaur toy.4 How many hearts does an octopus have?A. OneB. TwoC. ThreeD. Four答案: C5 ts bloom at _____ (夜晚). Some pla6 What do we call a person who sings?A. SingerB. MusicianC. PerformerD. All of the above7 The __________ (全球化) has changed how we view history.8 The _____ (chicken) lays eggs.9 The flowers in the park are ________.10 We will go ______ during the summer. (camping)11 In which continent is Egypt located?A. AsiaB. EuropeC. AfricaD. South America答案:C12 We play basketball in the ______. (gym)13 A ______ is a geographical feature that attracts scientists.14 We can _____ (share) plants with friends.15 A solution that contains very little solute is called ______.16 A bluebird is a symbol of _______ (快乐).17 Herbs can be grown in ______ (花盆).18 How many legs does a spider have?A. SixB. EightC. TenD. Four答案：B19 The ________ was a series of conflicts fought for independence in Latin America.20 My mom is a __________ (心理辅导师).21 What is the main language spoken in the United States?A. SpanishB. FrenchC. EnglishD. Mandarin22 A ____ is known for its ability to jump great distances.23 What is the capital city of Finland?A. HelsinkiB. TampereC. OuluD. Espoo24 Which animal is known for its ability to change colors?A. ChameleonB. ElephantC. LionD. Eagle答案: A25 I like to _____ (探险) outdoors.26 The __________ (历史的视角变化) can illuminate new truths.27 The Earth's tilt causes the ______.28 The Moon has no water and very little ______.29 The process of condensation collects ______.30 The unit for measuring mass is ______.31 I have a toy _______ that can make me laugh.32 The movement of tectonic plates can cause ______ to form.33 My favorite type of ________ (饮料) is soda.34 What do we call a story with a moral lesson, often featuring animals?A. FableB. MythC. TaleD. Novel答案: A35 My ___ (小兔子) likes to jump around.36 The Earth's surface is covered with various types of ______.37 The girl loves to ________.38 The ________ (生态恢复行动) is ongoing.39 What color is the center of a target?A. RedB. BlueC. YellowD. Black答案:A40 What do we call the part of a tree that grows underground?A. TrunkB. BranchC. LeafD. Root答案: D. Root41 Which animal is known for its ability to change colors?A. ChameleonB. SnakeC. FrogD. Lizard答案:A42 What is the capital city of Nicaragua?A. ManaguaB. LeónC. GranadaD. Masaya43 The sun helps plants to ______ (生长) by providing light.44 The chemical reaction that occurs in batteries involves _______ reactions.45 What is the opposite of bright?A. DarkB. DullC. FadedD. Blurry46 The __________ (自然环境) influences our daily lives.47 My dad is my strong _______ who teaches me valuable lessons about life.48 The _______ is often used in herbal medicine.49 The _____ (ancient) Greeks made significant contributions to philosophy.50 My _______ (兔子) is very playful.51 My dog loves to . (我的狗喜欢_。

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Now, it is very clear that a microscopic study of the relativistic pion dispersion relation is needed. The pion dispersion relation has been studied extensively in the nonrelativistic nuclear matter5−7), the nonrelativistic particle - hole (ph) and delta - hole (∆h) excitation and short range correlation via Landau - Migdal parameters g′ are taken into account. The main conclusion is that the pion condensation, or the space - like branch of the pion dispersion relation in the critical region – zero energy and ﬁnite momentum, is removed by the short range correlation. Recently, there are some quasi-relativistic calculations on the ∆h excitation of the pion propagator at ﬁnite temperature8,9,10). In ref. 10, Helgesson and Randrup used a so called realistic π + NN−1 + ∆N−1 model to calculate the pion dispersion relation in nuclear matter, they found a very unusual but interesting result10). That is, besides the usual collective modes there is a number of modes they named noncollective modes. One group of this noncollective modes shows pion condensation. These are diﬀerent from the previous results. The real relativistic calculation can be found in a recent comprehensive study11). But as we have pointed out and will show it later that by using ”Feynman” and ”Density dependent” nucleon propagator and Feynman propagator for delta isobars, the formulae for the relativistic ph and ∆h excitation can not be derived correctly12,13). We have found a new method and solved this problem 12,13). This method has been used to study other properties of nuclear matter , such as dimesonic function14) and the binding energy of nuclear matter 15,16). Our method is as follows: to express nucleon propagator in nuclear matter in terms of particle,
1
1 Introduction
The pionic collective excitation and pion dispersion relation in nuclear matter (or in ﬁnite nuclei) is very important to many ﬁelds in nuclear physics. A typical example is the dilepton production in relativistic heavy - ion collision in the energy region of ρ meson production1−4), where the production rate is determined by the pion dispersion relation and its derivative. The vanishing derivatives of the dispersion relation curve may lead to a huge enhancement of the dilepton production rate. In ref.2), Xia et al calculated the rate by using nonrelativistic pion dispersion relation which has very good behavior for all momentum and energy. But it is not sure whether the nonrelativistic approximation is still applicable to very high energy momentum transfer region. On the other hand, as far as pion dispersion relation is concerned, the imaginary part of the polarization insertion of pion propagator should not be ignored in the calculation.
2
hole, antiparticle propagators, and particle, antiparticle propagators for ∆-isobars. Then the polarization insertion can be explicitly split as ph, particle - antiparticle (NN¯ ) and ∆h, antidelta - particle (∆¯ N), delta - antiparticle (∆N¯ ) excitations contribution. The ph and ∆h excitations are ﬁnite, others are divergent and need a scheme to renormalize it. The ph and ∆h are the most fundamental and important excitation modes for pion propagator in nuclear matter, the thresholds for their physical production are the lowest among all possible excitations. So it is necessary to understand their contribution to the pion propagator ﬁrst. In this paper, we will study their polarization insertions, especially the imaginary part, and pion dispersion relation.
AND
Department of Physics, Zhongshan University Guangzhou, Guangdong 51027akano University of Occupational and Environmental Health
Kitakyusyu 807, Japan
Abstract We put forward a formalism to calculate the relativistic particle - hole and delta hole excitation polarization insertion for pion propagator by using the particle - hole antiparticle representation of nucleon and delta propagators in nuclear matter. The real and the imaginary part of the polarization insertion and the dispersion relation for pion propagator are calculated numerically. We ﬁnd that the short range correlation enhances the delta - hole excitation but suppresses the particle - hole excitation, it also suppresses the pion condensation. We ﬁnd that the eﬀect of the short range correlation on the pion dispersion relation depends very much on the form of the short range correlation and the parameters involved.