Dynamical Properties of a Haldane Gap Antiferromagnet

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Abstract
The phase-ﬁeld method has become an important and extremely versatile technique for simulating microstructure evolution at the mesoscale. Thanks to the diffuse-interface approach, it allows us to study the evolution of arbitrary complex grain morphologies without any presumption on their shape or mutual distribution. It is also straightforward to account for different thermodynamic driving forces for microstructure evolution, such as bulk and interfacial energy, elastic energy and electric or magnetic energy, and the effect of different transport processes, such as mass diffusion, heat conduction and convection. The purpose of the paper is to give an introduction to the phase-ﬁeld modeling technique. The concept of diffuse interfaces, the phase-ﬁeld variables, the thermodynamic driving force for microstructure evolution and the kinetic phase-ﬁeld equations are introduced. Furthermore, common techniques for parameter determination and numerical solution of the equations are discussed. To show the variety in phase-ﬁeld models, different model formulations are exploited, depending on which is most common or most illustrative. c 2007 Elsevier Ltd. All rights reserved.

Understanding individual human mobility patterns

a r X i v :0806.1256v 1 [p h y s i c s .s o c -p h ] 7 J u n 2008Understanding individual human mobility patternsMarta C.Gonz´a lez,1,2C´e sar A.Hidalgo,1and Albert-L´a szl´o Barab´a si 1,2,31Center for Complex Network Research and Department of Physics and Computer Science,University of Notre Dame,Notre Dame IN 46556.2Center for Complex Network Research and Department of Physics,Biology and Computer Science,Northeastern University,Boston MA 02115.3Center for Cancer Systems Biology,Dana Farber Cancer Institute,Boston,MA 02115.(Dated:June 7,2008)Despite their importance for urban planning [1],trafﬁc forecasting [2],and the spread of biological [3,4,5]and mobile viruses [6],our understanding of the basic laws govern-ing human motion remains limited thanks to the lack of tools to monitor the time resolved location of individuals.Here we study the trajectory of 100,000anonymized mobile phone users whose position is tracked for a six month period.We ﬁnd that in contrast with the random trajectories predicted by the prevailing L´e vy ﬂight and random walk models [7],human trajectories show a high degree of temporal and spatial regularity,each individual being characterized by a time independent characteristic length scale and a signiﬁcant prob-ability to return to a few highly frequented locations.After correcting for differences in travel distances and the inherent anisotropy of each trajectory,the individual travel patterns collapse into a single spatial probability distribution,indicating that despite the diversity of their travel history,humans follow simple reproducible patterns.This inherent similarity in travel patterns could impact all phenomena driven by human mobility,from epidemic prevention to emergency response,urban planning and agent based modeling.Given the many unknown factors that inﬂuence a population’s mobility patterns,ranging from means of transportation to job and family imposed restrictions and priorities,human trajectories are often approximated with various random walk or diffusion models [7,8].Indeed,early mea-surements on albatrosses,bumblebees,deer and monkeys [9,10]and more recent ones on marine predators [11]suggested that animal trajectory is approximated by a L´e vy ﬂight [12,13],a random walk whose step size ∆r follows a power-law distribution P (∆r )∼∆r −(1+β)with β<2.While the L´e vy statistics for some animals require further study [14],Brockmann et al.[7]generalized this ﬁnding to humans,documenting that the distribution of distances between consecutive sight-ings of nearly half-million bank notes is fat tailed.Given that money is carried by individuals, bank note dispersal is a proxy for human movement,suggesting that human trajectories are best modeled as a continuous time random walk with fat tailed displacements and waiting time dis-tributions[7].A particle following a L´e vyﬂight has a signiﬁcant probability to travel very long distances in a single step[12,13],which appears to be consistent with human travel patterns:most of the time we travel only over short distances,between home and work,while occasionally we take longer trips.Each consecutive sightings of a bank note reﬂects the composite motion of two or more indi-viduals,who owned the bill between two reported sightings.Thus it is not clear if the observed distribution reﬂects the motion of individual users,or some hitero unknown convolution between population based heterogeneities and individual human trajectories.Contrary to bank notes,mo-bile phones are carried by the same individual during his/her daily routine,offering the best proxy to capture individual human trajectories[15,16,17,18,19].We used two data sets to explore the mobility pattern of individuals.Theﬁrst(D1)consists of the mobility patterns recorded over a six month period for100,000individuals selected randomly from a sample of over6million anonymized mobile phone users.Each time a user initiates or receives a call or SMS,the location of the tower routing the communication is recorded,allowing us to reconstruct the user’s time resolved trajectory(Figs.1a and b).The time between consecutive calls follows a bursty pattern[20](see Fig.S1in the SM),indicating that while most consecutive calls are placed soon after a previous call,occasionally there are long periods without any call activity.To make sure that the obtained results are not affected by the irregular call pattern,we also study a data set(D2)that captures the location of206mobile phone users,recorded every two hours for an entire week.In both datasets the spatial resolution is determined by the local density of the more than104mobile towers,registering movement only when the user moves between areas serviced by different towers.The average service area of each tower is approximately3km2 and over30%of the towers cover an area of1km2or less.To explore the statistical properties of the population’s mobility patterns we measured the dis-tance between user’s positions at consecutive calls,capturing16,264,308displacements for the D1and10,407displacements for the D2datasets.Weﬁnd that the distribution of displacements over all users is well approximated by a truncated power-lawP(∆r)=(∆r+∆r0)−βexp(−∆r/κ),(1)withβ=1.75±0.15,∆r0=1.5km and cutoff valuesκ|D1=400km,andκ|D2=80km(Fig.1c,see the SM for statistical validation).Note that the observed scaling exponent is not far fromβB=1.59observed in Ref.[7]for bank note dispersal,suggesting that the two distributions may capture the same fundamental mechanism driving human mobility patterns.Equation(1)suggests that human motion follows a truncated L´e vyﬂight[7].Yet,the observed shape of P(∆r)could be explained by three distinct hypotheses:A.Each individual follows a L´e vy trajectory with jump size distribution given by(1).B.The observed distribution captures a population based heterogeneity,corresponding to the inherent differences between individuals.C.A population based heterogeneity coexists with individual L´e vy trajectories,hence(1)represents a convolution of hypothesis A and B.To distinguish between hypotheses A,B and C we calculated the radius of gyration for each user(see Methods),interpreted as the typical distance traveled by user a when observed up to time t(Fig.1b).Next,we determined the radius of gyration distribution P(r g)by calculating r g for all users in samples D1and D2,ﬁnding that they also can be approximated with a truncated power-lawP(r g)=(r g+r0g)−βr exp(−r g/κ),(2) with r0g=5.8km,βr=1.65±0.15andκ=350km(Fig.1d,see SM for statistical validation). L´e vyﬂights are characterized by a high degree of intrinsic heterogeneity,raising the possibility that(2)could emerge from an ensemble of identical agents,each following a L´e vy trajectory. Therefore,we determined P(r g)for an ensemble of agents following a Random Walk(RW), L´e vy-Flight(LF)or Truncated L´e vy-Flight(T LF)(Figure1d)[8,12,13].Weﬁnd that an en-semble of L´e vy agents display a signiﬁcant degree of heterogeneity in r g,yet is not sufﬁcient to explain the truncated power law distribution P(r g)exhibited by the mobile phone users.Taken together,Figs.1c and d suggest that the difference in the range of typical mobility patterns of indi-viduals(r g)has a strong impact on the truncated L´e vy behavior seen in(1),ruling out hypothesis A.If individual trajectories are described by a LF or T LF,then the radius of gyration should increase in time as r g(t)∼t3/(2+β)[21,22]while for a RW r g(t)∼t1/2.That is,the longer we observe a user,the higher the chances that she/he will travel to areas not visited before.To check the validity of these predictions we measured the time dependence of the radius of gyration for users whose gyration radius would be considered small(r g(T)≤3km),medium(20<r g(T)≤30km)or large(r g(T)>100km)at the end of our observation period(T=6months).Theresults indicate that the time dependence of the average radius of gyration of mobile phone users is better approximated by a logarithmic increase,not only a manifestly slower dependence than the one predicted by a power law,but one that may appear similar to a saturation process(Fig.2a and Fig.S4).In Fig.2b,we have chosen users with similar asymptotic r g(T)after T=6months,and measured the jump size distribution P(∆r|r g)for each group.As the inset of Fig.2b shows,users with small r g travel mostly over small distances,whereas those with large r g tend to display a combination of many small and a few larger jump sizes.Once we rescale the distributions with r g(Fig.2b),weﬁnd that the data collapses into a single curve,suggesting that a single jump size distribution characterizes all users,independent of their r g.This indicates that P(∆r|r g)∼r−αg F(∆r/r g),whereα≈1.2±0.1and F(x)is an r g independent function with asymptotic behavior F(x<1)∼x−αand rapidly decreasing for x≫1.Therefore the travel patterns of individual users may be approximated by a L´e vyﬂight up to a distance characterized by r g. Most important,however,is the fact that the individual trajectories are bounded beyond r g,thus large displacements which are the source of the distinct and anomalous nature of L´e vyﬂights, are statistically absent.To understand the relationship between the different exponents,we note that the measured probability distributions are related by P(∆r)= ∞0P(∆r|r g)P(r g)dr g,whichsuggests(see SM)that up to the leading order we haveβ=βr+α−1,consistent,within error bars, with the measured exponents.This indicates that the observed jump size distribution P(∆r)is in fact the convolution between the statistics of individual trajectories P(∆r g|r g)and the population heterogeneity P(r g),consistent with hypothesis C.To uncover the mechanism stabilizing r g we measured the return probability for each indi-vidual F pt(t)[22],deﬁned as the probability that a user returns to the position where it was ﬁrst observed after t hours(Fig.2c).For a two dimensional random walk F pt(t)should follow ∼1/(t ln(t)2)[22].In contrast,weﬁnd that the return probability is characterized by several peaks at24h,48h,and72h,capturing a strong tendency of humans to return to locations they visited before,describing the recurrence and temporal periodicity inherent to human mobility[23,24].To explore if individuals return to the same location over and over,we ranked each location based on the number of times an individual was recorded in its vicinity,such that a location with L=3represents the third most visited location for the selected individual.Weﬁnd that the probability ofﬁnding a user at a location with a given rank L is well approximated by P(L)∼1/L, independent of the number of locations visited by the user(Fig.2d).Therefore people devote mostof their time to a few locations,while spending their remaining time in5to50places,visited with diminished regularity.Therefore,the observed logarithmic saturation of r g(t)is rooted in the high degree of regularity in their daily travel patterns,captured by the high return probabilities(Fig.2b) to a few highly frequented locations(Fig.2d).An important quantity for modeling human mobility patterns is the probabilityΦa(x,y)toﬁnd an individual a in a given position(x,y).As it is evident from Fig.1b,individuals live and travel in different regions,yet each user can be assigned to a well deﬁned area,deﬁned by home and workplace,where she or he can be found most of the time.We can compare the trajectories of different users by diagonalizing each trajectory’s inertia tensor,providing the probability ofﬁnding a user in a given position(see Fig.3a)in the user’s intrinsic reference frame(see SM for the details).A striking feature ofΦ(x,y)is its prominent spatial anisotropy in this intrinsic reference frame(note the different scales in Fig3a),and weﬁnd that the larger an individual’s r g the more pronounced is this anisotropy.To quantify this effect we deﬁned the anisotropy ratio S≡σy/σx, whereσx andσy represent the standard deviation of the trajectory measured in the user’s intrinsic reference frame(see SM).Weﬁnd that S decreases monotonically with r g(Fig.3c),being well approximated with S∼r−ηg,forη≈0.12.Given the small value of the scaling exponent,other functional forms may offer an equally goodﬁt,thus mechanistic models are required to identify if this represents a true scaling law,or only a reasonable approximation to the data.To compare the trajectories of different users we remove the individual anisotropies,rescal-ing each user trajectory with its respectiveσx andσy.The rescaled˜Φ(x/σx,y/σy)distribution (Fig.3b)is similar for groups of users with considerably different r g,i.e.,after the anisotropy and the r g dependence is removed all individuals appear to follow the same universal˜Φ(˜x,˜y)prob-ability distribution.This is particularly evident in Fig.3d,where we show the cross section of ˜Φ(x/σ,0)for the three groups of users,ﬁnding that apart from the noise in the data the curves xare indistinguishable.Taken together,our results suggest that the L´e vy statistics observed in bank note measurements capture a convolution of the population heterogeneity(2)and the motion of individual users.Indi-viduals display signiﬁcant regularity,as they return to a few highly frequented locations,like home or work.This regularity does not apply to the bank notes:a bill always follows the trajectory of its current owner,i.e.dollar bills diffuse,but humans do not.The fact that individual trajectories are characterized by the same r g-independent two dimen-sional probability distribution˜Φ(x/σx,y/σy)suggests that key statistical characteristics of indi-vidual trajectories are largely indistinguishable after rescaling.Therefore,our results establish the basic ingredients of realistic agent based models,requiring us to place users in number propor-tional with the population density of a given region and assign each user an r g taken from the observed P(r g)ing the predicted anisotropic rescaling,combined with the density function˜Φ(x,y),whose shape is provided as Table1in the SM,we can obtain the likelihood ofﬁnding a user in any location.Given the known correlations between spatial proximity and social links,our results could help quantify the role of space in network development and evolu-tion[25,26,27,28,29]and improve our understanding of diffusion processes[8,30].We thank D.Brockmann,T.Geisel,J.Park,S.Redner,Z.Toroczkai and P.Wang for discus-sions and comments on the manuscript.This work was supported by the James S.McDonnell Foundation21st Century Initiative in Studying Complex Systems,the National Science Founda-tion within the DDDAS(CNS-0540348),ITR(DMR-0426737)and IIS-0513650programs,and the U.S.Ofﬁce of Naval Research Award N00014-07-C.Data analysis was performed on the Notre Dame Biocomplexity Cluster supported in part by NSF MRI Grant No.DBI-0420980.C.A.Hi-dalgo acknowledges support from the Kellogg Institute at Notre Dame.Supplementary Information is linked to the online version of the paper at /nature.Author Information Correspondence and requests for materials should be addressed to A.-L.B.(e-mail:alb@)[1]Horner,M.W.&O’Kelly,M.E.S Embedding economies of scale concepts for hub networks design.Journal of Transportation Geography9,255-265(2001).[2]Kitamura,R.,Chen,C.,Pendyala,R.M.&Narayaran,R.Micro-simulation of daily activity-travelpatterns for travel demand forecasting.Transportation27,25-51(2000).[3]Colizza,V.,Barrat,A.,Barth´e l´e my,M.,Valleron,A.-J.&Vespignani,A.Modeling the WorldwideSpread of Pandemic Inﬂuenza:Baseline Case and Containment Interventions.PLoS Medicine4,095-0110(2007).[4]Eubank,S.,Guclu,H.,Kumar,V.S.A.,Marathe,M.V.,Srinivasan,A.,Toroczkai,Z.&Wang,N.Controlling Epidemics in Realistic Urban Social Networks.Nature429,180(2004).[5]Hufnagel,L.,Brockmann,D.&Geisel,T.Forecast and control of epidemics in a globalized world.Proceedings of the National Academy of Sciences of the United States of America101,15124-15129 (2004).[6]Kleinberg,J.The wireless epidemic.Nature449,287-288(2007).[7] D.Brockmann,D.,Hufnagel,L.&Geisel,T.The scaling laws of human travel.Nature439,462-465(2006).[8]Havlin,S.&ben-Avraham,D.Diffusion in Disordered Media.Advances in Physics51,187-292(2002).[9]Viswanathan,G.M.,Afanasyev,V.,Buldyrev,S.V.,Murphy,E.J.,Prince,P.A.&Stanley,H.E.L´e vyFlight Search Patterns of Wandering Albatrosses.Nature381,413-415(1996).[10]Ramos-Fernandez,G.,Mateos,J.L.,Miramontes,O.,Cocho,G.,Larralde,H.&Ayala-Orozco,B.,L´e vy walk patterns in the foraging movements of spider monkeys(Ateles geoffroyi).Behavioral ecol-ogy and Sociobiology55,223-230(2004).[11]Sims D.W.et al.Scaling laws of marine predator search behaviour.Nature451,1098-1102(2008).[12]Klafter,J.,Shlesinger,M.F.&Zumofen,G.Beyond Brownian Motion.Physics Today49,33-39(1996).[13]Mantegna,R.N.&Stanley,H.E.Stochastic Process with Ultraslow Convergence to a Gaussian:TheTruncated L´e vy Flight.Physical Review Letters73,2946-2949(1994).[14]Edwards,A.M.,Phillips,R.A.,Watkins,N.W.,Freeman,M.P.,Murphy,E.J.,Afanasyev,V.,Buldyrev,S.V.,da Luz,M.G.E.,Raposo,E.P.,Stanley,H.E.&Viswanathan,G.M.Revisiting L´e vyﬂightsearch patterns of wandering albatrosses,bumblebees and deer.Nature449,1044-1049(2007). [15]Sohn,T.,Varshavsky,A.,LaMarca,A.,Chen,M.Y.,Choudhury,T.,Smith,I.,Consolvo,S.,High-tower,J.,Griswold,W.G.&de Lara,E.Lecture Notes in Computer Sciences:Proc.8th International Conference UbiComp2006.(Springer,Berlin,2006).[16]Onnela,J.-P.,Saram¨a ki,J.,Hyv¨o nen,J.,Szab´o,G.,Lazer,D.,Kaski,K.,Kert´e sz,K.&Barab´a si A.L.Structure and tie strengths in mobile communication networks.Proceedings of the National Academy of Sciences of the United States of America104,7332-7336(2007).[17]Gonz´a lez,M.C.&Barab´a si,plex networks:From data to models.Nature Physics3,224-225(2007).[18]Palla,G.,Barab´a si,A.-L.&Vicsek,T.Quantifying social group evolution.Nature446,664-667(2007).[19]Hidalgo C.A.&Rodriguez-Sickert C.The dynamics of a mobile phone network.Physica A387,3017-30224.[20]Barab´a si,A.-L.The origin of bursts and heavy tails in human dynamics.Nature435,207-211(2005).[21]Hughes,B.D.Random Walks and Random Environments.(Oxford University Press,USA,1995).[22]Redner,S.A Guide to First-Passage Processes.(Cambridge University Press,UK,2001).[23]Schlich,R.&Axhausen,K.W.Habitual travel behaviour:Evidence from a six-week travel diary.Transportation30,13-36(2003).[24]Eagle,N.&Pentland,A.Eigenbehaviours:Identifying Structure in Routine.submitted to BehavioralEcology and Sociobiology(2007).[25]Yook,S.-H.,Jeong,H.&Barab´a si A.L.Modeling the Internet’s large-scale topology.Proceedings ofthe Nat’l Academy of Sciences99,13382-13386(2002).[26]Caldarelli,G.Scale-Free Networks:Complex Webs in Nature and Technology.(Oxford UniversityPress,USA,2007).[27]Dorogovtsev,S.N.&Mendes,J.F.F.Evolution of Networks:From Biological Nets to the Internet andWWW.(Oxford University Press,USA,2003).[28]Song C.M.,Havlin S.&Makse H.A.Self-similarity of complex networks.Nature433,392-395(2005).[29]Gonz´a lez,M.C.,Lind,P.G.&Herrmann,H.J.A system of mobile agents to model social networks.Physical Review Letters96,088702(2006).[30]Cecconi,F.,Marsili,M.,Banavar,J.R.&Maritan,A.Diffusion,peer pressure,and tailed distributions.Physical Review Letters89,088102(2002).FIG.1:Basic human mobility patterns.a,Week-long trajectory of40mobile phone users indicate that most individuals travel only over short distances,but a few regularly move over hundreds of kilometers. Panel b,displays the detailed trajectory of a single user.The different phone towers are shown as green dots,and the V oronoi lattice in grey marks the approximate reception area of each tower.The dataset studied by us records only the identity of the closest tower to a mobile user,thus we can not identify the position of a user within a V oronoi cell.The trajectory of the user shown in b is constructed from186 two hourly reports,during which the user visited a total of12different locations(tower vicinities).Among these,the user is found96and67occasions in the two most preferred locations,the frequency of visits for each location being shown as a vertical bar.The circle represents the radius of gyration centered in the trajectory’s center of mass.c,Probability density function P(∆r)of travel distances obtained for the two studied datasets D1and D2.The solid line indicates a truncated power law whose parameters are provided in the text(see Eq.1).d,The distribution P(r g)of the radius of gyration measured for the users, where r g(T)was measured after T=6months of observation.The solid line represent a similar truncated power lawﬁt(see Eq.2).The dotted,dashed and dot-dashed curves show P(r g)obtained from the standard null models(RW,LF and T LF),where for the T LF we used the same step size distribution as the onemeasured for the mobile phone users.FIG.2:The bounded nature of human trajectories.a,Radius of gyration, r g(t) vs time for mobile phone users separated in three groups according to theirﬁnal r g(T),where T=6months.The black curves correspond to the analytical predictions for the random walk models,increasing in time as r g(t) |LF,T LF∼t3/2+β(solid),and r g(t) |RW∼t0.5(dotted).The dashed curves corresponding to a logarithmicﬁt of the form A+B ln(t),where A and B depend on r g.b,Probability density function of individual travel distances P(∆r|r g)for users with r g=4,10,40,100and200km.As the inset shows,each group displays a quite different P(∆r|r g)distribution.After rescaling the distance and the distribution with r g(main panel),the different curves collapse.The solid line(power law)is shown as a guide to the eye.c,Return probability distribution,F pt(t).The prominent peaks capture the tendency of humans to regularly return to the locations they visited before,in contrast with the smooth asymptotic behavior∼1/(t ln(t)2)(solid line)predicted for random walks.d,A Zipf plot showing the frequency of visiting different locations.The symbols correspond to users that have been observed to visit n L=5,10,30,and50different locations.Denoting with(L)the rank of the location listed in the order of the visit frequency,the data is well approximated by R(L)∼L−1. The inset is the same plot in linear scale,illustrating that40%of the time individuals are found at theirﬁrsttwo preferred locations.FIG.3:The shape of human trajectories.a,The probability density functionΦ(x,y)ofﬁnding a mobile phone user in a location(x,y)in the user’s intrinsic reference frame(see SM for details).The three plots, from left to right,were generated for10,000users with:r g≤3,20<r g≤30and r g>100km.The trajectories become more anisotropic as r g increases.b,After scaling each position withσx andσy theresulting˜Φ(x/σx,y/σy)has approximately the same shape for each group.c,The change in the shape of Φ(x,y)can be quantiﬁed calculating the isotropy ratio S≡σy/σx as a function of r g,which decreases as S∼r−0.12(solid line).Error bars represent the standard error.d,˜Φ(x/σx,0)representing the x-axis cross gsection of the rescaled distribution˜Φ(x/σx,y/σy)shown in b.。

外文翻译---深部综放开采顶煤稳定性与支架承载研究

翻译部分Research on support bearing and top coal stability of fully mechanized caving face in deep mineABSTRACT: On the basis of geological and production conditions of 34223 fullymechanized caving face in Quantaicoal mine, the distribution of displacement field of topcoal deformation is analyzed by means of UDEC3.0 numerical calculating method, which indicates that the top coal deformation shows a characteristic offront-to-back dynamicunstable areas. And the impact of support rigidity and rotation angle of main roof onsupport bearing and on top coal deformation is investigated. Last, the feasibility of light-duty support used in fully mechanized caving face is also analyzed. introductionAlong with the wide application of top coal caving technology in fullymechanized mining face, the powered support for the top coal caving shows a varietyof development. And compared with the high-resistance powered support for top coal caving, the light-duty support for top coal caving is in common use due to suchadvantages as the lower working resistance, lower cost, light weight, and theconvenient operation. With the increase of mining depth, the face condition of “isolated island” formed by the mining sequence and the high stress ca used by deep mining results in a superimposition of rock stress in working face, which has a greatimpact on the rock and coal control and on the safetyin production. Under this condition, whether the light-duty support for top coal caving can be used successfully or not to realize a safe mining of a thick coal seam has become a hot topic. In this paper, on the basis of geological and production conditions of fully mechanized caving face with deep high stress in Quantai colliery, UDEC3.0 numerical calculating method is used to analyze and discuss the relations of the main roof movement and top coal deformation with the support bearing in order to provide some references for rational lectotype of the powered support in fully mechanized caving face in deep mining of thick coal seam.SIMULATED GEOLOGICAL AND PRODUCTIVE CONDITIONS No.3 coal seam is now exploited by 34223 working face of Quantai mine, the thickness of coal seam is 4.5 m, the dip angle is 2 ~ 14°, averaged by 7°. Its Protodyakonov coefficient f is 1.0, being soft in hardness and simple in structure, with a buried depth of 800 m. The inclined length of the working face is 140 m and the strike length is 708 m. Since the upper and low adjacent coal seams of this working face have already been mined out, during the face mining, the working face will become an “isolated island” form, being pendent in three sides. The immediate roof consists of sandy mudstone with a thickness of 3.4 m, and the main roof consists of sandstone with a thickness of 4.6 m. The immediate floor is composed of sandy mudstone with a thickness of 1.7 m. The geological structure of the working face is quite simple. And ZFZ2600-16/24 powered support for lower top coal caving is used as the face support. The setting load of the support is 1950 kN, with a workingresistance of 2600 kN and a supporting strength of 0.45 MPa. ESTABLISHMENT OF NUMERICAL CALCULATING MODEL The stability of top coal is influenced by both the support rigidity and the movement of main roof, but it can impact on the support bearing as well. In order to analyze the impact of the support rigidity and main roof movement on the stability of top coal and the impact of the stability of top coal on the working resistance of support, the numerical calculation model is established according to the geological condition of 34223 working face (Fig. 1). The model is 150min length and 30min height, with asimulating mining depth of800m. The gravity stress of the upper strata is exerted on the upper boundary of the model.The immediate roof and the top coal in the range of the roof-controlled area of the working face are considered as an emphasis to be studied.. In the calculation model, the excavation of the coal seam starts from the left boundary to make the rotation of main roof form a certain rotation angle. But the rotation angle of the main roof is relevant to the backfilling degree of the goaf, and in the simulation, the rotation angles of the main roof are determined to be 4.98°, 5.81°, and 8.16°, respectively. The simulated support is replaced by the rod element with certain rigidities, such as 40 kN/mm, 85 kN/mm, and 120 kN/mm, respectively. The mechanical parameters of various strata in the calculating model are listed in Table 1 and Table 2.Table 1 Simulating mechanical parameters of strataTable 2 Mechanical parameters of joint surface in simulating strataANALYSIS AND NUMERICALCALCULATING RESULTDeformation characteristic of top coalIf the support rigidity is 80 kN/mm and the rotation angle of the main roof is 5.81°,the displacement vector distribution of the top coal is shown in Figure 2. From Figure 2, it can be seen that the deformation of the top coal has mainly two areas. The first is the deformation nearby the goaf-side which causes the support to move toward the goaf direction, resulting in the transverse instability of support. And the softer the top coal is, the larger this area will be. The second is the deformation at the end face nearby the rib, which results in a serious deformation of the top coal at the end face and an enlargement of fall area.Therefore, according to the deformationImpact of rotation of main roof on top coal stabilityThe rotation of the main roof is an important factor influencing on the rock deformation, and its rotation angle is relevant to the backfilling degree of the rock fall in the goaf.It can be seen that the vertical and horizontal displacements of the top coal increase with the increase of the rotation angle. But if the rotation angle of main roof is small, the displacement is not obvious. The obvious impact of main roof rotation on the top coal deformation is shown in the vertical displacement of upper top coal and the horizontal displacement of lower top coalImpact of support rigidity on stability of top coalThe support rigidity is an important parameter to reflect the supporting performance of the support. Usually, to increase the support rigidity is favorable for controlling the roof. But as for the top coal caving, the impact degree of the support rigidity on top coal deformation is different under the influence of the mechanical characteristics of the top coal. .It can be seen that the increase of support rigidity can reduce the vertical displacement of top coal, and finally the vertical displacements of both upper and lower top coals tend to be the same. Meanwhile, the horizontal displacement wouldincrease with the increase of the support rigidity. So, if the support rigidity is raised properly and the horizontal component of the support toward the rib direction is kept unchanged, it should be favorable for the roof stability of the end face and for the stability of the rock-support system.From the above analysis, the support bearing is the comprehensive result of the support rigidity, the deformation and breakage degree of the top coal, and the rotation degree of the main roof. The increase of mining depth will increase the breakage degree of the top coal. The deformation and breakage characteristic of top coal determines that the support bearing is lowered with the increase of the support rigidity. Therefore, under mining condition of the fully mechanized caving face, if the main roof can form a relatively stable st ructure of “voussior beam”, the working resistance of support will be properly decreased and the light-duty support of top coal caving can be used.CONCLUSIONS1) The deformation of the top coal in roof-controlled area can be divided into two dynamic instable areas: the front one and the back one. And the size of the dynamic instable area is relevant to the hardness of the top coal. The joint of both areas may result in an instability of rock-support system. And under the condition of the soft coal, the occurrence of the front instable area should be avoided and the back instable area should be also reduced. But, in the condition of the hard coal, the back instable area should be properly enlarged to make it be favorable for the top coal caving.2) To increase the rotation angle of main roof will increase both the vertical displacement of upper top coal and the horizontal displacement of lower top coal. And to increase the support rigidity will decrease the vertical displacement of the top coal but increase the horizontal displacement, with the lower top coal in particular.3) The support bearing is the comprehensive result of the support rigidity, the deformation degree of the top coal, and the rotation degree of the main roof. As for fully mechanized caving face, if the main roof can form a relatively stable structure of “voussior beam”, the working resistance of support should be properly lowered, and then the light-duty support of top coal caving used is feasible.REFERENCES[1] Liu, C.Y., Cao, S.G. & Fang, X.Q. 2003. Relation between rock and support instope and its monitoring. Xuzhou: Press of China University of Mining & Technology.[2] Liu, C.Y., Cao, S.G. & Yang, P.J. 1999. Research on bearing characteristics of immediate roof in stope. Journal of Rock Pressure and Ground Control (3 - 4): 35 - 39.中文译文：深部综放开采顶煤稳定性与支架承载研究摘要:依据权台煤矿34223综放工作面的地质及生产条件，采用UDEC3.0数值计算方法，分析了顶煤变形的位移场分布，得出了顶煤变形呈前后动态失稳区特征，分析了老顶回转角、支架刚度对顶煤变形以及支架承载的影响规律，分析了综放开采采用轻型支架的可行性。

Fundamental properties and applications of quasi-local black hole horizons

a r X i v :0712.1575v 1 [g r -q c ] 10 D e c 2007Fundamental properties and applications of quasi-local black hole horizonsBadri Krishnan Max Planck Institut f¨u r Gravitationsphysik,Am M¨u hlenberg 1,D-14476Golm,Germany E-mail:badri.krishnan@aei.mpg.de Abstract.The traditional description of black holes in terms of event horizons is inadequate for many physical applications,especially when studying black holes in non-stationary spacetimes.In these cases,it is often more useful to use the quasi-local notions of trapped and marginally trapped surfaces,which lead naturally to the framework of trapping,isolated,and dynamical horizons.This framework allows us to analyze diverse facets of black holes in a uniﬁed manner and to signiﬁcantly generalize several results in black hole physics.It also leads to a number of applications in mathematical general relativity,numerical relativity,astrophysics,and quantum gravity.In this short review,I will discuss the basic ideas and recent developments in this framework,and summarize some of its applications with an emphasis on numerical relativity.1.Introduction The surface of a black hole has traditionally been deﬁned using event horizons.Event horizons play a fundamental role in many seminal investigations in black hole physics.This includes Hawking’s area increase theorem,black hole thermodynamics,the uniqueness theorems,black hole perturbation theory and the topological censorship results.Moreover,the most important family of black holes for many purposes are the Kerr-Newman black holes.Similarly for almost all astrophysical purposes,most studies are carried our using Kerr black holes.Given this list of successful results and applications,is there any real need to go beyond event horizons and Kerr black holes?There are indeed some situations where event horizons are not suﬃcient,and most of these have to do with the global nature of event horizons;we need to know the entire history of the spacetime in order to locate them.This leads to a practical problem for numerical relativity simulations.There is no way to locate event horizons using only Cauchy data at a given time without actually performing the simulation and constructing the full spacetime.Moreover,even after the event horizon is located,using it to calculate the physical parameters is fraught with diﬃculties.In particular,the Hamiltonian methods used to deﬁne the black hole parameters as generators of symmetries are not well adapted to the event horizon.All these problems are resolvedin the case when the spacetime is stationary.However we would like to go beyond stationarity,and even for black holes in equilibrium,it should not be necessary to require the entire spacetime to be stationary.One of the classic results of crucial importance to black holes which does not use event horizons are the singularity theorems of Penrose and Hawking[1,2].The presence of a closed trapped surface implies geodesic incompleteness in the future.Theﬁrst singularity theorem was proved by Penrose in1965[1],and this paper also introduced the notion of a trapped surface.We shall use Penrose’s trapped surfaces to study black holes quasi-locally,without relying on global properties of the spacetime.The rest of this review is organized as follows.Following a discussion of basic notions and deﬁnitions,we discuss the existence and non-uniqueness of quasi-local horizons,and the time evolution of marginally trapped surfaces in Sec.2.Sec.3discusses the black hole area increase law.Finally Sec.4describes some applications in numerical relativity. The reader should beware that this is a biased review of quasi-local horizons with a focus on numerical relativity applications.There are a number of other interesting mathematical and physical aspects of quasi-local horizons which we shall not have time to discuss.The reader is referred to[3,4,5]for more complete reviews and references. Trapped surfaces and the trapping regionThe expansion of a congruence of null geodesics is deﬁned as the rate of increase of an inﬁnitesimal transverse2-dimensional cross-section areaδA carried along with the geodesics:Θ=1dt.(1)The deﬁnitions of the shearσab and twistωab are also based on deformations of the cross-section.The particular geodesic congruence we consider are the ones orthogonal to a2-surface S.Let us denote the in-going and out-going null normals to S byℓa and n a respectively,and letΘ(ℓ)andΘ(n)be their respective expansions.For a sphere in ﬂat space,the out-going light rays are diverging and the ingoing ones are converging, i.e.Θ(ℓ)>0andΘ(n)<0.S is said to be a trapped surface if both sets of null-normals are converging:Θ(ℓ)<0andΘ(n)<0.A marginally trapped surface(MTS)is one for whichΘ(ℓ)=0andΘ(n)<0.As shown by the singularity theorems,the presence of such surfaces is the signature of a spacetime containing a black hole.Note however that this is not necessarily a signature of strong gravitationalﬁeld;they are present even for large black holes which have correspondingly small tidal forces at the horizon.It can be shown that trapped surfaces must lie inside the event horizon,and that cross-sections of the event horizon for stationary black holes are MTSs.The spacetime region T containing trapped surfaces is called the trapped region. Similarly,if we restrict our attention to a initial-data surfaceΣ,and to trapped surfaces lying onΣ,we can similarly deﬁne the trapped region TΣ⊂Σwhich is,by deﬁnition,a subset of the full four-dimensional trapped region.An apparent horizon is the outermost2.Fundamental properties of black hole horizonsLet us outline some basic deﬁnitions and properties of quasi-local horizons.The starting point for most of these constructions is the notion of a marginally trapped tube(MTT) deﬁned to be a three-surface of topology S2×R foliated by MTSs.It is useful to think of a MTT as being obtained by the time evolution of a MTS.The MTT is thus constructed by stacking up MTSs found at diﬀerent times.The various kinds of quasi-local horizons are MTTs with additional conditions on whether it is a spacelike,timelike or null surface, and additional geometric requirements onΘ(n).Name Additional conditions onΘ(n)andΘ(ℓ)NullSpacelikeTimelikeNo restrictionAn MTS S on a spatial sliceΣis said to be strictly-stably-outermost if there exists an inﬁnitesimalﬁrst order outward deformation which makes S strictly untrapped. Explicitly,if r is the unit spacelike normal to S onΣ,then we consider displacements of S(and geometricﬁelds on S)along f r for some function f;outward deformations have f≥0.Then S is strictly-stably-outermost if theﬁrst order variation of the expansion Θ(ℓ)is positive:δf rΘ(ℓ)>0for f≥0.A crucial tool in these results is the stability operator L r[f]:=δf rΘ(ℓ)which turns out to be an elliptic operator,and the stability condition can be recast as a condition on the principal eigenvalue of L;see also If this stability condition is satisﬁed,then the MTT produced by the time evolution of S exists at least for a suﬃciently short duration,and it continues to exist as long as this stability condition holds.Furthermore,the MTT in the neighborhood of S is either null or spacelike.It is spacelike of the matterﬂux T abℓaℓb is non-vanishing somewhere on S.The elliptic nature of L ensures that the MTT is spacelike everywhere in a neighborhood of S if theﬂux T abℓaℓb is non-zero even in a very small region on S.It should be emphasized that these results do not imply that the time development of S is unique.It in fact implies quite the opposite:for every choice of time evolution by a foliation by spacelike surfaces(i.e.for every choice of lapse and shift functions)there exists an MTT and the diﬀerent MTTs constructed from the diﬀerent gauge choices are,in general,distinct from each other.It is also worth noting that not all MTSs will satisfy the stability condition;the unstable MTSs will be inner horizons and actually occur quite frequently in numerical simulations[28](though they are usually not looked for).However,even the unstable MTSs always seem to evolve smoothly as far as the numerical simulations are concerned.This leads us to believe that the existence result might be of more general validity and it might be possible to extend the above techniques to prove this.See[33,34,35]for further results on trapped surfaces and quasi-local horizons using similar techniques.See also[36]for interesting numerical results on the behavior of MTTs in binary black hole spacetimes.Complementary to these existence results,there are other important results on dynamical horizons worth mentioning.In[37]it is proved that the foliation of a dynamical horizon H by MTSs is unique.This,together with the existence results above implies that for a given MTSs on an initial sliceΣ,the MTTs corresponding diﬀerent time developments must really be distinct as3-manifolds.There are also some restrictions on the location of the various dynamical horizons.For example,it is shown in[37]that for a given dynamical horizon H,there cannot be any closed MTSs(and thus no other DH)lying in the past domain of dependence of H.Thus, while DHs are far from unique,there are some restrictions on where they can occur.We brieﬂy mention results regarding the(non-)existence of dynamical horizons in spacetimes with symmetries[37,38,39].For example,it is shown in[38]that strictly stationary spacetime regions cannot contain trapped or marginally trapped surfaces,and thus no quasi-local horizons as well.Finally,a diﬀerent approach to studying dyamical horizons is presented in[40]which considers the conditions on the Cauchy data on H that must be satisﬁed if H is a dynamical horizon.This can be studied in spherical symmetry,and it leads to necessary conditions for the spacetime to contain a dynamical horizon; in this regard,see also[41].3.The second lawIn this section,we outline the second law for dynamical/trapping horizons and its ramiﬁcations.But before doing so,it is worth mentioning the signiﬁcant amount of work devoted to understanding theﬁrst law for quasi-local horizons.Theﬁst law connects variations in the mass M between two nearby black hole solutions to the surface gravity κ,area A,angular velocityΩand angular momentum J(the presence of other conserved charges is easy to incorporate):δM=κdt2−κdAThe right hand side of this equation contains the source terms from the infalling matter/radiation which causes the black hole to grow,and all terms in thus equation are quasi-local.The sign ofκis however a problem;it will generically lead to an exponential divergence if we attempt to solve(4)as an initial value problem.In fact,we need to impose dA/dt→0as t→∞to getﬁnite solutions.Can we reformulate the second law for quasi-local horizons?In fact,∆A>0is a simple consequence ofΘ(ℓ)=0andΘ(n)<0for dynamical horizons.We can do better. Performing the decomposition of all geometricﬁelds on a dynamical horizon,and using the constraint equations on a dynamical horizon,it can be shown thatR22G =F(R)m+F(R)g(5)whereF(R)g :=1dt2+κ′dAThey have so far been primarily used to extract gauge invariant information about the black hole such as its mass,angular momentum etc.,and this is what we shall mostly focus on in this section.However,there are also other important applications which we will not be able to discuss.This includes the construction of initial data with trapped and marginally trapped surfaces as the inner boundary[44,45,46,47,48,49],and the possibility of using fully constrained evolution schemes with a dynamical horizon as the inner boundary[50].There has also been interest in clarifying the deﬁnition of surface gravity pf a quasi-local horizon,and the closely related notion of extremality[51,52,53]. This could prove to be useful for mathematical and astrophysical applications.Mass and angular momentumNumerical simulations are based on the initial value formulation of general relativity. Thus we are given an initial data set(Σ,h ab,K ab)whereΣis a3-manifold embedded in the full spacetime,h ab a Riemannian metric onΣ,and K ab the second fundamental form describing howΣis embedded in the spacetime.Such an initial data set is evolved in time to construct the full spacetime.There are various formalisms for performing these evolutions and there are diﬀerent choices of the variables that can be evolved,but these issues are not of much concern for our purposes.We instead pose a straightforward question.AssumingΣto be some slice of the Kerr spacetime,and assuming thatΣintersects the event horizon in a complete sphere‡,how can we determine its parameters, i.e.its mass and angular momentum?Depending on the choice ofΣand the choice of coordinates onΣ,the shape of the apparent horizon may turn out to be quite complicated.It may not seem axisymmetric and it may even be diﬃcult to say whether we have a stationary black hole.Let us reformulate this question in a much more general context.Consider a quasi-local horizon H(i.e.an isolated,dynamical or trapping horizon)and let us assume that Σintersects H in a cross-section S which is a marginally trapped surface.We assume thatΣis an asymptoticallyﬂat slice with S as its inner boundary(the generalization to multiple black holes,i.e.when S consists of several disconnected components is straightforward).Let us assume that H is axisymmetric,i.e.it has a rotational vectorϕa which has closed orbits,vanishes at two points on each cross-section of the MTSs which foliate H,and which is a symmetry of the geometricalﬁelds on H.In particularϕa is a symmetry of the two metric q ab on every cross-section S of H.Note that we only asked forϕa to exist on H,and not in the full spacetime and not even in a neighborhood of H.of the horizon.Just like in It is then possible to associate an angular momentum J(ϕ)Sclassical mechanics where conserved quantities are deﬁned as generators of symmetries, this calculation is based on a Hamiltonian formalism.We calculate the generator of diﬀeomorphisms along a rotational vectorﬁeldφa which coincides withϕa on H and with an asymptotic rotational symmetry at inﬁnity[14,15,16,17,18](analogous calculations also work in2+1[19]and higher[20,21]dimensions).It is then easy to identify the ‡And also assuming that we have an eﬃcient way of locating marginally trapped surfaces onΣ.contribution of the horizon to the angular momentum,and it turns out to be given by a surface integral over S[54]:J(ϕ) S =1A S/4π,the horizon mass M(ϕ)SisM(ϕ)S =1R4S+4(J(ϕ)S)2.(9)This will give the correct answer for Kerr,and it is in fact also the result of a Hamiltonian calculation in the more general case of an axisymmetric quasi-local horizon.Apart from getting the magnitude of the spin,it is also possible to estimate the direction of the angular momentum vector.The basic idea is to use the poles ofϕa to deﬁne the axis of rotation.While the poles themselves are well deﬁned on a given quasi-local horizon,the procedure of assigning a vector is not as clear cut.For example, it is not clear how the spin direction thus obtained can be compared with the spin direction calculated at spatial inﬁnity.Nevertheless,this method has been applied and preliminary results are promising[57].Equation(8)is now being used fairly widely in numerical relativity,though there is possibly room for improvement in the calculation of the symmetry vectorﬁeldϕa along the lines of[55],for having a better conceptual understanding of the meaning of J(ϕ)Swhenϕa is only an approximate symmetry vector(which is invariably the case in numerical simulations),and also a better understanding of the spin direction which is important for astrophysical applications.§This may seem surprising because this is certainly not the case for a normal S2×R cylinder in Euclidean space.If there is a symmetry vectorϕa on the cylinder,it need not project to a symmetry vector on a given cross-section S of the cylinder.It is nevertheless true for an isolated horizon because ifϕa is a symmetry,then so isϕa+fℓa for any function f and null generatorℓa;projectingϕa to S is equivalent to a particular choice of f.Higher multipole momentsApart from calculating the angular momentum and mass,it turns out that it is also possible to meaningfully deﬁne the higher multipole moments of a quasi-local horizon, at least in the axi-symmetric case.This construction wasﬁrst carried out by[58]for isolated horizons,and subsequently applied by[3,28]to the general case of a dynamical horizon.The construction starts with a coordinate system built using the given axial vectorϕa.φ∈[0,2π)is aﬃne parameter alongϕa andζ=cosθdeﬁned by dζ∝⋆ϕ(the proportionality factor is chosen by requiring Sζd2V=0).Then we use the spherical harmonics in these(θ,φ)coordinates to deﬁne the mass and current multipole moments:M(ϕ)n=R n S M(ϕ)S8πSP′n(ζ)¯K abϕa d2S b(10)where P n is the n th order Legendre polynomial and P′n its derivative.These equations provides the source multipole moments of black hole,which are in general distinct from theﬁeld multipole moments deﬁned at inﬁnity.For isolated horizons,it can be shown[58]that the intrinsic horizon geometry is completely characterized by these multipole moments,i.e.any two isolated horizons with the same multipole moments are diﬀeomorphic to each other.J0vanishes by absence of monopole (NUT)charges,M0is mass and J1is angular momentum.In Kerr,M0and J1determine all higher moments.In Schwarzschild,only M0=0.The higher moments provide a convenient way of quantifying the deviation from Kerr.These multipole moments were applied in some example numerical simulations in[28]where it was shown that the black holes do indeed converge to Kerr very quickly after merger.However,the simulations were unfortunately not accurate enough to extract the late time decay rates of the multipole moments which would be the analog of Price’s law for dynamical horizons. Hopefully this can be measured in the future using long duration accurate simulations. Quasi-local linear momentumThe calculation of black hole linear momentum is of astrophysical importance in the context of the recoil velocity produced during the merger of two black holes.The reason for the recoil is the anisotropic emission of gravitational radiation.It has been found that certain initial spin conﬁgurations lead to a much larger than expected value of this recoil velocity and the largest contribution turns out to be from the merger phase.This result is especially interesting for the case of super-massive black holes;if the recoil is large enough,the remnant black hole may be kicked out of the host galaxy and this has important astrophysical implications.Most calculations of the recoil velocity are based on the gravitational waveform extracted far away from the black hole which measures the center-of-mass momentum of the system.It is thus natural to ask whether one can measure the momentum quasi-locally for the two individual black holes.This would be a useful consistency check and it could also give us more detailed information about the dynamics of the merger.The possibility of measuring the linear momentum,andmore generally the quasi-local energy-momentum four-vector,is also of mathematical interest.So far,we have justiﬁed the equations for angular momentum,mass and energy by Hamiltonian methods.For the angular momentum we assumed the existence of a rotational symmetry and for energy and mass we need to pick out a preferred time evolution vectorﬁeld at the horizon.Following the same line of reasoning,one might think of deﬁning linear momentum by assuming the existence of a translational symmetry in a neighborhood of the horizon,or at least some preferred translational vectorﬁeld.While it might be possible to do this in special cases,for example when the data is conformallyﬂat,it is clearly not something we can assume generally.Unlike for angular momentum where there are interesting regimes where approximate axisymmetry is a valid assumption,the basis for carrying over this approach to linear momentum is much less secure.Let us then try a more heuristic approach.Just as the formula for horizon angular momentum is analogous to the angular momentum at spatial inﬁnity,let us apply the formula for linear momentum at inﬁnity to the horizon.At spatial inﬁnity,for a given asymptotic translational Killing vectorﬁeldξa,the momentum isP ADM ξ=18πS(K ab−Kh ab)ξa dS b(12)whereξa is some translational vector at the ing the constraint equations of Σ,it is easy to showP ADM ξ−P(S)ξ=15060708090100110120t/M −80−60−40−20020406080P y /M (k m s −1)M/32M/48M/646575859510521252933Figure 2.Linear momentum of the remnant black hole produced by the headonmerger of black holes with anti-aligned spins for diﬀerent resolutions.behaved as one might have thought based on intuition about apparent horizons.It is possible to prove useful and interesting mathematical results about them and they can be used to study black hole physics.They have 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ZnS宽禁带半导体毕业设计

宽禁带半导体ZnS物性的第一性原理研究摘要硫化锌（ZnS）是一种新型的II-VI族宽禁带电子过剩本征半导体材料，其禁带宽度为3.67eV,具有良好的光致发光性能和电致发光性能。

在常温下禁带宽度是3.7eV，具有光传导性好，在可见光和红外范围分散度低等优点。

ZnS和基于ZnS的合金在半导体研究领域己经得到了越来越广泛的关注。

由于它们具有较宽的直接带隙和很大的激子结合能，在光电器件中具有很好的应用前景。

本文介绍了宽禁带半导体ZnS目前国内外的研究现状及其结构性质和技术上的应用。

阐述了密度泛函理论的基本原理，对第一性原理计算的理论基础作了详细的总结，并采用密度泛函理论的广义梯度近似（GGA）下的平面波贋势法，利用Castep软件计算了闪锌矿结构ZnS晶体的电子结构和光学性质。

电子结构如闪锌矿ZnS晶体的能带结构，态密度。

光学性质如反射率，吸收光谱，复数折射率，介电函数，光电导谱和损失函数谱。

通过对其能带及结构的研究，可知闪锌矿硫化锌为直接带隙半导体，通过一系列对光学图的分析，可以对闪锌矿ZnS的进一步研究做很好的预测。

关键词ZnS;宽禁带半导体；第一性原理；闪锌矿结构-I -First-principles Research on Physical Properties of Wide Bandgap Semiconductor ZnSAbstractZinc sulfide (ZnS) is a new family of ll-VI wide band gap electronic excess in tri nsic semic on ductor material with good photolu min esce nee properties and electroluminescent properties. At room temperature band gap is 3.7 eV, and there is good optical transmission in the visible and infrared range and low dispersi on. ZnS and Zn S-based alloy in the field of semic on ductor research has bee n paid more and more atte nti on. Because of their wide direct ban dgap and large excit on binding en ergy, the photovoltaic device has a good prospect.This thesis describes the current research status and structure of nature and tech ni cal applicati ons on wide band gap semic on ductor ZnS. Described the basic principles density functional theory, make a detailed summary for the basis of first principles theoretical calculations, using the density functional theory gen eralized gradie nt approximati on (GGA) un der the pla ne wave pseudopote ntial method, calculated using Castep software sphalerite ZnS crystal structure of electronic structure and optical properties. Electronic structures, such as sphalerite ZnS crystal band structure, density of states. Optical properties such as reflecta nee, absorpti on spectra, complex refractive in dex, dielectric function, optical conductivity spectrum and the loss function spectrum. Band and the structure through its research known as zin cble nde ZnS direct band gap semic on ductor,Through a series of optical map an alysis, can make a good predicti on for further study on zin cble nde ZnS.Keywords ZnS; Wide ban dgap semic on ductor; First-pri nciples; Zin cble nde structure-2-目录摘要 (I)Abstract (II)第1章绪论 ........................................................... 1..1.1 ZnS半导体材料的研究背景 ....................................... 1.1.2 ZnS的基本性质和应用........................................... 1.1.3 ZnS材料的研究方向和进展 (3)1.4 ZnS的晶体...................................................... 4.1.4.1 ZnS晶体结构 ............................................... 4.1.4.2 ZnS的能带结构............................................. 5.1.5 ZnS的发光机理................................................. 6.1.6研究目的和主要内容.............................................. 7.2.1相关理论......................................................... 9.2.1.1密度泛函理论 (9)2.1.2交换关联函数近似........................................... 1.12.2总能量的计算 (13)2.2.1势平面波方法 (14)2.2.2结构优化 (16)2.3 CASTEP软件包功能特点........................................ 1.8第3章ZnS晶体电子结构和光学性质.................................... 1.93.1闪锌矿结构ZnS的电子结构 (19)3.1.1晶格结构 (19)3.1.2能带结构 (20)3.1.3态密度 (21)3.2闪锌矿ZnS晶体的光学性质 (24)结论 (30)致谢 (31)参考文献 (32)附录A (33)附录B (45)-ill -第1章绪论1.1 ZnS半导体材料的研究背景Si是应用最为广泛的半导体材料，现代的大规模集成电路之所以成功推广应用，关键就在于Si半导体在电子器件方面的突破。

Studying of dynamic bear characteristics and adaptability of support in top coal caving

* Corresponding author. Tel.: 010-84263880-8108; fax: 010-84263556 E-mail address: lngdyulei@.
1877-7058 © 2011 Published by Elsevier Ltd. doi:10.1016/j.proeng.2011.11.2217
Table 1. The equipment coordination of 8105 working face Number 1 2 3 4 5 6 7 8 Name Shearer Front conveyor Rear conveyor Reloader Crusher Belt conveyor Emulsion pump Water spray pump Specifications MG750/1915-GWD SGZ1000/1710 SGZ1200/2000 PF6/1542 SK1118 DSJ140/350ห้องสมุดไป่ตู้3×500 BRW400/31.5 250kW BRW500/12.5 132kW Power(kW) 1915 2×855 2×1000 450 400 3×500 250 132 Capacity(t/h) 2000 2500 3000 3500 4250 3500 400L 500L
© 2011 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of China Academy of Safety Science and Technology, China University of Mining and Technology(Beijing), McGill University and Wollongong University

The Formation of Coral Reefs and Atolls

The Formation of Coral Reefs and Atolls Coral reefs and atolls are some of the most fascinating and diverse ecosystems on the planet. They are formed from the accumulation of calcium carbonate exoskeletons of coral polyps, which are tiny, invertebrate animals that live in colonies. These structures provide a habitat for a wide variety of marine life, including fish, invertebrates, and algae. The formation of coral reefs and atolls is a complex process that involves geological, biological, and environmental factors.One of the key factors in the formation of coral reefs and atolls is the presence of suitable substrate for coral growth. Coral polyps require a hard surface on which to attach and grow, and they typically thrive in warm, shallow, clear waters. As the polyps grow and reproduce, they form colonies that eventually build up into large, solid structures. Over time, the accumulation of coral skeletons creates the framework for a reef or atoll.The geological processes that contribute to the formation of coral reefs and atolls are also important to consider. Reefs often form along the edges of continents or around volcanic islands, where the ocean floor is relatively shallow. As the Earth's tectonic plates shift and move, these areas can experience changes in sea level and land elevation, which can impact the growth and development of coral reefs. Additionally, the presence of ocean currents and wave action can influence the shape and structure of reefs, as well as the distribution of coral species.In addition to geological factors, biological processes play a crucial role in the formation of coral reefs and atolls. Coral polyps rely on a symbiotic relationship with photosynthetic algae called zooxanthellae, which live within their tissues and provide them with essential nutrients. This relationship allows corals to thrive in nutrient-poor waters, but it also makes them sensitive to environmental stressors such as changes in temperature and water quality. When corals are stressed, they can expel their zooxanthellae, a process known as coral bleaching, which can have devastating effects on reef ecosystems.The environmental conditions in which coral reefs and atolls form and grow are also significant. These ecosystems are typically found in tropical and subtropical regions, wherethe water is warm and clear. The availability of sunlight is crucial for the photosynthetic processes of both corals and their symbiotic algae, so reefs are most commonly found in shallow waters where light can penetrate. Additionally, the stability of water temperature and chemistry is important for the health and growth of coral reefs, as they are sensitive to changes in conditions such as ocean acidification and pollution.Human activities also play a role in the formation and degradation of coral reefs and atolls. Overfishing, destructive fishing practices, coastal development, and pollution can all have negative impacts on reef ecosystems. Additionally, climate change is a major threat to coral reefs, as rising sea temperatures and ocean acidification are causing widespread coral bleaching and mortality. Conservation efforts, such as marine protected areas and sustainable fishing practices, are essential for the preservation of these valuable and vulnerable ecosystems.In conclusion, the formation of coral reefs and atolls is a complex and dynamic process that involves a combination of geological, biological, and environmental factors. These ecosystems are not only incredibly diverse and beautiful, but they also provide important ecological and economic benefits. Understanding the processes that shape coral reefs and atolls is crucial for their conservation and management, especially in the face of growing threats from human activities and climate change. As stewards of the natural world, it is our responsibility to protect and preserve these irreplaceable ecosystems for future generations.。

dynamic kinetic resolution

dynamic kinetic resolutionDynamic kinetic resolution (DKR) is an innovative process developed to achieve asymmetric synthesis in complex molecules. It is a type of chemical reaction which helps to obtain a target product with enhanced asymmetric selectivity by using a dynamic kinetic process. It is an environmentally friendly process which is cost-effective and offers shorter reaction timelines as compared to conventional methods.Dynamic kinetic resolution (DKR) consists of two parts, i.e., a kinetic resolution part and a dynamic resolution part. During the kinetic resolution part, a catalyst is used to promote a reaction between two similar molecules. The dynamicresolution part, on the other hand, involves a complex set of reactions in which two different components of a mixture are separated into two different fractions. The reaction is carried out at a temperature and pressure over a certain period of time such that the components are rearranged in accordance with the desired target product.The main advantage of dynamic kinetic resolution (DKR) is that it allows for the production of a target product with high chiral selectivity. This feature is essential for the production of enhanced enantioselective products. It also offers other advantages such as shorter reaction times, cost savings, and reduction of the use of hazardous chemicals. Moreover, it is a selective and targeted process which avoids the use of toxic and hazardous solvents and catalysts. Moreover, itis capable of producing chiral compounds in yields that exceed 50%.Dynamic kinetic resolution (DKR) is most commonly employed in the synthesis of chiral compounds such as natural products, pharmaceuticals, fine chemicals, and agrochemicals. This process is also used in the development of new drugs, fragrances, and optical brighteners. It is also used for the production of complex compounds and the separation of optically active compounds from racemic mixtures. DKR is a versatile and powerful method which provides high yields of the desired product with excellent selectivity.In conclusion, dynamic kinetic resolution (DKR) is a powerful and selective process which offers a number of advantages. It has many applications in the production of chiral compounds and the separation of optically active compoundsfrom racemic mixtures. It is also cost-effective, environmentally friendly and offers shorter reaction times as compared to conventional methods. Thus, DKR is an important tool for the production of complex molecules in organic chemistry.。

KMS states and complex multiplication

a r X i v :m a t h /0501424v 1 [m a t h .O A ] 24 J a n 2005KMS STATES AND COMPLEX MULTIPLICATIONALAIN CONNES,MATILDE MARCOLLI,AND NIRANJAN RAMACHANDRAN1.Introduction Several results point to deep relations between noncommutative geometry and class ﬁeld theory ([2],[9],[18],[20]).In [2]a quantum statistical mechanical system is exhibited,with partition function the Riemann zeta function,and whose arithmetic properties are related to the Galois theory of the maximal abelian extension of Q .In [9],this system is reinterpreted in terms of the geometry of commensurable 1-dimensional Q -lattices,and a generalization is constructed for 2-dimensional Q -lattices.The arithmetic properties of this GL 2-system and its KMS states at zero temperature related to the Galois theory of the modular ﬁeld.The ground states and the Galois properties are analyzed in [9]for the generic case of elliptic curves with transcendental j -invariant.As the results of [9]show,one of the main new features of the GL 2-system is the presence of symmetries by endomorphism ,through which the full Galois group of the modular ﬁeld appears as symmetries acting on the KMS equilibrium states of the system.In both the original BC system and in the GL 2-system,the arithmetic properties of zero temperature KMS states rely on an underlying result of compatibility between ad`e lic groups of symmetries and Galois groups.This correspondence between ad`e lic and Galois groups naturally arises within the context of Shimura varieties.In fact,a Shimura variety is a pro-variety deﬁned over Q ,with a rich ad`e lic group of symmetries.In that context,the compatibility of the Galois action and the automorphisms is at the heart of Langlands program.This leads us to give a reinterpretation of the BC and the GL 2systems in the language of Shimura varieties,with the BC system corresponding to the simplest (zero dimensional)Shimura variety.In the case of the GL 2system,we show how the data of 2-dimensional Q -lattices and commensurability can be also described in terms of elliptic curves together with a pair of points in the total Tate module,and the system is related to the Shimura variety of GL2.This viewpoint suggests considering our systems as noncommutative pro-varieties deﬁned over Q ,more speciﬁcally as noncommutative Shimura varieties.We then present our main result,which is the construction of a new system,whose arithmetic prop-erties fully incorporate the explicit class ﬁeld theory for an imaginary quadratic ﬁeld K ,and whose partition function is the Dedekind zeta function of K .The underlying geometric structure is given by commensurability of 1-dimensional K -lattices.This new system can be regarded in two diﬀerent ways.On the one hand,it is a generalization ofthe BC system of [2],when changing the ﬁeld from Q to K ,and is in fact Morita equivalent to the one considered in [18],but with no restriction on the class number.On the other hand,it is also a specialization of the GL 2-system of [9]to elliptic curves with complex multiplication by K .In this case the ground states can be related to the non-generic ground states of the GL 2-system,associated to points τ∈H with complex multiplication,and the group of symmetries is the Galois group of the maximal abelian extension of K .Here also we show that symmetries by endomorphisms play a crucial role,as they allow for the action of the class group Cl(O ),so that our results hold for any class ﬁeld.Since this complex multiplication (CM)case can be realized as a subgroupoid of the GL 2-system,it has a natural choice of a rational subalgebra (an arithmetic structure)inherited from that of the GL 2-system.This is crucial,in order to obtain the intertwining of Galois action on the values of extremal states and action of symmetries of the system.12CONNES,MARCOLLI,AND RAMACHANDRANWe summarize and compare the main properties of the three systems(BC,GL2,and CM)in the following table.GL1CMpartition functionζ(β)ζ(β−1)A∗/Q∗A∗K,f/K∗fautomorphisms GL2(ˆZ)Cl(O)Galois group Aut(F)Sh(GL1,±1)A∗K,f/K∗The paper consists of two parts,with sections2and3centered on the relation of the BC and GL2 system to the arithmetic of Shimura varieties,and sections4and5dedicated to the construction of the CM system and its relation to the explicit classﬁeld theory for imaginary quadraticﬁelds.The two parts are closely interrelated,but can also be read independently.2.Quantum Statistical Mechanics and Explicit Class Field TheoryThe BC quantum statistical mechanical system[1,2]exhibits generators of the maximal abelian extension of Q,parameterizing ground states(i.e.at zero temperature).Moreover,the system has the remarkable property that these ground states take algebraic values,when evaluated on a rational subalgebra of the C∗-algebra of observables.The action on these values of the absolute Galois group factors through the abelianization Gal(Q ab/Q)and is implemented by the action of the id`e le class group as symmetries of the system,via the classﬁeld theory isomorphism.This suggests the intriguing possibility of using the setting of quantum statistical mechanics to address the problem of explicit classﬁeld theory for other numberﬁelds.In this section we recall some basic notions of quantum statistical mechanics and of classﬁeld theory, which will be used throughout the paper.We also formulate a general conjectural relation between quantum statistical mechanics and the explicit classﬁeld theory problem for numberﬁelds.Quantum Statistical Mechanics.A quantum statistical mechanical system consists of an algebra of observables,given by a unital C∗-algebra A,together with a time evolution,consisting of a1-parameter group of automorphismsσt, (t∈R),whose inﬁnitesimal generator is the Hamiltonian of the system.The analog of a probability measure,assigning to every observable a certain average,is given by a state,namely a continuous linear functionalϕ:A→C satisfying positivity,ϕ(x∗x)≥0,for all x∈A,and normalization,ϕ(1)=1.In the quantum mechanical framework,the analog of the classical Gibbs measure is given by states satisfying the KMS condition(cf.[13]).Deﬁnition2.1.A triple(A,σt,ϕ)satisﬁes the Kubo-Martin-Schwinger(KMS)condition at inverse temperature0≤β<∞,if,for all x,y∈A,there exists a bounded holomorphic function F x,y(z)on the strip0<Im(z)<β,continuous on the boundary of the strip,such that(2.1)F x,y(t)=ϕ(xσt(y))and F x,y(t+iβ)=ϕ(σt(y)x),∀t∈R.KMS AND CM3 We also say thatϕis a KMSβstate for(A,σt).The set Kβof KMSβstates is a compact convex Choquet simplex[3,II§5]whose set of extreme points Eβconsists of the factor states.At0temperature(β=∞)the KMS condition(2.1)says that,for all x,y∈A,the function(2.2)F x,y(t)=ϕ(xσt(y))extends to a bounded holomorphic function in the upper half plane H.This implies that,in the Hilbert space of the GNS representation ofϕ(i.e.the completion of A in the inner productϕ(x∗y)), the generator H of the one-parameter groupσt is a positive operator(positive energy condition). However,this notion of0-temperature KMS states is in general too weak,hence the notion of KMS∞states that we shall consider is the following.Deﬁnition2.2.A stateϕis a KMS∞state for(A,σt)if it is a weak limit ofβ-KMS states for β→∞.One can easily see the diﬀerence between these two notions in the case of the trivial evolutionσt= id,∀t∈R,where any state has the property that(2.2)extends to the upper half plane(as a constant),while weak limits ofβ-KMS states are automatically tracial states.With Deﬁnition2.2we still obtain a weakly compact convex setΣ∞and we can consider the set E∞of its extremal points.The typical framework for spontaneous symmetry breaking in a system with a unique phase transition (cf.[12])is that the simplexΣβconsists of a single point forβ≦βc i.e.when the temperature is larger than the critical temperature T c,and is non-trivial(of some higher dimension in general)when the temperature lowers.A(compact)group of automorphisms G⊂Aut(A)commuting with the time evolution,(2.3)σtαg=αgσt∀g∈G,t∈R,is a symmetry group of the system.Such G acts onΣβfor anyβ,hence on the extreme points E(Σβ)=Eβ.The choice of an equilibrium stateϕ∈Eβmay break this symmetry to a smaller subgroup given by the isotropy group Gϕ={g∈G,gϕ=ϕ}.The unitary group U of theﬁxed point algebra ofσt acts by inner automorphisms of the dynamical system(A,σt),by(2.4)(Ad u)(a):=u a u∗,∀a∈A,for all u∈U.One can deﬁne an action modulo inner of a group G on the system(A,σt)as a map α:G→Aut(A,σt)fulﬁlling the condition(2.5)α(gh)α(h)−1α(g)−1∈Inn(A,σt),∀g,h∈G,i.e.,as a homomorphism of G to Aut(A,σt)/U.The KMSβcondition shows that the inner automor-phisms Inn(A,σt)act trivially on KMSβstates,hence(2.5)induces an action of the group G on the setΣβof KMSβstates,for0<β≤∞.More generally,one can consider actions by endomorphisms(cf.[9]),where an endomorphismρof the dynamical system(A,σt)is a∗-homomorphismρ:A→A commuting with the evolutionσt.There is an induced action ofρon KMSβstates,for0<β<∞,given by(2.6)ρ∗(ϕ):=Z−1ϕ◦ρ,Z=ϕ(e),provided thatϕ(e)=0,where e=ρ(1)is an idempotentﬁxed byσt.An isometry u∈A,u∗u=1,satisfyingσt(u)=λit u for all t∈R and for someλ∈R∗+,deﬁnes an inner endomorphism Ad u of the dynamical system(A,σt),again of the form(2.4).The KMSβcondition shows that the induced action of Ad u onΣβis trivial,cf.[9].The induced action(modulo inner)of a semigroup of endomorphisms of(A,σt)on the KMSβstates in general may not extend directly to KMS∞states(in a nontrivial way),but it may be deﬁned on E∞by“warming up and4CONNES,MARCOLLI,AND RAMACHANDRANcooling down”(cf.[9]),provided the“warming up”map Wβ:E∞→Eβis a bijection between KMS∞states(in the sense of Deﬁnition2.2)and KMSβstates,for suﬃciently largeβ.The map is given byTr(πϕ(a)e−βH)(2.7)Wβ(ϕ)(a)=−d),for some positive integer d>1.We denote byˆZ the proﬁnite completion of Z and by A f=ˆZ⊗Q the ring ofﬁnite adeles of Q.For any abelian group G,we denote by G tors the subgroup of elements ofﬁnite order.For any ring R,we write R∗for the group of invertible elements,while R×denotes the set of nonzero elements of R,which is a semigroup if R is an integral domain.We write O for the ring of algebraic integers of K.We setˆO:=(O⊗ˆZ)and write A K,f=A f⊗Q K and I K=A∗K,f=GL1(A K,f). Note that K∗embeds diagonally into I K.The classﬁeld theory isomorphism provides the canonical identiﬁcation(2.8)θ:I K/K∗∼−→Gal(K ab/K),with K∗replaced by Q∗+when K=Q.KMS AND CM5Fabulous states for numberﬁelds.The connection between classﬁeld theory and quantum statistical mechanics can be formulated as the problem of constructing a class of quantum statistical mechanical systems,whose set of ground states E∞has special arithmetic properties,because of which we refer to such states as“fabulous states”. Given a numberﬁeld K,with a choice of an embedding K⊂C,the“problem of fabulous states”consists of constructing a C∗-dynamical system(A,σt),with an arithmetic subalgebra A Q of A,with the following properties:(1)The quotient group G=C K/D K acts on A as symmetries compatible withσt.(2)The statesϕ∈E∞,evaluated on elements of the arithmetic subalgebra A Q,satisfy:•ϕ(a)∈6CONNES,MARCOLLI,AND RAMACHANDRANaction(by S=R∗+in the1-dimensional case,or by S=C∗in the2-dimensional case),the algebra of coordinates associated to the quotient R/S is obtained by restricting the convolution product of thealgebra of R to weight zero functions with S-compact support.The algebra obtained this way,whichis unital in the1-dimensional case,but not in the2-dimensional case,has a natural time evolution given by the ratio of the covolumes of a pair of commensurable lattices.Every unit y∈R(0)of Rdeﬁnes a representationπy by left convolution of the algebra of R on the Hilbert space H y=ℓ2(R y),where R y is the set of elements with source y.This construction passes to the quotient by the scaling action of S.Representations corresponding to points that acquire a nontrivial automorphism groupwill no longer be irreducible.If the unit y∈R(0)corresponds to an invertible Q-lattice,thenπy is apositive energy representation.In both the1-dimensional and the2-dimensional case,the set of extremal KMS states at low tem-perature is given by a classical ad`e lic quotient,namely,by the Shimura varieties for GL1and GL2,respectively,hence we argue here that the noncommutative space describing commensurability classes of Q-lattices up to scale can be thought of as a noncommutative Shimura variety,whose set of classicalpoints is the corresponding classical Shimura variety.In both cases,a crucial step for the arithmetic properties of the action of symmetries on extremal KMS states at zero temperature is the choice of an arithmetic subalgebra of the system,on whichthe ground states are evaluated.Such choice gives the underlying noncommutative space a more rigidstructure,of“noncommutative arithmetic variety”.Tower Power.If V is an algebraic variety–or a scheme or a stack–over aﬁeld k,a“tower”T over V is a family V i(i∈I)ofﬁnite(possibly branched)covers of V such that for any i,j∈I,there is a l∈I with V l a cover of V i and V j.Thus,I is a partially ordered set.In case of a tower over a pointed variety(V,v),oneﬁxes a point v i over v in each V i.Even though V i may not be irreducible,we shall allow ourselves to loosely refer to V i as a variety.It is convenient to view a“tower”T as a category C with objects(V i→V)and morphisms Hom(V i,V j)being maps of covers of V.One has the group Aut T(V i)of invertible self-maps of V i over V(the group of deck transformations);the deck transformations are not required to preserve the points v i.There is a(proﬁnite)group of symmetries associated to a tower,namely(3.2)G:=lim←−i Aut T(V i).The simplest example of a tower is the“fundamental group”tower associated with a(smooth con-nected)complex algebraic variety(V,v)and its universal covering(˜V,˜v).Let C be the category of all ﬁnite´e tale(unbranched)intermediate covers˜V→W→V of V.In this case,the symmetry group G of(3.2)is the algebraic fundamental group of V;it is also the proﬁnite completion of the(topological) fundamental groupπ1(V,v).Simple variants of this example include allowing controlled ramiﬁcation. Other examples of towers are those deﬁned by iteration of self maps of algebraic varieties.For us,the most important examples of“towers”will be the cyclotomic tower and the modular tower.Another very interesting case of towers is that of more general Shimura varieties.These,however,will not be treated in this paper.(For a more general treatment of noncommutative Shimura varieties see [11].)The cyclotomic tower and the BC system.In the case of Q,an explicit description of Q ab is provided by the Kronecker–Weber theorem.Thisshows that theﬁeld Q ab is equal to Q cyc,theﬁeld obtained by attaching all roots of unity to Q. Namely,Q ab is obtained by attaching the values of the exponential function exp(2πiz)at the torsion points of the circle group R/ing the isomorphism of abelian groups¯Q∗tors∼=Q/Z and the identiﬁcation Aut(Q/Z)=GL1(ˆZ)=ˆZ∗,the restriction to¯Q∗tors of the natural action of Gal(¯Q/Q) on¯Q∗factors asGal(¯Q/Q)→Gal(¯Q/Q)ab=Gal(Q ab/Q)∼−→ˆZ∗.KMS AND CM7 Geometrically,the above setting can be understood in terms of the cyclotomic tower.This has base Spec Z=V1.The family is Spec Z[ζn]=V n whereζn is a primitive n-th root of unity(n∈N∗). The set Hom(V m→V n),non-trivial for n|m,corresponds to the map Z[ζn]֒→Z[ζm]of rings.Thegroup Aut(V n)=GL1(Z/n Z)is the Galois group Gal(Q(ζn)/Q).The group of symmetries(3.2)of the tower is then(3.3)G=lim←−n GL1(Z/n Z)=GL1(ˆZ),which is isomorphic to the Galois group Gal(Q ab/Q)of the maximal abelian extension of Q.The classical object that we consider,associated to the cyclotomic tower,is the Shimura variety given by the ad`e lic quotient(3.4)Sh(GL1,{±1})=GL1(Q)\(GL1(A f)×{±1})=A∗f/Q∗+.Now we consider the space of1-dimensional Q-lattices up to scaling modulo commensurability.This can be described as follows([9]).In one dimension,every Q-lattice is of the form(3.5)(Λ,φ)=(λZ,λρ),for someλ>0and someρ∈Hom(Q/Z,Q/Z).Since we can identify Hom(Q/Z,Q/Z)endowed with the topology of pointwise convergence with(3.6)Hom(Q/Z,Q/Z)=lim←−n Z/n Z=ˆZ,we obtain that the algebra C(ˆZ)is the algebra of coordinates of the space of1-dimensional Q-lattices up to scaling.The groupˆZ is the Pontrjagin dual of Q/Z,hence we also have an identiﬁcation C(ˆZ)=C∗(Q/Z).The group of deck transformations G=ˆZ∗of the cyclotomic tower acts by automorphisms on the algebra of coordinates C(ˆZ).In addition to this action,there is a semigroup action of N×=Z>0 implementing the commensurability relation.This is given by endomorphisms that move vertically across the levels of the cyclotomic tower.They are given by(3.7)αn(f)(ρ)=f(n−1ρ),∀ρ∈nˆZ.Namely,αn is the isomorphism of C(ˆZ)with the reduced algebra C(ˆZ)πby the projectionπn givennby the characteristic function of nˆZ⊂ˆZ.Notice that the action(3.7)cannot be restricted to the set of invertible Q-lattices,since the range ofπn is disjoint from them.The algebra of coordinates A1on the noncommutative space of equivalence classes of1-dimensional Q-lattices modulo scaling,with respect to the equivalence relation of commensurability,is given then by the semigroup crossed product(3.8)A=C(ˆZ)⋊αN×.Equivalently,we are considering the convolution algebra of the groupoid R1/R∗+given by the quotient by scaling of the groupoid of the equivalence relation of commensurability on1-dimensional Q-lattices, namely,R1/R∗+has as algebra of coordinates the functions f(r,ρ),forρ∈ˆZ and r∈Q∗such that rρ∈ˆZ,with the convolution product(3.9)f1∗f2(r,ρ)= f1(rs−1,sρ)f2(s,ρ),and the adjoint f∗(r,ρ)=8CONNES,MARCOLLI,AND RAMACHANDRANAs a set,the space of commensurability classes of1-dimensional Q-lattices up to scaling can also be described by the quotient(3.10)GL1(Q)\A·/R∗+=GL1(Q)\(A f×{±1}),where A·:=A f×R∗is the set of ad`e les with nonzero archimedean component.Rather than considering this quotient set theoretically,we regard it as a noncommutative space,so as to be able to extend to it the ordinary tools of geometry that can be applied to the“good”quotient(3.4).The noncommutative algebra of coordinates of(3.10)is the crossed product(3.11)C0(A f)⋊Q∗+.This is Morita equivalent to the algebra(3.8).In fact,(3.8)is obtained as a full corner of(3.11),C(ˆZ)⋊N×= C0(A f)⋊Q∗+ π,by compression with the projectionπgiven by the characteristic function ofˆZ⊂A f(cf.[17]).The quotient(3.10)with its noncommutative algebra of coordinates(3.11)can then be thought of as the noncommutative Shimura variety(3.12)Sh(nc)(GL1,{±1}):=GL1(Q)\(A f×{±1})=GL1(Q)\A·/R∗+,whose set of classical points is the well behaved quotient(3.4).This has a compactiﬁcation,obtained by replacing A·by A,as in[7],(3.13)−1)c(Z)=1.One considers the rational subalgebra A1,Q of(3.8)generated by the functions e1,a(r,ρ):=e1,a(ρ)and by the functionsµn(r,ρ)=1for r=n and zero otherwise,that implement the semigroup action of N×in(3.8).As proved in[9],the algebra A1,Q is the same as the rational subalgebra considered in[2],generated over Q by theµn and the exponential functions(3.17)e(r)(ρ):=exp(2πiρ(r)),forρ∈Hom(Q/Z,Q/Z),and r∈Q/Z,KMS AND CM9 with relations e(r+s)=e(r)e(s),e(0)=1,e(r)∗=e(−r),µ∗nµn=1,µkµn=µkn,and(3.18)µn e(r)µ∗n=1ζ(β)∞n=1n−βρ(ζk r).•The group GL1(ˆZ)acts by automorphisms of the system.The induced action of GL1(ˆZ)on the set of extreme KMS states below critical temperature is free and transitive.•The vacuum states(β=∞)are fabulous states for theﬁeld K=Q,namelyϕ(A1,Q)⊂Q cycl and the classﬁeld theory isomorphismθ:Gal(Q cycl/Q)∼=→ˆZ∗intertwines the Galois action on values with the action ofˆZ∗by symmetries,(3.21)γϕ(x)=ϕ(θ(γ)x),for allϕ∈E∞,for allγ∈Gal(Q cycl/Q)and for all x∈A1,Q.The modular tower and the GL2-system.Modular curves arise as moduli spaces of elliptic curves endowed with additional level structure.Every congruence subgroupΓ′ofΓ=SL2(Z)deﬁnes a modular curve YΓ′;we denote by XΓ′the smooth compactiﬁcation of the aﬃne curve YΓ′obtained by adding cusp points.Especially important among these are the modular curves Y(n)and X(n)corresponding to the principal congruence subgroups Γ(n)for n∈N∗.Any XΓ′is dominated by an X(n).We refer to[15,29]for more details.We have the following descriptions of the modular tower.10CONNES,MARCOLLI,AND RAMACHANDRANCompact version:The base is V=P1over Q.The family is given by the modular curves X(n),consid-ered over the cyclotomicﬁeld Q(ζn)[23].We note that GL2(Z/n Z)/±1is the group of automorphisms of the projection V n=X(n)→X(1)=V1=V.Thus,we have(3.22)G=GL2(ˆZ)/±1=lim←−n GL2(Z/n Z)/{±1}.Non-compact version:The open modular curves Y(n)form a tower with base the j-line Spec Q[j]= A1=V1−{∞}.The ring of modular functions is the union of the rings of functions of the Y(n),with coeﬃcients in Q(ζn)[15].This shows how the modular tower is a natural geometric way of passing from GL1(ˆZ)to GL2(ˆZ). The formulation that is most convenient in our setting is the one given in terms of Shimura varieties. In fact,rather than the modular tower deﬁned by the projective limit(3.23)Y=lim←−n Y(n)of the modular curves Y(n),it is better for our purposes to consider the Shimura variety(3.24)Sh(H±,GL2)=GL2(Q)\(GL2(A f)×H±)=GL2(Q)\GL2(A)/C∗,of which(3.23)is a connected component.In fact,it is well known that,for arithmetic purposes,it is always better to work with nonconnected rather than with connected Shimura varieties(cf.e.g.[23]). The simple reason why it is necessary to pass to the nonconnected case is the following.The varieties in the tower are arithmetic varieties deﬁned over numberﬁelds.However,the numberﬁeld typically changes along the levels of the tower(Y(n)is deﬁned over the cyclotomicﬁeld Q(ζn)).Passing to nonconnected Shimura varieties allows precisely for the deﬁnition of a canonical model where the whole tower is deﬁned over the same numberﬁeld.This distinction is important to our viewpoint,since we want to work with noncommutative spaces endowed with an arithmetic structure,speciﬁed by the choice of an arithmetic subalgebra.Every2-dimensional Q-lattice can be described by data(3.25)(Λ,φ)=(λ(Z+Z z),λα),for someλ∈C∗,some z∈H,andα∈M2(ˆZ)(using the basis(1,−z)of Z+Z z as in(87)[9]to view αas a mapφ).The diagonal action ofΓ=SL2(Z)yields isomorphic Q-lattices,and(cf.(87)[9])the space of2-dimensional Q-lattice up to scaling can be identiﬁed with the quotient(3.26)Γ\(M2(ˆZ)×H).The relation of commensurability is implemented by the partially deﬁned action of GL+2(Q)on(3.26). The groupoid R2of the commensurability relation on2-dimensional Q-lattices not up to scaling(i.e. the dual space)has as algebra of coordinates the convolution algebra ofΓ×Γ-invariant functions on (3.27)˜U={(g,α,u)∈GL+2(Q)×M2(ˆZ)×GL+2(R)|gα∈M2(ˆZ)}.Up to Morita equivalence,this can also be described as the crossed product(3.28)C0(M2(A f)×GL2(R))⋊GL2(Q).When we pass to Q-lattices up to scaling,we take the quotient R2/C∗.If(Λk,φk)k=1,2are a pair of commensurable2-dimensional Q-lattices,then for anyλ∈C∗,the Q-lattices(λΛk,λφk)are also commensurable,withr(g,α,uλ)=λ−1r(g,α,u).However,the action of C∗on Q-lattices is not free due to the presence of lattices L=(0,z),where z∈Γ\H has nontrivial automorphisms.Thus,the quotient Z=R2/C∗is no longer a groupoid.This can be seen in the following sim-ple example.Consider the two Q-lattices(α1,z1)=(0,2i)and(α2,z2)=(0,i).The composite ((α1,z1),(α2,z2))◦((α2,z2),(α1,z1))is equal to the identity((α1,z1),(α1,z1)).We can also considerthe composition (i (α1,z 1),i (α2,z 2))◦((α2,z 2),(α1,z 1)),where i (α2,z 2)=(α2,z 2),but this is not the identity,since i (α1,z 1)=(α1,z 1).However,we can still consider the convolution algebra of Z ,by restricting the convolution product of R 2to homogeneous functions of weight zero with C ∗-compact support,where a function f has weight k if it satisﬁesf (g,α,uλ)=λk f (g,α,u ),∀λ∈C ∗.This is the analog of the description (3.8)for the 1-dimensional case.The noncommutative algebra of coordinates A 2is thus given by a Hecke algebra of functions on(3.29)U ={(g,α,z )∈GL +2(Q )×M 2(ˆZ )×H ,gα∈M 2(ˆZ )}invariant under the Γ×Γaction(3.30)(g,α,z )→(γ1gγ−12,γ2α,γ2(z )),with convolution(3.31)(f 1∗f 2)(g,α,z )= s ∈Γ\GL +2(Q ),sα∈M 2(ˆZ )f 1(gs −1,sα,s (z ))f 2(s,α,z )and adjoint f ∗(g,α,z )=Another reformulation uses the Pontrjagin duality between proﬁnite abelian groups and discrete tor-sion abelian groups given by Hom(−,Q/Z).This reformulates the datumφof a Q-lattice as aˆZ-linear map Hom(QΛ/Λ,Q/Z)→ˆZ⊕ˆZ,which is identiﬁed withΛ⊗ˆZ→ˆZ⊕ˆZ.Here we use the fact that ΛandΛ⊗ˆZ∼=H1(E,ˆZ)are both self-dual(Poincar´e duality of E).In this dual formulation com-mensurability means that the two maps agree on the intersection of the two commensurable lattices,(Λ1∩Λ2)⊗ˆZ.With the formulation of Proposition3.2,can then give a new interpretation of the result of Proposition 43of[9],which shows that the space of commensurability classes of2-dimensional Q-lattices up to scaling is described by the quotient(3.36)Sh(nc)(H±,GL2):=GL2(Q)\(M2(A f)×H±).In fact,the data(Λ,φ)of a Q-lattice in C are equivalent to data(E,η)of an elliptic curve E=C/Λand an A f-homomorphism(3.37)η:Q2⊗A f→Λ⊗A f,withΛ⊗A f=(Λ⊗ˆZ)⊗Q,where we can identifyΛ⊗ˆZ with the total Tate module of E,as in(3.35). Since the Q-lattice need not be invertible,we do not require thatηbe an A f-isomorphism(cf.[23]). The commensurability relation between Q-lattices corresponds to the equivalence(E,η)∼(E′,η′) given by an isogeny g:E→E′andη′=(g⊗1)◦η.Namely,the equivalence classes can be identiﬁed with the quotient of M2(A f)×H±by the action of GL2(Q),(ρ,z)→(gρ,g(z)).Thus,(3.36)describes a noncommutative Shimura variety which has the Shimura variety(3.24)as the set of its classical points.The results of[9]show that,as in the case of the BC system,one recovers the classical points from the low temperature extremal KMS states.We shall return to this in the next section.In this case,the“compactiﬁcation”,analogous to passing from(3.10)to(3.14),corresponds to the replacing(3.36)by the noncommutative space(3.38)in[31].This suggests that modular functions should appear naturally in the arithmetic subalgebra A2,Q of the GL2-system,but that requires working with unbounded multipliers.This is indeed the case for the arithmetic subalgebra A2,Q deﬁned in[9],which we now recall.Let F be the modularﬁeld,namely theﬁeld of modular functions over Q ab(cf.e.g.[19]).This is the union of theﬁelds F N of modular functions of level N rational over the cyclotomicﬁeld Q(ζN),that is,such that the q-expansion at a cusp has coeﬃcients in the cyclotomicﬁeld Q(ζN).The action of the Galois groupˆZ∗≃Gal(Q ab/Q)on the coeﬃcients of the q-expansion determines a homomorphism(3.42)cycl:ˆZ∗→Aut(F).If f is a continuous functions on Z=R2/C∗,we writef(g,α)(z)=f(g,α,z)so that f(g,α)∈C(H).For p N:M2(ˆZ)→M2(Z/N Z)the canonical projection,we say that f is of level N iff(g,α)=f(g,p(α))∀(g,α).NThen f is completely determined by the functionsf(g,m)∈C(H),for m∈M2(Z/N Z).Notice that the invariance f(gγ,α,z)=f(g,γα,γ(z)),for allγ∈Γand for all(g,α,z)∈U,implies that f(g,m)|γ=f(g,m),for allγ∈Γ(N)∩g−1Γg,i.e.f is invariant under a congruence subgroup. The arithmetic algebra A2,Q deﬁned in[9]is a subalgebra of continuous functions on Z=R2/C∗with the convolutions product(3.31)and with the properties:•The support of f inΓ\GL+2(Q)isﬁnite.•The function f is ofﬁnite level withf(g,m)∈F∀(g,m).•The function f satisﬁes the cyclotomic condition:f(g,α(u)m)=cycl(u)f(g,m),for all g∈GL+2(Q)diagonal and all u∈ˆZ∗,withα(u)= u001and cycl as in(3.42).Here F is the modularﬁeld,namely theﬁeld of modular functions over Q ab.This is the union of the ﬁelds F N of modular functions of level N rational over the cyclotomicﬁeld Q(ζN).The cycloomic condition is a consistency condition on the roots of unity that appear in the coeﬃcients of the q-series,which allows for the existence of“fabulous states”(cf.[9]).Forα∈M2(ˆZ),let Gα⊂GL+2(Q)be the set ofGα={g∈GL+2(Q):gα∈M2(ˆZ)}.Then,as shown in[9],an element y=(α,z)∈M2(ˆZ)×H determines a unitary representation of the Hecke algebra A on the Hilbert spaceℓ2(Γ\Gα),(3.43)((πy f)ξ)(g):= s∈Γ\Gαf(gs−1,sα,s(z))ξ(s),∀g∈Gαfor f∈A andξ∈ℓ2(Γ\Gα).Invertible Q-lattices determine positive energy representations,due to the fact that the condition gα∈M2(ˆZ)for g∈GL+2(Q)andα∈GL2(ˆZ)(invertible case)implies g∈M2(Z)+,hence the time evolution(3.32)is implemented by the positive Hamiltonian with spectrum{log det(m)}⊂[0,∞)for。

Investigations on the stability of dynamic avalanche in IGBTs

It is known that dynamic avalanche can be avoided by use of very high gate resistors t o keep the n-channel open until the load current decreases [3] (figure 2). The negative electron charge compensates the space charge resulting from the moving holes. This supression of dynamic avalanche, however, enhances the turn-off loss similarly and it is not clear from single cell simulation why this should be such a benefit for the device.
The electron current generated by dynamic avalanche can not much exceed the hole current which limits this “current gain” PAva[an&e close to one [SI. This is confirmed by our simulation results. In the IGBTs considered in this paper (as in most IGBTs), the pnpTransistor current gain is far below one, because of very shallow anode doping. Therefore, the regenerative feedback condition

动态平衡的英语

动态平衡的英语Dynamic EquilibriumEquilibrium is a fundamental concept in science, describing a state of balance where opposing forces or influences are in a state of stability. This concept can be applied to various fields, including physics, chemistry, biology, and even social and economic systems. One particular type of equilibrium is known as dynamic equilibrium, which is the focus of this essay.Dynamic equilibrium refers to a state where there is a continuous exchange or flow of energy, matter, or information, yet the overall system remains in a stable state. This is in contrast to a static equilibrium, where the system is completely at rest and there is no change or movement. Dynamic equilibrium is a common phenomenon in nature and is essential for the functioning of many complex systems.One of the most well-known examples of dynamic equilibrium is the chemical equilibrium observed in reversible chemical reactions. In a reversible reaction, the forward and reverse reactions occur simultaneously, with the rates of the forward and reverse reactionsbeing equal. As a result, the concentrations of the reactants and products remain constant over time, even though the individual molecules are constantly being converted from one form to the other. This dynamic balance is essential for maintaining the stability of chemical systems and is crucial in many industrial and biological processes.Another example of dynamic equilibrium can be found in the human body. The body's internal environment, known as the homeostasis, is maintained through a complex network of regulatory systems that constantly monitor and adjust various physiological parameters, such as temperature, pH, and blood pressure. These regulatory systems work to maintain a delicate balance, ensuring that the body's internal conditions remain within a narrow range, even in the face of external changes or disturbances. This dynamic equilibrium is essential for the proper functioning of the body's cells and organs.In the field of ecology, dynamic equilibrium is observed in the interactions between different species within an ecosystem. In a stable ecosystem, there is a continuous exchange of energy and matter, with producers, consumers, and decomposers all playing essential roles. The populations of different species may fluctuate over time, but the overall structure and function of the ecosystem remain relatively constant. This dynamic equilibrium is crucial for the sustainability of the ecosystem and the maintenance of biodiversity.In the realm of social and economic systems, dynamic equilibrium can be observed in the interactions between various stakeholders, such as governments, businesses, and consumers. These systems are constantly in flux, with new policies, technologies, and market forces constantly shaping the landscape. Yet, despite these changes, the overall system may maintain a state of dynamic equilibrium, where the various components work together to maintain a stable and functional state.One of the key features of dynamic equilibrium is the concept of feedback loops. Feedback loops are mechanisms that allow a system to self-regulate, adjusting its behavior in response to changes in the environment or internal conditions. Positive feedback loops, for example, can amplify changes, while negative feedback loops can dampen them, helping to maintain the overall equilibrium. These feedback mechanisms are essential for the stability and resilience of dynamic systems.Another important aspect of dynamic equilibrium is the concept of adaptation. In order to maintain a state of dynamic equilibrium, systems must be able to adapt to changing conditions and disturbances. This may involve the development of new strategies, the reorganization of internal structures, or the exploitation of new resources. Adaptability is a key characteristic of dynamic systems andis essential for their long-term sustainability.In conclusion, dynamic equilibrium is a fundamental concept that underlies the behavior of many complex systems in the natural and social world. By understanding the principles of dynamic equilibrium, we can gain valuable insights into the functioning of these systems and develop strategies for maintaining their stability and resilience in the face of change and uncertainty. Whether in the realm of chemistry, biology, ecology, or economics, the study of dynamic equilibrium remains a crucial area of scientific inquiry and practical application.。

A dynamical system with a strange attractor and invariant tori.

Physics Letters A 378(2014)1361–1363Contents lists available at ScienceDirectPhysics Letters A/locate/plaA dynamical system with a strange attractor and invariant toriJ.C.SprottDepartment of Physics,University of Wisconsin-Madison,Madison,WI 53706,USAa r t i c l e i n f o ab s t r ac tArticle history:Received 15January 2014Received in revised form 13March 2014Accepted 17March 2014Available online 21March 2014Communicated by C.R.Doering Keywords:Dynamical system Strange attractor Invariant torusThis paper describes a simple three-dimensional time-reversible system of ODEs with quadratic nonlinearities and the unusual property that it is exhibits conservative behavior for some initial conditions and dissipative behavior for others.The conservative regime has quasi-periodic orbits whose amplitude depend on the initial conditions,while the dissipative regime is chaotic.Thus a strange attractor coexists with an inﬁnite set of nested invariant tori in the state space.©2014Elsevier B.V.All rights reserved.1.IntroductionContinuous-time dynamical systems governed by a set of ﬁrst-order ordinary differential equations are usually categorized as be-ing either conservative or dissipative.Conservative systems main-tain the state space volume when time-averaged along the tra-jectory and are usually characterized by some conserved quantity such as a Hamiltonian function.Depending on the initial condi-tions,they typically have orbits that are quasi-periodic and lie on surfaces of nested tori surrounded by a chaotic sea whose dimen-sion is equal to the dimension of the state space.Dissipative systems have a state space volume that decreases on average along the trajectory so that the orbit approaches an at-tractor of measure zero in the state space.If the dissipative system is chaotic,the attractor is strange with a non-integer dimension and fractal structure.Furthermore,it is possible for the same dissi-pative system to have coexisting stable equilibria,limit cycles,and strange attractors each with its own dimension and basin of at-traction [1,2].However,if the dissipation is nonlinear and thus dependent on the position in state space,systems can be dissipative for some ini-tial conditions,while other initial conditions lead to solutions for which the dissipation averages exactly to zero along the orbit [3].The next section describes a simple example of such a system in which a strange attractor with chaotic orbits coexists with an inﬁ-nite set of nested invariant tori containing quasi-periodic orbits.E-mail address:sprott@ .URL: .2.ExampleIn a numerical search for chaotic systems that have no equilib-rium points and only bounded orbits for all initial conditions,the following unusual system was discovered:˙x=y +2xy +xz ˙y=1−2x 2+yz ˙z=x −x 2−y 2(1)The numerical evidence of boundedness is that the ﬂow vec-tor is everywhere inward on a sphere of radius R centered on the point (1,0,−1)except for small holes at (0,0,±R )that occupy a vanishingly small fraction of the sphere as R →∞.Furthermore,orbits with initial conditions within these holes loop back to the interior of the sphere for R suﬃciently large.Since the system is bounded with no equilibrium points (stable or unstable),the only possible solutions are (quasi)-periodic or chaotic.Because the system is invariant under the transformation (x ,y ,z ,t )→(x ,−y ,−z ,−t ),two types of solutions can occur.The ﬁrst type is symmetric under a 180◦rotation about the x -axis and is time-reversal invariant.Thus it exhibits conservative behav-ior.The second type has an attractor in forward time and another attractor in reversed time that are symmetric with one another through a 180◦rotation about the x -axis.This reversed time at-tractor is a repellor in forward time.Since the same points in state space cannot be both an attractor and a repellor,any symmet-ric solutions necessarily conserve state space volume on average (non-attracting).In fact,it turns out that the system displays both behaviors depending on the initial conditions./10.1016/j.physleta.2014.03.0280375-9601/©2014Elsevier B.V.All rights reserved.1362J.C.Sprott/Physics Letters A378(2014)1361–1363Fig.1.A strange attractor(red)interlinked with a coexisting invariant torus(green) for System(1).(For interpretation of the references to color in thisﬁgure legend, the reader is referred to the web version of this article.)The dissipation is given by the trace of the Jacobian matrix, Tr(J)=2(y+z)whose value depends on y and z and thus should be time-averaged along the orbit,and whose average value is the sum of the Lyapunov exponents.The surprise was that the time average of y+z is negative for some initial conditions such as (x0,y0,z0)=(2,0,0)and zero for others such as(1,0,0).The boundedness of the system ensures that y+z cannot be positive, and the absence of equilibrium points ensures that all orbits are time-dependent.Theﬁrst initial condition gives a strange attrac-tor with Lyapunov exponents(0.0540,0,−0.1575)and a Kaplan–Yorke dimension of2.3429,and the second initial condition gives a torus with Lyapunov exponents(0,0,0)and a dimension of2.0.The strange attractor is strongly multifractal with a capacity di-mension of about2.92and a correlation dimension of about1.49. Since there are no equilibrium points,the strange attractor is“hid-den”in the sense described by Leonov and Kuznetsov[4,5],mean-ing that its basin does not intersect with small neighborhoods of any equilibrium points,and thus it cannot be found by standard computational methods.However,because the system is bounded, any initial condition suﬃciently far from the origin will go to the attractor(R=5is suﬃcient).The two solutions are shown in Fig.1projected onto the xy-plane.The strange attractor and torus are interlinked,with the attractor resembling the“cord”attractor described by Letellier and Aguirre[6].A different projection edge-on to the torus and also showing the intertwined repellor is in Fig.2.The attractor and re-pellor are tightly twisted like the strands of a rope where they pass through the hole in the torus.The repellor is identiﬁed by simply reversing the sign of time in the equations and showing a portion of the resulting orbit after discarding the initial transient.Addi-tional conﬁrmation that the torus is non-attracting comes from a very long calculation(to a time of t=1×1010)using a fourth-order Runge–Kutta integrator with adaptive step size,which gives an upper bound of| y+z |<1×10−10.Like all strange attractors,this one is dense in unstable periodic orbits.The orbit with the shortest period lies close to the surface of the outermost torus and makesﬁve loops projected onto the xy-plane while linking the torus once.It has a period of approxi-mately12.58,a net dissipation of2 y+z −0.0121,and can be observed by using the initial conditions(0.5002,0.0023,−0.0791).Fig.3shows a cross section of theﬂow in the z=0plane for80 initial conditions uniformly distributed over the range−2<x0<3Fig.2.A different view of the strange attractor(red)intertwined with a symmetric repellor(black)and both interlinked with a coexisting invariant torus(green)for System(1).(For interpretation of the references to color in thisﬁgure legend,the reader is referred to the web version of thisarticle.)Fig.3.Cross section in the z=0plane showing nested invariant tori surrounded by a multifractal strange attractor for System(1).Initial conditions in the conservative region are shown in blue,and initial conditions in the basin of attraction of the strange attractor are shown in yellow.(For interpretation of the references to color in thisﬁgure legend,the reader is referred to the web version of this article.)with y0=z0=0.This plot is called a“cross section”rather than a“Poincarésection”because the crossings of the z=0plane are plotted in both directions rather than a single direction.The nested invariant tori are surrounded by a strange attractor.The basin boundary of the strange attractor appears to be coincident with the outermost toroidal surface,and its basin extends to inﬁnity in all directions.The background colors in theﬁgure show the regions of conservative and dissipative behavior,respectively.The boundary between the conservative and dissipative region in the z=0plane is near a circle given by(x−1/√2)2+y2=1,a result that begs for an explanation.Initial conditions near that boundary such as(0,0.707,0)or near one of the separatrices within the toroidal region such as(0.4999,0.01,0)can appear to be conservative and chaotic,but either the largest Lyapunov expo-nent eventually converges to zero or the orbit eventually reachesJ.C.Sprott/Physics Letters A378(2014)1361–13631363the strongly dissipative strange attractor.There is no convincing evidence for a conservative chaotic sea.3.ConclusionsThis paper describes an unusual example of a chaotic dynamical system that exhibits conservative behavior for some initial condi-tions and dissipative behavior for others so that an inﬁnite set of nested invariant tori coexist with and are linked by a strange at-tractor.For initial conditions suﬃciently close to the origin,the quasi-periodic orbits are such that the time average of y+z is identically zero to within numerical precision,while orbits start-ing farther from the origin have a strongly negative value of that quantity with a sharp,nearly circular toroidal boundary separating the two regions.It would be good to have a better understanding of this phenomenon,a theory for when it will occur,a prediction for the location of the boundary,and details of the bifurcations that occur in theﬁve-dimensional parameter space,but those chal-lenges will be left for the future.Shortly after discovering this system,another similar example was found in a nonlinearly dissipative Nosé–Hoover oscillator with a hyperbolic tangent nonlinearity and four equilibrium points[7]. In that case,an attracting limit cycle coexists with two sets of in-variant tori for some values of the parameters,while a space-ﬁlling multifractal strange attractor with a Kaplan–Yorke dimension of 2.945coexists with the tori for other values of the parameters. This result suggests that the behavior described here may be com-mon in time-reversible dynamical systems with nonlinear damping but apparently not widely known or appreciated.AcknowledgementsI am grateful to Zeraoulia Elhadj for suggesting the search that uncovered this example and to Bill Hoover for extensive discus-sions.References[1]J.C.Sprott,X.Wang,G.Chen,Int.J.Bifurc.Chaos Appl.Sci.Eng.23(2013)1350093.[2]C.Li,J.C.Sprott,Int.J.Bifurc.Chaos Appl.Sci.Eng.23(2013)1350199.[3]A.Politi,G.L.Oppo,R.Badii,Phys.Rev.A(1986)4055.[4]G.A.Leonov,N.V.Kuznetsov,V.I.Vagaitsev,Phys.Lett.A375(2011)2230.[5]G.A.Leonov,N.V.Kuznetsov,Int.J.Bifurc.Chaos Appl.Sci.Eng.23(2013)12330002.[6]C.Letellier,L.A.Aguirre,Phys.Rev.E85(2012)036204.[7]J.C.Sprott,W.G.Hoover,C.G.Hoover,arXiv:1401.1762[cond-mat.stat-mech].。

资源勘查工程专业外语

专业外语复习题英译汉、汉译英:1) abnormal high formation pressure 异常高地层压力 2) reservoir drive 油藏驱动 3) hydrostatic pressure gradient 静水压力梯度 4) geothermal gradient 地温梯度 5) dolomitization 白云岩化作用 6) rollover anticline 滚动背斜 7) unconformity trap 不整合圈闭 8) faulting trap 断层圈闭 9) salt plug 盐丘 10) the use of well logging 测井应用 11) stratigraphic trap 地层圈闭 12) Permian sandstone reservoir 二叠系砂岩储层 13) the late petroleum generation hypothesis 晚期石油生成说 14) organic-rich shale 富含有机质页岩 15) buoyancy 浮力 16) clastic or detrial rock 碎屑岩 17) the strike contours 等值高线 18) transgressive sequence 水进层序 19) desgressive sequence 水退层序 20) sequence stratigraphy 层序地层学 21) well —sorted sands 分选好的砂 22) secondary growth of quartz 石英次生加大 23) the capacity of a fault 断层封闭 24) growth fault 同生（生长)断层 25) fluvial facies 河流相 26) Carboniferous limestone 石炭化石灰岩 27) Cretaceous dolomite 白垩纪白云岩 28) fan —delta 扇三角洲 29) insoluble organic matter 30) a potential source rock 潜在烃源岩 31) evolutionary stages of kerogen 干酪根的演化阶段 32) secondary pores 次生孔隙 33) petroleum migration 石油运移 34) hydrocarbon accumulation 烃类聚集 35) kerogen 干酪根 36) porosity 孔隙度37) permeability 渗透率 38) water —saturation 含水饱和度39) hydrodynamic condition 水动力条件40) oils and source rocks correlation 油源岩对比 41) effective porosity 有效孔隙度 42) types of reservoir drives 油藏驱动类型 43) lens of sandstones 砂岩透镜体 44) sedimentary facies 沉积相 45) minor structure 微幅构造 46) subsidence or depression belt 沉陷带47) nose structure 鼻状构造 48) reservoir heterogeneity 储集层非均质性 49) high point of structure 构造高点 50) oil-field water 油田水 51) original reservoir pressure 原始储层压力 52) salinity 盐度(矿化度） 53) anticline 背斜 54) syncline 向斜 55) normal fault 正断层 56) reverse fault 逆断层57) geological mapping 地质制图 58) organic matter 有机质 59) residual oil 剩余油 60) primary pore 原生孔隙 secondary pore 次生孔隙61) coarse —sandstone 粗砂岩 62) fine —sandstone 细砂岩 63) silt stone 粉砂岩 64) mature stage of hydrocarbon source rock 烃源岩成熟阶段 65) structural strike contours 构造等值线 66) absolute permeability 绝对渗透率 67) arkoses 长石砂岩 68) elaborate geological description of oil pools 油藏精细地质描述名词解释：1、Fossils： are the recognizable remains or traces of animals and plants that were preserved in sediments,rocks and other materials。

cbida_building_sl

Building Sustainable Livelihoods through Agriculture in HondurasBy Duncan HanksAs the international community strives to meet its commitments for poverty reduction articulated in the UN Millennium Development Goals, governments and NGOs are accelerating the pace to scale up successful and sustainable models and practices. CIDA has been assisting the Canadian Baha’i International Development Services (CBIDS) to implement a successful tutorial learning system developed by FUNDAEC, the Foundation for the Application and Teaching of the Sciences Foundation, in Colombia. The tutorial learning system, or “sistema de aprendizaje tutorial” (SAT), i s a formal but flexible secondary educational system that holistically integrates diverse aspects of community development. The approach emerged out of a desire for a curriculum that is not only appropriate for rural communities but which simultaneously creates alternatives for primary and secondary agricultural production, social organization, micro economic development, and the creation of conditions for community wellbeing.Since 1974, FUNDAEC has been engaged in an ongoing process of experimentation, reflection and consultation, examining viable approaches to create prosperous conditions in rural and agricultural communities. FUNDAEC has successfully implemented SAT in Colombia through an NGO network working in collaboration with the Ministry of Education, benefiting over 35,000 student participants in rural communities. The success of the SAT model has prompted CIDA and CBIDS to support the ongoing refinement of the SAT texts, and the organizational capacity building for SAT program delivery in Honduras and Colombia.Since 1996, the Bayan Association in Honduras has been delivering the SAT program to an estimated 4,000 participants, primarily in coastal and hillside farming communities. The program emphasizes authentic participation in appropriate organizational structures and a systematic learning process that enables access to global knowledge. With these two eleme nts in place “rural populations … interact in equal terms with others and cease to be the objects of the plans (beneficial or harmful) of other individuals and institutions.1One of the successes of the Building Sustainable Livelihoods through Agriculture program in Honduras has been the rapid acceptance by the Departmental representatives of the Ministry of Education, and the development of a consortium of NGOs to accompany the Bayan Association with the delivery of the program. What attracts the interest of the international community to support SAT is the dynamic role of the SAT participant as a social change agent, rather than a passive learner. In the program, SAT students are considered protagonists of their own education, seeking out answersto the questions posed in the curriculum, and playing a central role in the cooperativeplanning involved in carrying out the projects that accompany many of the texts. SATmakes service to others the central axis around which the process of knowledge-acquisition revolves. As a result, the group projects that help students practice theirskills and develop greater understanding of the subject at hand are simultaneouslysmall-scale social and economic development initiatives addressing issues of health,literacy, agricultural technology, small business practices, environmental projects, andother issues of concern in their community.21 CELATER, FUNDAEC: Its Principles and Its Activities, p. 5A very clever SAT groupIt is for precisely these reasons that SAT is not a typical education program, but rather a program that contributes systematically to developing the individual and organizational capacities for eradicating poverty, sustaining livelihoods and building healthy and prosperous communities. Delivered in a non-traditional manner, the SAT program engages students, families and communities in a search for alternative systems of production in small farms, as well as in small scale production for groups and families with little access to land. The program also fosters the establishment and strengthening of micro-enterprises that stimulate a localized rural economy.An interesting feature of the SAT program in Honduras is that the majority of students are women, and that their retention in the program and academic achievement surpasses traditional educational approaches.3 This is in part due to the unique delivery system, and the attention to gender equality that emphasizes not only women’s empowerment, but the re-education of men and boys on the subject of gender. Gender is a cross-cutting theme introduced in numerous texts, and is a core aspect of the educational program.Multiple responsibilities: Student,Mother, Business woman2Cited in Catherine Honeyman’s essay entitled An Orientation Towards Human Progress: Developing Social Responsibility in Rural Honduran Youth through SAT, a terminal paper prepared for Harvard College in partial fulfillment of the requirements for an undergraduate degree.3 For a more thorough review of academic performance of SAT students, see Erin Murphy-Graham’s doctoral thesis entitled “Para Seguir Adelante:” Women’s Empowerm ent and the Sistema de Aprendizaje Tutorial (SAT) Program in Honduras, presented to the Faculty of the Graduate School of Harvard University, 2005.Another very exciting and unanticipated outcome of the SAT program in Honduras has been the complementary effect it has on basic education. As service to the community is a key component of the SAT program, many SAT participants serve as mentors to children in primary schools. In a recent evaluation of primary education conducted by a USAID financed Honduran NGO called ANEDH, it cited that in nine schools where the SAT participants tutored younger children, the desertion and failure rates of those children was approximately half that of those that did not receive this assistance.4The success of the SAT program in Honduras has resulted in its official recognition by Departmental authorities of the Ministry of Education. The Ministry of Education is now supporting the program financially, and calling for its implementation nationally. With CIDA support, the Bayan Association has created and leads a consortium of five NGOs called CEEDUCA, which is facilitating the gradual expansion of the SAT program across the country. The Bayan Association has also successfully attracted additional international donor agencies including the Ford Foundation and the Pestalozzi Children’s Fo undation to fund specific aspects of the program. Recently, the InterAmerican Development Bank in defining the scope of its Middle Education and Labor program (HO-0202), identified the Bayan Association and its SAT program as an intended recipient of funding for rural education nationally. While the Bayan Association reports that working with bilateral and multilateral funding requires additional patience and perseverance, they are confident that these funds will ultimately be made available to benefit rural communities.The SAT program has gradually attracted the attention of the international community, and FUNDAEC received the European Expo Jury Verdict Award (2000) and the Club of Budapest “Change the World Award” in 2002. CIDA funding has enabled the ongoing revision, adaptation and translation to English of the first fifteen of seventy-four SAT texts that correspond to the latter years of basic education. Additional materials that use the same approach, conceptual frameworks, and delivery system designed for youth aged 11—15 are already in use, and the Canadian Baha’i International Development Services, with CIDA’s continued support, is now planning to introduce SAT related programs for training junior youth capacities for sustainable development in Africa. Duncan Hanks is the Executive Director of the Canadian Baha’i International Development Services, the Canadian NGO partner of the Bayan Association (Honduras) and FUNDAEC (Colombia). E-mail: dhanks@sympatico.ca4 Cited in an e-mail communication dated 24 January 2006 from the Bayan Association to the Canadian Baha’i International Development Services.。

光伏发电英文文献Ultra-High Efficiency Photovoltaic

Ultra-High Efﬁciency Photovoltaic Cells for Large Scale Solar Power GenerationYoshiaki NakanoAbstract The primary targets of our project are to dras-tically improve the photovoltaic conversion efﬁciency and to develop new energy storage and delivery technologies. Our approach to obtain an efﬁciency over40%starts from the improvement of III–V multi-junction solar cells by introducing a novel material for each cell realizing an ideal combination of bandgaps and lattice-matching.Further improvement incorporates quantum structures such as stacked quantum wells and quantum dots,which allow higher degree of freedom in the design of the bandgap and the lattice strain.Highly controlled arrangement of either quantum dots or quantum wells permits the coupling of the wavefunctions,and thus forms intermediate bands in the bandgap of a host material,which allows multiple photon absorption theoretically leading to a conversion efﬁciency exceeding50%.In addition to such improvements, microfabrication technology for the integrated high-efﬁ-ciency cells and the development of novel material systems that realizes high efﬁciency and low cost at the same time are investigated.Keywords Multi-junctionÁQuantum wellÁConcentratorÁPhotovoltaicINTRODUCTIONLarge-scale photovoltaic(PV)power generation systems, that achieve an ultra-high efﬁciency of40%or higher under high concentration,are in the spotlight as a new technology to ease drastically the energy problems.Mul-tiple junction(or tandem)solar cells that use epitaxial crystals of III–V compound semiconductors take on the active role for photoelectric energy conversion in such PV power generation systems.Because these solar cells operate under a sunlight concentration of5009to10009, the cost of cells that use the epitaxial crystal does not pose much of a problem.In concentrator PV,the increased cost for a cell is compensated by less costly focusing optics. The photons shining down on earth from the sun have a wide range of energy distribution,from the visible region to the infrared region,as shown in Fig.1.Multi-junction solar cells,which are laminated with multilayers of p–n junctions conﬁgured by using materials with different band gaps,show promise in absorbing as much of these photons as possible,and converting the photon energy into elec-tricity with minimum loss to obtain high voltage.Among the various types of multi-junction solar cells,indium gallium phosphide(InGaP)/gallium arsenide(GaAs)/ger-manium(Ge)triple-junction cells that make full use of the relationship between band gaps and diverse lattice con-stants offered by compound semiconductors have the advantage of high conversion efﬁciency because of their high-quality single crystal with a uniform-size crystal lat-tice.So far,a conversion efﬁciency exceeding41%under conditions where sunlight is concentrated to an intensity of approximately5009has been reported.The tunnel junction with a function equivalent to elec-trodes is inserted between different materials.The positive holes accumulated in the p layer and the electrons in the adjacent n layer will be recombined and eliminated in the tunnel junction.Therefore,three p–n junctions consisting of InGaP,GaAs,and Ge will become connected in series. The upper limit of the electric current is set by the mini-mum value of photonﬂux absorbed by a single cell.On the other hand,the sum of voltages of three cells make up the voltage.As shown in Fig.1,photons that can be captured in the GaAs middle cell have a smallﬂux because of the band gap of each material.As a result,the electric currentoutputAMBIO2012,41(Supplement2):125–131 DOI10.1007/s13280-012-0267-4from the GaAs cell theoretically becomes smaller than that of the others and determines the electric current output of the entire tandem cell.To develop a higher efﬁciency tandem cell,it is necessary to use a material with a band gap narrower than that of GaAs for the middle cell.In order to obtain maximum conversion efﬁciency for triple-junction solar cells,it is essential to narrow down the middle cell band gap to 1.2eV and increase the short-circuit current density by 2mA/cm 2compared with that of the GaAs middle cell.When the material is replaced with a narrower band gap,the output voltage will drop.However,the effect of improving the electric current balance out-performs this drop in output voltage and boosts the efﬁ-ciency of the entire multi-junction cell.When a crystal with such a narrow band gap is grown on a Ge base material,lattice relaxation will occur in the middle of epitaxial crystal growth because the lattice constants of narrower band-gap materials are larger than that of Ge (as shown in Fig.2).As a result,the carrier transport properties will degrade due to dislocation.Researchers from the international research center Solar Quest,the University of Tokyo,aim to move beyond such material-related restrictions,and obtain materials and structures that have effective narrow band gaps while maintaining lattice matching with Ge or GaAs.To achieve this goal,we have taken three approaches as indicated in Fig.3.These approaches are explained in detail below.DILUTE NITROGEN-ADDED BULK CRYSTAL Indium gallium nitride arsenide (InGaNAs)is a bulk material consists of InGaAs,which contains several percent of nitrogen.InGaNAs has a high potential for achieving a narrow band gap while maintaining lattice matching with Ge or GaAs.However,InGaNAs has a fatal problem,that is,a drop in carrier mobility due to inhomogeneousdistribution of nitrogen (N).To achieve homogeneous solid solution of N in crystal,we have applied atomic hydrogen irradiation in the ﬁlm formation process and addition of a very small amount of antimony (Sb)(Fig.3).The atomic hydrogen irradiation technology and the nitrogen radical irradiation technology for incorporating N efﬁciently into the crystal can be achieved only through molecular beam epitaxy (MBE),which is used to fabricate ﬁlms under high vacuum conditions.(Nitrogen radical irradiation is a technology that irradiates the surface of a growing crystal with nitrogen atoms that are resolved by passing nitrogen through a plasma device attached to the MBE system.)Therefore,high-quality InGaNAs has been obtained only by MBE until now.Furthermore,as a small amount of Sb is also incorporated in a crystal,it is nec-essary to control the composition of ﬁve elements in the crystal with a high degree of accuracy to achieve lattice matching with Ge or GaAs.We have overcome this difﬁculty by optimizing the crystal growth conditions with high precision and devel-oped a cell that has an InGaNAs absorption layer formed on a GaAs substrate.The short-circuit current has increased by 9.6mA/cm 2for this cell,compared with a GaAs single-junction cell,by narrowing the band gap down to 1.0eV.This technology can be implemented not only for triple-junction cells,but also for higher efﬁciency lattice-matched quadruple-junction cells on a Ge substrate.In order to avoid the difﬁculty of adjusting the compo-sition of ﬁve elements in a crystal,we are also taking an approach of using GaNAs with a lattice smaller than that of Ge or GaAs for the absorption layer and inserting InAs with a large lattice in dot form to compensate for the crystal’s tensile strain.To make a solid solution of N uniformly in GaNAs,we use the MBE method for crystal growth and the atomic hydrogen irradiation as in the case of InGaNAs.We also believe that using 3D-shaped InAs dots can effectively compensate for the tensile strainthatFig.1Solar spectrum radiated on earth and photon ﬂux collected by the top cell (InGaP),middle cell (GaAs),and bottom cell (Ge)(equivalent to the area of the ﬁlled portions in the ﬁgure)occurs in GaNAs.We have measured the characteristics of a single-junction cell formed on a GaAs substrate by using a GaNAs absorption layer with InAs dots inserted.Figure 4shows that we were able to succeed in enhancing the external quantum efﬁciency in the long-wavelength region (corresponding to the GaNAs absorp-tion)to a level equal to GaAs.This was done by extending the absorption edge to a longer wavelength of 1200nm,and increasing the thickness of the GaNAs layer by increasing the number of laminated InAs quantum dot layers.This high quantum efﬁciency clearly indicates that GaNAs with InAs dots inserted has the satisfactory quality for middle cell material (Oshima et al.2010).STRAIN-COMPENSATED QUANTUM WELL STRUCTUREIt is extremely difﬁcult to develop a narrow band-gap material that can maintain lattice matching with Ge orGaAs unless dilute nitrogen-based materials mentioned earlier are used.As shown in Fig.2,the conventionally used material InGaAs has a narrower band gap and a larger lattice constant than GaAs.Therefore,it is difﬁcult to grow InGaAs with a thickness larger than the critical ﬁlm thickness on GaAs without causing lattice relaxation.However,the total ﬁlm thickness of InGaAs can be increased as an InGaAs/GaAsP strain-compensated multi-layer structure by laminating InGaAs with a thickness less than the critical ﬁlm thickness in combination with GaAsP that is based on GaAs as well,but has a small lattice constant,and bringing the average strain close to zero (Fig.3.).This InGaAs/GaAsP strain-compensated multilayer structure will form a quantum well-type potential as shown in Fig.5.The narrow band-gap InGaAs layer absorbs the long-wavelength photons to generate electron–hole pairs.When these electron–hole pairs go over the potential bar-rier of the GaAsP layer due to thermal excitation,the electrons and holes are separated by a built-in electricﬁeldFig.2Relationship between band gaps and lattice constants of III–V-based and IV-based crystalsto generate photocurrent.There is a high probability of recombination of electron–hole pairs that remain in the well.To avoid this recombination,it is necessary to take out the electron–hole pairs efﬁciently from the well and transfer them to n-type and p-type regions without allowing them to be recaptured into the well.Designing thequantumFig.3Materials and structures of narrow band-gap middle cells being researched by thisteamFig.4Spectral quantum efﬁciency of GaAs single-junction cell using GaNAs bulk crystal layer (inserted with InAs dots)as the absorption layer:Since the InAs dot layer and the GaNAs bulk layer are stacked alternately,the total thickness of GaNAs layers increases as the number of stacked InAs dot layers is increased.The solid line in the graph indicates the data of a reference cell that uses GaAs for its absorption layer (Oshima et al.2010)well structure suited for this purpose is essential for improving conversion efﬁciency.The high-quality crystal growth by means of the metal-organic vapor phase epitaxy (MOVPE)method with excellent ability for mass production has already been applied for InGaAs and GaAsP layers in semiconductor optical device applications.Therefore,it is technologically quite possible to incorporate the InGaAs/GaAsP quantum well structure into multi-junction solar cells that are man-ufactured at present,only if highly accurate strain com-pensation can be achieved.As the most basic approach related to quantum well structure design,we are working on fabrication of super-lattice cells with the aim of achieving higher efﬁciency by making the GaAsP barrier layer as thin as possible,and enabling carriers to move among wells by means of the tunnel effect.Figure 6shows the spectral quantum efﬁ-ciency of a superlattice cell.In this example,the thickness of the GaAsP barrier layer is 5nm,which is not thin enough for proper demonstration of the tunnel effect.When the quantum efﬁciency in the wavelength range (860–960nm)that corresponds to absorption of the quan-tum well is compared between a cell,which has a con-ventionally used barrier layer and a thickness of 10nm or more,and a superlattice cell,which has the same total layer thickness of InGaAs,the superlattice cell demonstrates double or higher quantum efﬁciency.This result indicates that carrier mobility across quantum wells is promoted by even the partial use of the tunnel effect.By increasing the P composition in the GaAsP layer,the thickness of well (or the In composition)can be increased,and the barrier layer thickness can be reduced while strain compensation is maintained.A cell with higher quantum efﬁciency can befabricated while extending the absorption edge to the long-wavelength side (Wang et al.2010,2012).GROWTH TECHNIQUE FOR STRAIN-COMPENSATED QUANTUM WELLTo reduce the strain accumulated in the InGaAs/GaAsP multilayer structure as close to zero as possible,it is nec-essary to control the thickness and atomic content of each layer with high accuracy.The In composition and thickness of the InGaAs layer has a direct effect on the absorption edge wavelength and the GaAsP layer must be thinned to a satisfactory extent to demonstrate fully the tunnel effect of the barrier layer.Therefore,it is desirable that the average strain of the entire structure is adjusted mainly by the P composition of the GaAsP layer.Meanwhile,for MOVPE,there exists a nonlinear rela-tionship between the P composition of the crystal layer and the P ratio [P/(P ?As)]in the vapor phase precursors,which arises from different absorption and desorption phenomena on the surface.As a result,it is not easy to control the P composition of the crystal layer.To break through such a difﬁculty and promote efﬁcient optimiza-tion of crystal growth conditions,we have applied a mechanism to evaluate the strain of the crystal layer during growth in real time by sequentially measuring the curvature of wafers during growth with an incident laser beam from the observation window of the reactor.As shown in Fig.7,the wafer curvature during the growth of an InGaAs/GaAsP multilayer structure indicates a periodic behavior.Based on a simple mechanical model,it has become clear that the time changes ofwaferFig.5Distribution of potential formed by the InGaAs/GaAsP strain-compensated multilayer structure:the narrow band-gap InGaAs layer is sandwiched between wide band-gap GaAsP layers and,as a result,it as quantum well-type potential distribution.In the well,electron–hole pairs are formed by absorption of long-wavelength photons and at the same time,recombination of electrons and holes takes place.The team from Solar Quest is focusing on developing a superlattice structure with the thinnest GaAsP barrier layercurvature are proportionate to the strain of the crystal layer relative to a substrate during the growing process.One vibration cycle of the curvature is same as the growth time of an InGaAs and GaAsP pair (Sugiyama et al.2011).Therefore,the observed vibration of the wafer curvature reﬂects the accumulation of the compression strain that occurs during InGaAs growth and the release of the strain that occurs during GaAsP growth.When the strain is completely compensated,the growth of the InGaAs/GaAsP pair will cause this strain to return to the initial value and the wafer curvature will vibrate with the horizontal line as the center.As shown in Fig.7,strain can be compensated almost completely by adjusting the layer structure.Only by conducting a limited number of test runs,the use of such real-time observation technology of the growth layer enables setting the growth conditions for fabricating the layer structure for which strain has been compensated with highaccuracy.Fig.6Spectral quantum efﬁciency of GaAs single-junction cell using InGaAs/GaAsP superlattice as theabsorption layer:This structure consists of 60layers of InGaAs quantum wells.The graph also shows data of a reference cell that uses GaAs for its absorption layer (Wang et al.2010,2012)Fig.7Changes in wafer curvature over time during growth of the InGaAs/GaAsP multilayer structure.This graph indicates the measurement result and the simulation result of the curvature based on the layer structure(composition ?thickness)obtained by X-ray diffraction.Since compressive strain is applied during InGaAs growth,the curvature decreases as time passes.On the other hand,since tensile strain is applied during GaAsP growth,the curvature changes in the oppositedirection (Sugiyama et al.2011)FUTURE DIRECTIONSIn order to improve the conversion efﬁciency by enhancing the current matching of multi-junction solar cells using III–V compound semiconductors,there is an urgent need to create semiconductor materials or structures that can maintain lattice matching with Ge or GaAs,and have a band gap of1.2eV.As for InGaNAs,which consists of InGaAs with several percent of nitrogen added,we have the prospect of extending the band edge to1.0eV while retaining sufﬁcient carrier mobility for solar cells by means of atomic hydrogen irradiation and application of a small quantity of Sb during the growth process.In addition,as for GaNAs bulk crystal containing InAs dots,we were able to extend the band edge to1.2eV and produce a high-quality crystal with enoughﬁlm thickness to achieve the quantum efﬁciency equivalent to that of GaAs.These crystals are grown by means of MBE. Therefore,measures that can be used to apply these crys-tals for mass production,such as migration to MOVPE, will be investigated after demonstrating their high efﬁ-ciency by embedding these crystals into multi-junction cells.As for the InGaAs/GaAsP strain-compensated quantum well that can be grown using MOVPE,we are working on the development of a thinner barrier layer while compen-sating for the strain with high accuracy by real-time observation of the wafer curvature.We have had the prospect of achieving a quantum efﬁciency that will sur-pass existing quantum well solar cells by promoting the carrier transfer within the multilayer quantum well struc-ture using the tunnel effect.As this technology can be transferred quite easily to the existing multi-junction solar cell fabrication process,we strongly believe that this technology can signiﬁcantly contribute to the efﬁciency improvement of the latest multi-junction solar cells. REFERENCESOshima,R.,A.Takata,Y.Shoji,K.Akahane,and Y.Okada.2010.InAs/GaNAs strain-compensated quantum dots stacked up to50 layers for use in high-efﬁciency solar cell.Physica E42: 2757–2760.Sugiyama,M.,K.Sugita,Y.Wang,and Y.Nakano.2011.In situ curvature monitoring for metalorganic vapor phase epitaxy of strain-balanced stacks of InGaAs/GaAsP multiple quantum wells.Journal of Crystal Growth315:1–4.Wang,Y.,Y.Wen,K.Watanabe,M.Sugiyama,and Y.Nakano.2010.InGaAs/GaAsP strain-compensated superlattice solar cell for enhanced spectral response.In Proceedings35th IEEE photovoltaic specialists conference,3383–3385.Wang,Y.P.,S.Ma,M.Sugiyama,and Y.Nakano.2012.Management of highly-strained heterointerface in InGaAs/GaAsP strain-balanced superlattice for photovoltaic application.Journal of Crystal Growth.doi:10.1016/j.jcrysgro.2011.12.049. AUTHOR BIOGRAPHYYoshiaki Nakano(&)is Professor and Director General of Research Center for Advanced Science and Technology,the University of Tokyo.His research interests include physics and fabrication tech-nologies of semiconductor distributed feedback lasers,semiconductor optical modulators/switches,monolithically integrated photonic cir-cuits,and high-efﬁciency heterostructure solar cells.Address:Research Center for Advanced Science and Technology, The University of Tokyo,4-6-1Komaba,Meguro-ku,Tokyo153-8904,Japan.e-mail:nakano@rcast.u-tokyo.ac.jp。

On the usage and measurement of landscape connectivity

OIKOS 90:7–19.Copenhagen 2000Minireviews provides an opportunity to summarize existing knowledge of selected ecological areas,with special emphasis on current topics where rapid and signiﬁcant advances are occurring.Reviews should be concise and not too wide-ranging.All key references should be cited.A summary is required.MINI-REVIEWOn the usage and measurement of landscape connectivityLutz Tischendorf and Lenore FahrigTischendorf,L.and Fahrig,L.2000.On the usage and measurement of landscape connectivity.–Oikos 90:7–19.This paper examines the usage and measurement of ‘‘landscape connectivity’’in 33recent studies.Connectivity is deﬁned as the degree to which a landscape facilitates or impedes movement of organisms among resource patches.However,connectivity is actually used in a variety of ways in the literature.This has led to confusion and lack of clarity related to (1)function vs structure,(2)patch isolation vs landscape connectivity and,(3)corridors vs connectivity.We suggest the term connectivity should be reserved for its original purpose.We highlight nine studies;these include modeling studies that actually measured connectivity in accordance with the deﬁni-tion,and empirical studies that measured key components of connectivity.We found that measurements of connectivity provide results that can be interpreted as recom-mending habitat fragmentation to enhance landscape connectivity.We discuss rea-sons for this misleading conclusion,and suggest a new way of quantifying connectivity,which avoids this problem.We also recommend a method for reducing sampling intensity in landscape-scale empirical studies of connectivity.L .Tischendorf and L .Fahrig ,Ottawa -Carleton Inst .of Biology ,Carleton Uni 6.,Ottawa ,ON ,Canada K 1S 5B 6(present address of LT :Busestrasse 76,D -28213Bremen ,Germany [tischendorf@cla 6is -bremen .de ]).What is landscape connectivity?The effects of spatial structure (patchiness)on popu-lation dynamics were ﬁrst examined in patch-based population models beginning in the early 1970s (e.g.,Levins 1969,Reddingius and den Boer 1970,Levin 1974,1976,Roff 1974).Further modeling studies showed that assumptions about movement among habitat patches greatly inﬂuence the predictions of such models (e.g.,Lefkovitch and Fahrig 1985,Fahrig 1988,1990,Fahrig and Paloheimo 1988,Henein and Merriam 1990,Adler and Nuernberger 1994,Lindenmayer and Lacy 1995,Lindenmayer and Possingham 1996,Frank and Wissel 1998,Henein et al.1998).Movement among habitat patches is,how-ever,not simply a function of an organism itself,but also depends on the landscape through which it must move.To emphasize the interaction between species’attributes and landscape structure in determining movement of organisms among habitat patches,Mer-riam (1984)introduced the concept of ‘‘landscape connectivity’’.OIKOS 90:1(2000)7Accepted 31January 2000Copyright ©OIKOS 2000ISSN 0030-1299Printed in Ireland –all rights reservedTaylor et al.(1993)deﬁned landscape connectivity as ‘‘the degree to which the landscape facilitates or im-pedes movement among resource patches’’.Similarly, With et al.(1997)deﬁned landscape connectivity as ‘‘the functional relationship among habitat patches, owing to the spatial contagion of habitat and the movement responses of organisms to landscape struc-ture’’.These deﬁnitions accentuate the dependence of movement on landscape structure,which suggests that connectivity is species-and landscape-speciﬁc.One must therefore describe landscape structure from a species’point of view(Wiens and Milne1989).This starts with deﬁning the species’habitat.The next step is to determine the scale at which the species responds to landscape structure,through itsﬁne-scale(grain)and large-scale(extent)movement(Wiens1997).This deter-mines the scale of habitat pattern as perceived by the organism.Finally,one must determine how the species responds to the different elements of a landscape.This comprises the species movement pattern and mortality risk on landscape elements(patches)as well as reactions at boundaries.Note that all of these behavioral facets contribute toward facilitating or impeding movement among resource patches.In summary,landscape connectivity encapsulates the combined effects of(1)landscape structure and(2)the species’use,ability to move and risk of mortality in the various landscape elements,on the movement rate among habitat patches in the landscape. Objective and approachWe reviewed the literature covered by the Agriculture, Biology&Environmental Sciences Edition of the Cur-rent Contents database(CC1998),from May1993to November1998.We searched article titles and key words for the term connecti6ity in combination with landscape or patch or habitat.The search resulted in49 papers.However,17of these papers did not use con-nectivity at all.We omitted these from the review,and included one other paper(Doak et al.1992)leaving33 papers,which are assembled in descending chronologi-cal and alphabetical order in Table1,and classiﬁed in Fig.1.Our objective was to examine the current usage and measurement of landscape connectivity.We start with a critical discussion of the diverse usage of connectivity, followed by a description of modeling and empirical studies that actually attempted to quantify connectivity or key components of it.We then discuss crucial model-ing assumptions and reveal the deceptive paradox of patch-based connectivity measurements,and its poten-tial for misleading conclusions.We end by suggesting ways to streamline and focus research on landscape connectivity.Current usage of connectivityStructure or function?The literature review revealed that the term connectiv-ity is sometimes used as a functional concept and other times in a structural way.Structural connectivity is equated with habitat contiguity and is measured by analyzing landscape structure,independent of any at-tributes of the organism(s)of interest(Collinge and Forman1998).The functional concept of connectivity explicitly con-siders the behavioral responses of an organism to the various landscape elements(patches and boundaries). Consequently,functional connectivity covers situations where organisms venture into non-habitat(matrix), where they may(1)face higher mortality risks(e.g., Lidicker1975,Gaines and McGlenaghan1980,Krohne and Burgin1987,Henein and Merriam1990,Schippers et al.1996,Charrier et al.1997,Poole1997,Sakai and Noon1997),(2)express different movement patterns (e.g.,Baars1979,Rijnsdorp1980,Wallin and Ekbom 1988,Wegner and Merriam1990,Hansson1991,John-son et al.1992a,Andreassen et al.1996b,Matter1996, Charrier et al.1997,Collins and Barrett1997),and(3) cross boundaries(e.g.,Mader1984,Wiens et al.1985, Bakowski and Kozakiewicz1988,Merriam et al.1989, Duelli et al.1990,Mader et al.1990,Frampton et al. 1995,Mauremooto et al.1995,Charrier et al.1997, Sakai and Noon1997).Depending on the movement attributes of the organ-ism,structural and functional connectivity can be syn-onymous.This occurs when the organism’s movement is conﬁned to its preferred habitat,i.e.,individuals do not cross the habitat/matrix boundary,and the organ-ism moves freely within the preferred habitat(e.g., Bascompte and Sole´1996).This is the assumption behind most percolation-based connectivity measures (Gardner et al.1987,Gardner and O’Neill1991,Green 1994).The fact that structural connectivity is relatively easy to measure could lead to the conclusion that connectiv-ity is a generalized feature of a landscape.This would be erroneous.In fact,the same landscape will have different connectivities for different organisms.Struc-turally connected habitat patches still may not be func-tionally connected and even non-contiguous habitat patches may be functionally connected,depending on the species(With1997).For example,if the only two habitat patches in a landscape are structurally con-nected by an inappropriate corridor for the species in question(too narrow or too long),structural connectiv-ity would exist without successful movement(functional response)from one patch to the other.Likewise,non-contiguous habitat patches may functionally be con-nected if the species can cross the non-habitat area (matrix)successfully and move between habitat8OIKOS90:1(2000)OIKOS 90:1(2000)9T a b l e 1.C h r o n o l o g i c a l a n d a l p h a b e t i c a l a s s e m b l a g e o f t h e 33r e v i e w e d c o n n e c t i v i t y s t u d i e s .S t u d y t y p e a n d d u r a t i o nS t u d yN o .M e a s u r e m e n t /u s a g e o f c o n n e c t i v i t yC o m m e n t s /s t u d y t a r g e t S p a t i a l s c a l e A n d r e a s s e n e t l a n d s c a p e e f f e c t s o n m o v e m e n t f r e q u e n c i e s e x p e r i m e n t ,r a d i o -t r a c k i n g ,13w k ,3p r e s e n c e /a b s e n c e o f c o r r i d o r s1g e n e r a t i o n s a l .1998e f f e c t o f s t r u c t u r a l p a t c h i s o l a t i o n o n s u m m e d i n ﬂu e n c e o f s i z e a n d s p a t i a l p a t c h o b s e r v a t i o n a l ,2y rA u l t a n d 2a r r a n g e m e n t o f n e i g hb o r i n g p a tc h e sc o m m u n i t y s t r u c t u r e a nd p o p u l a t i o n J o h n s o n 1998d e n s i t y e x p e r i m e n t ,l i v e -t r a p p i n g ,13w k ,3e f f e c t o n d i s p e r s a l d i s t a n c e s a n d s p a t i a l p r e s e n c e /a b s e n c e o f c o r r i d o r s l a n d s c a p eB j o r n s t a d e t a l .3a g g r e g a t i o n g e n e r a t i o n 1998l a n d s c a p e ,10e x p e r i m e n tp e r c e n t o f e q u a l l y s p a c e d s t r a i g h t l i n e s 4C o l l i n g e a n d e f f e c t o f s t r u c t u r a l c o n n e c t i v i t y m ×10mm e a s u r e m e n t o n i n s e c t d e n s i t y ,r i c h n e s s ,F o r m a n 1998c o v e r i n g h a b i t a t w i t h i n a l a nd s c a pe a n d c o m m u n i t y s t r u c t u r e d i s c u s s i o nr a t i o n a l e o n t h e q u a n t i ﬁc a t i o n o f l a n d s c a p es t r u c t u r a l p a t c h i s o l a t i o n D a v i d s o n 19985l a n d s c a p e f r a g m e n t a t i o n l a n d s c a p em o v e m e n t o f w a t e r b i r d s a m o n g h a b i t a t d i s c u s s i o nH a i g e t a l .1998r a t i o n a l e o n t h e i m p o r t a n c e o f f u n c t i o n a l 6p a t c h e s c o n n e c t i v i t y f o r w a t e r b i r d c o n s e r v a t i o n s p a t i a l l y e x p l i c i t s i m u l a t i o n m o d e l ,25y rH e n e i n e t a l .p r e s e n c e ,a b s e n c e a n d q u a l i t y o f f e n c e r o w s 7e f f e c t s o n p o p u l a t i o n s u r v i v a l l a n d s c a p ei n s i m u l a t e d l a n d s c a p e 1998e f f e c t o f s t r u c t u r a l a n d f u n c t i o n a l 8l a n d s c a p ee x p e r i m e n t ,o n e s e a s o nP e t i t a n d B u r e l d i s t a n c e s (e u c l i d i a n ,a l o n g h e d g e r o w s a n d ,w e i g h t e d b y m o v e m e n t i n t e n s i t y a n d c o n n e c t i v i t y o n s p e c i e s ’l o c a l a b u n d a n c e 1998bm o r t a l i t y i n d i f f e r e n t h a b i t a t t y p e s )b e t w e e n s a m p l e s i t e s 9l a n d s c a p ee x p e r i m e n t ,o n e s e a s o n‘‘f u n c t i o n a l d i s t a n c e ’’(w e i g h t e d b y P e t i t a n d B u r e l e f f e c t o f f u n c t i o n a l c o n n e c t i v i t y o n 1998am o v e m e n t i n t e n s i t y a n d m o r t a l i t y i n s p e c i e s ’l o c a l a b u n d a n c e d i f f e r e n t h a b i t a t t y p e s )l a n d s c a p em a n i p u l a t i v e m a r k -r e c a p t u r e e x p e r i m e n t ,e f f e c t s o f l a n d s c a p e s t r u c t u r e o n m o v e m e n t a b i l i t y o f d a m s e l ﬂi e s t h r o u g h 10P i t h e r a n d d i f f e r e n t h a b i t a t t y p e s m o v e m e n t f r e q u e n c i e s o n e s e a s o n T a y l o r 1998e f f e c t o f s t r u c t u r a l c o n n e c t i v i t y o n l a n d s c a p eG I S b a s e d p o p u l a t i o n d y n a m i c s m o d e l n e a r e s t n e i g h b o r d i s t a n c e (c o m b i n e d w i t h 11R o o t 1998d i s pe r s a lf r e q u e n c y d i s t r i b u t i o n )b e t w e e n (m e t a )p o p u l a t i o n s i z e (R A M A S )h a b i t a t p a t c h e s 12p a t c hv e g e t a t i o n s u r v e ya m o u n t o f f o r e s t h ab i t a t a r o u n d p a tc h e s e f f e c t o f s t r u c t u r a l p a t c h i s o l a t i o n o n G r a s h o f b o kd a m 1997w i t h i n t h r e e z o n e s u p t o 1000m z o o c h o r o u s a n d a n e m o c h o r o u s p l a n t s p e c i e s l a n d s c a p es t a t i c o p t i m i z a t i o n a n d s i m u l a t i o n m o d e lp o p u l a t i o n a b u n d a n c e r e l a t i o n s h i p 13H o f a n d c o n n e c t i v i t y m e a s u r e a s s u m e d t o b e b e t w e e n a d j a c e n t c e l l s i n a g r i d m o d e l s p a t i a l l i m i t a t i o n f a c t o r R a p h a e l 1997c o n n e c t i v i t y c o m p o n e n t s :a )d e g r e e o f r a t i o n a l e o n t h e e f f e c t o f c o n n e c t i v i t y o n l a n d s c a p ec o n c e p t u a l m ode l ,d i s c u s s i o n14M e t z g e r a n d h a b i t a t p e r c o l a t i o n ,b )c o r r i d o r a n d b i o d i v e r s i t y D e ´c a m p s 1997s t e p p i n g s t o n e n e t w o r k s ,c )m a t r i x p e r m e a b i l i t y e f f e c t o n l o c a l b i r d c o m m u n i t y (s p e c i e s S c h m i e g e l o w e t p a t c he x p e r i m e n t ,1y rc o r r id o r s (r i p a r i a n b u f fe r s t r i p s )b e t w e e n 15f o r e s t f r ag m e n t s a b u n d a n c e s )a l .1997e f f e c t s o f s i m u l a t e d l a n d s c a p e ch a n g e s o n p r o xi m i t y i n d e x -s u m m a r i z e d (p a t c h p a t c hq u a n t i ﬁc a t i o n o f s p a t i a l p a t t e r n i n G I SS p e t i c h e t a l .161997m a p ss t r u c t u r a l p a t c h i s o l a t i o n (p r o x i m i t y )a r e a /d i s t a n c e t o f o c a l p a t c h )r e l a t i o n s h i p f o r a l l p a t c h e s l o c a t e d w i t h i n r e c t a n g u l a r b u f f e r z o n e a r o u n d f o c a l p a t c h e s t i m a t i o n o f e f f e c t s o n s p e c i a l i s t l a n d s c a p ec o n c e p t u a l m ode li n t r i n s i c (j u x t a p o s i t i o n o f s i m i l a r h a b i t a t )T i e b o u t a n d 17c o l o n i z i n g a b i l i t y a nde x t r i n s i c (c o r r i d o r )c o n n e c t i v i t y A n d e r s o n 1997W i t h e t a l .ef f e c t o f l a n d s c a p e s p a t i a l s t r u c t u r e o n a v e r ag e d i s t a n c e b e t w e e n t w o s i t e s o f a l a n d s c a p e r a n d o m w a l k s i m u l a t i o n m o d e l o n 18n e u t r a l (r a n d o m a n d f r a c t a l )l a n d s c a p e 1997g r i d b e l o n g i n g t o t h e s a m e (p e r c o l a t i o n )p e r c o l a t i o n t h r e s h o l d a n d p o p u l a t i o n s ’s p a t i a l d i s t r i b u t i o nm a p sc l u s t e r ,p o p u l a t i o n s ’s p a t i a ld i s t r i b u t i o n10OIKOS 90:1(2000)T a b l e 1.(C o n t i n u e d )S p a t i a l s c a l e S t u d y t y p e a n d d u r a t i o nS t u d yN o .M e a s u r e m e n t /u s a g e o f c o n n e c t i v i t yC o m m e n t s /s t u d y t a r g e t p a t c h (c o r r i d o r )e x p e r i m e n t ,3m oA n d r e a s s e n e t a l .19s t r u c t u r a l d i s c o n t i n u i t i e s i n c o r r i d o r s e f f e c t s o n m o v e m e n t r a t e s 1996b e f f e c t s o n m o v e m e n t r a t e s p a t c h (c o r r i d o r )w i d t h o f c o r r i d o r s e x p e r i m e n t ,3m oA n d r e a s s e n e t a l .201996a l a n d s c a p e p h y s i c a l c o n n e c t i o n b e t w e e n p a t c h e s m e t a p o p u l a t i o n m o d e lH e s s 1996e f f e c t o n r e c o l o n i z a t i o n a n d e x t i n c t i o n 21(c o r r i d o r s )r a t e e f f e c t o f f u n c t i o n a l p a t c h i s o l a t i o n o n p a t c h h a b i t a t i s o l a t i o n b a s e d o n d i s p e r s a l o b s e r v a t i o n a l ,2y rH j e r m a n n a n d 22s p e c i e s p a t c h o c c u p a n c y d i s t a n c e d i s t r i b u t i o n s a n d n e g a t i v e I m s 1996e x p o n e n t i a l d i s p e r s a l f u n c t i o n e f f e c t o n p o p u l a t i o n m e a n s a n d 23p a t c h o p t i m i z a t i o n m o d e lb e t w e e n -p a tc h m o v e m e n t p r o b a b i l i t y H o f a nd F l a t he r v a r i a n c e s 1996d e p e n d e n t o n a )s p e c i e s d i s p e r s a l c a p a b i l i t y ,b )h a r s h n e s s of i n t e r -p a t c h e n v i r o n m e n t ,c )i n t e r -p a t c h d i s t a n c e e x p e r i m e n t ,1y rL e c o m t e a n d s i m u l a t e d p r e s e n c e /a b s e n c e o f 24e f f e c t s o n i n t e r -p a t c h d i s p e r s a l p a t c h C l o b e r t 1996c o r r i d o r s i n a n e x p e r i m e n t a l l a n d s c a p e p a t c h o b s e r v a t i o n a l ,1y rt o t a l l e n g t h o f h e d g e s i n a 0.5-k m P a i l l a t a n d B u t e t e f f e c t o f s t r u c t u r a l p a t c h i s o l a t i o n o n 25r a d i u s a r o u n d a s a m p l i n g p l o t (p a t c h )s p e c i e s a b u n d a n c e a n d ﬂu c t u a t i o n s 1996e f f e c t o f r e a l l a n d s c a p e s t r u c t u r e o n l a n d s c a p e G I S -r e l a t e d r a n d o m w a l k s i m u l a t i o n m o d e l26S c h i p p e r s e t a l .m o v e m e n t p r o b a b i l i t i e s b e t w e e n a l l f u n c t i o n a l c o n n e c t i v i t y p a i r s o f h a b i t a t p a t c h e s 1996G I S -r e l a t e d r a n d o m w a l k s i m u l a t i o n m o d e ld i s pe r s a l s u c c e s s r a t e ,f r a c t i o n o f S c h u m a k e r 1996e f f e c t o f l a n d s c a p e s t r u c t u r e o n 27l a n d s c a p e f u n c t i o n a l c o n n e c t i v i t y i n d i v i d u a l s t h a t l o c a t e d n e w t e r r i t o r i e s p r e s e n c e /a b s e n c e o f c o r r i d o r s i n e f f e c t o n m e t a p o p u l a t i o n p e r s i s t e n c e S w a r t a n d L a w e s l a n d s c a p e 28m o d e lm e t a p o p u l a t i o n m o d e l 1996G I S -r e l a t e d r a n d o m w a l k a n d p o p u l a t i o n d y n a m i c s 29D e m e r s e t a l .l a n d s c a p e e f f e c t o f r e a l l a n d s c a p e s t r u c t u r e o n d i s p e r s a l (c o l o n i z a t i o n )s u c c e s s s i m u l a t i o n m o d e l f u n c t i o n a l c o n n e c t i v i t y 1995l a n d s c a p e o b s e r v a t i o n a l ,3y rp r e s e n c e /a b s e n c e o f c o r r i d o r s a n d /o r 30e f f e c t o n m o v e m e n t r a t e s a n d d i s t a n c e s A r n o l d e t a l .1993s t e p p i n g s t o n e s s t a t i c o p t i m i z a t i o n m o d e ll a n d s c a p e o p t i m i z a t i o n o f h a b i t a t p l a c e m e n t p r o b a b i l i s t i c ,d i s t a n c e d e p e n d e n t H o f a n d J o y c e 31i s o l a t i o n o f a c e l l i n a g r i d m o d e l 1993d e g r e e t o w h i c h t h e l a n d s c a p e l a n d s c a p e c o n c e p t u a l d i s c u s s i o nT a y l o r e t a l .199332d e ﬁn i t i o n o f f u n c t i o n a l c o n n e c t i v i t y f a c i l i t a t e s o r i m p e d e s m o v e m e n t a m o n g r e s o u r c e p a t c h e s e f f e c t o f s c a l e o f c l u s t e r i n g o n s e a r c h t i m e -n u m b e r o f m o v e m e n t l a n d s c a p e r a n d o m w a l k s i m u l a t i o n m o d e l o n h i e r a r c h i c a l ,n e u t r a l 33D o a k e t a l .1992l a n d s c a p e m a p ss t e p s r e q u i r e d t o ﬁn d a n e w h a b i t a t f u n c t i o n a l c o n n e c t i v i t y p a t c hpatches.Research is needed to determine what,if any, simple measures of landscape structure can be used as measures of landscape connectivity.Patch isolation or landscape connectivity?Patch isolation is determined by the rate of immigration into the patch;the lower the immigration rate,the more isolated is the patch.Immigration rate depends on(1) the amount of occupied habitat surrounding the focal patch,(2)the number of emigrants leaving the sur-rounding habitat,(3)the nature of the intervening matrix,(4)the movement and perceptual abilities of the organism,and(5)the mortality risk of dispersers (Wiens et al.1993).Since(1)and(3)are landscape structural features and(4)and(5)are the organisms’responses to landscape structure,patch isolation de-pends on‘‘the degree to which the landscape facilitates or impedes movement...’’(Taylor et al.1993).Patch isolation is therefore imbedded within the concept of landscape connectivity.In fact,landscape connectivity is essentially equivalent to the inverse of the average degree of patch isolation over the landscape;a land-scape including mostly patches with a high degree of isolation will be less connected than vice versa.Five of the33studies we reviewed equated patch isolation with connectivity(Hjermann and Ims1996, Paillat and Butet1996,Grashofbokdam1997,Spetich et al.1997,Ault and Johnson1998).Even though patch isolation is clearly part of landscape connectivity (above),none of these studies estimated immigration rates into patches.Rather,they related a species’abun-dance or presence/absence in a patch to structural attributes of the surrounding landscape,such as dis-tance to the nearest occupied patch,or amount of habitat in a circle surrounding the patch.Such studies may reveal the relative importance of local patch vs surrounding landscape effects.However,they do not directly contribute to determining landscape connectiv-ity,because they do not actually determine rates of movement among patches.Corridors or connectivity?Corridors are narrow,continuous strips of habitat that structurally connect two otherwise non-contiguous habitat patches.The corridor concept(e.g.,Forman 1983,Bennett1990,Merriam1991,Saunders and Hobbs1991,Lindenmayer and Nix1993,Merriam and Saunders1993,Bonner1994,Dawson1994,Rosenberg et al.1997,Tischendorf1997a)originated from the generalized assumption that organisms do not venture into non-habitat.Under this assumption,addition of any habitat to a landscape increases the ability of organisms to move.Corridors in a landscape may therefore be a component of its connectivity if they promote movement among habitat patches,but they do not determine its connectivity.The degree to which corridors contribute to landscape connectivity depends on the nature of the corridors,the nature of the matrix and the response of the organism to both(Rosenberg et al.1997,Beier and Noss1998).Six of the reviewed studies equated the term connec-tivity with the presence/absence of corridors(Hess 1996,Lecomte and Clobert1996,Swart and Lawes 1996,Schmiegelow et al.1997,Andreassen et al.1998, Bjornstad et al.1998),and two studies associated con-nectivity with corridor width(Andreassen et al.1996a) or corridor continuity(Andreassen et al.1996b).The studies investigated(1)what features of a corridorFig.1.Classiﬁcation of the33reviewed studiesaccording to study type(a),year of publication(b),andusage of the termconnectivity(c).OIKOS90:1(2000)11determine its use by the organism,(2)space-use of organisms as a function of corridor presence/absence, and(3)population or community responses to corridors, e.g.,species richness,diversity or abundance.None of the studies explicitly recognized that corridors are only a component of the concept of landscape connectivity;they actually equated the connecting function of corridors with connectivity.Measurements of connectivityIn this section we review studies that quantiﬁed connec-tivity or key components of it.Recall that connectivity is deﬁned as the degree to which the landscape facilitates or impedes movement among resource patches.Only four of the studies(Doak et al.1992,Demers et al.1995, Schippers et al.1996,Schumaker1996)measured move-ments among resource patches over the entire landscape and actually quantiﬁed connectivity in accordance with its deﬁnition.All of these were modeling studies and were based on simulated movements across heterogeneous landscapes.We also reviewﬁve other studies which we think made an important contribution toward the con-cept of landscape connectivity(as explained below),even though they did not measure movement among resource patches directly(Arnold et al.1993,With et al.1997,Petit and Burel1998a,b,Pither and Taylor1998). Modeling studiesDispersal successDispersal success is usually deﬁned as the proportion of individuals that successfully immigrate into a new habitat patch during the course of a simulation run.Three of the modeling studies quantiﬁed connectivity using dispersal success.Schippers et al.(1996)(no.26in Table1)simulated the badger’s(Meles meles)response(movement proba-bility and mortality risk)to landscape structure using a classiﬁed GIS grid map and empirical expertise.Move-ment probabilities between cells were derived by compar-ing the quality(for badger use)of adjacent cells.Higher quality cells attracted moving individuals.Mortality rates were higher in low-quality cells.The number of simulated movement steps corresponded to an estimated actual time of badger movement within a four-year period.The authors produced inter-patch transition probabilities and movement frequency maps(visits per grid cell),based on dispersal success.Schumaker(1996)(no.27in Table1)analyzed the potential of indices of landscape structure to predict dispersal success.He created landscape models in two ways:(1)sample landscapes were randomly drawn from a GIS data set to cover a range of different landscape conﬁgurations;(2)artiﬁcial landscape grids were created by randomly designating habitat cells.Cells of the grid represented territories.An individual-based correlated random walk model was used to simulate movements across the landscape.Individuals were released in a randomly selected50%of habitat territories,and were allowed to settle in any unoccupied territory,which then became unavailable to subsequent nd-scape boundaries reﬂected approaching individuals. Connectivity was measured as the mean fraction(over several runs)of individuals that successfully dispersed into new territories during the course of a simulation.The results revealed correlations between each of ten indices of landscape structure and dispersal success(connectiv-ity).Demers et al.(1995)(no.29in Table1)investigated the relationship between colonization success of edge-preferring organisms,and the amount and change of edge habitat,in real agricultural landscapes.A vector-based GIS data set containing fencerow and forest-edge cover-ages was used as a model landscape.Individuals were allowed to move only in suitable habitat after being dropped at random points across the landscape.Individ-uals could cross inhospitable habitat(matrix)up to a maximum distance,after any edge habitat in the land-scape was successfully colonized.Occupied habitat could not be colonized by subsequent dispersers.The authors measured connectivity as the‘‘total length and area of hedgerow and forest edge colonized by the offspring of each successful virtual organism’’.The results showed higher connectivity in landscapes with more and longer overall edge habitat.Search timeOne paper(Doak et al.1992)(no.33in Table1)used search time to quantify connectivity.Search time is the number of movement steps individuals require toﬁnd a new habitat patch.Doak et al.(1992)examined the effect of spatial scale on the success of dispersing individuals.An artiﬁcial landscape was modeled by a hierarchical grid of three layers(spatial scales).Clusters of habitat cells were created on different spatial scales.Virtual individuals were released in the habitat and followed a random walk until a new habitat patch(different from the origin)was ndscape boundaries acted as reﬂecting borders. For each individual the number of movement steps required toﬁnd a new habitat patch(search time)was recorded.The mean and standard deviation over all individual search times were calculated and related to the scale of rge-scale clustering(few large patches)induced longer search times than small-scale clustering(more smaller patches)(see also Ruckelshaus et al.1997).Population spatial distributionWith et al.(1997)(no.18in Table1)investigated the effects of landscape spatial structure on(1)the probabil-12OIKOS90:1(2000)。

ld1.x产生赝势文档

Notes on pseudopotential generationPaolo GiannozziUniversit`a di Udine and IOM-Democritos,TriesteURL:http://www.fisica.uniud.it/∼giannozzApril6,2012Contents1Introduction21.1Who needs to generate a pseudopotential? (2)1.2About similar work (3)1.3Pseudopotential generation,in general (3)2Step-by-step Pseudopotential generation42.1Choosing the generation parameters (4)2.1.1Exchange-correlation functional (4)2.1.2Valence-core partition (5)2.1.3Electronic reference conﬁguration (5)2.1.4Nonlinear core correction (7)2.2Type of pseudization (7)2.2.1Pseudization energies (8)2.2.2Pseudization radii (9)2.2.3Choosing the local potential (9)2.3Generating the pseudopotential (10)2.4Checking for transferability (11)3A worked example:Ti113.1Single-projector,norm-conserving,no semicore (12)3.1.1Generation (12)3.1.2Testing (16)3.2Single-projector,norm-conserving,with semicore states (19)3.3Testing in molecules and solids (22)A Atomic Calculations22A.1Nonrelativistic case (22)A.1.1Useful formulae (23)A.2Fully relativistic case (23)A.3Scalar-relativistic case (23)A.4Numerical solution (24)1B Equations for the Troullier-Martins method251IntroductionWhen I started to do myﬁrstﬁrst-principle calculation(that is,myﬁrst2-principle calculation)with Stefano Baroni on CsI under pressure(1985),it became quickly evi-dent that available pseudopotentials(PP’s)couldn’t do the job.So we generated ourown PP’s.Since thatﬁrst experience I have generated a large number of PP’s andpeople keep asking me new PP’s from time to time.I am happy that”my”PP’s are appreciated and used by other people.I don’t think however that the generation ofPP’s is such a hard task that it requires an oﬃcial(or unoﬃcial)PP wizard to do this.For this reason I want to share here my(little)experience.These notes are written in general but having in mind the capabilities of the atomicpackage,included in the Quantum ESPRESSO distribution( atomic,mostly written and maintained by Andrea Dal Corso and others,is the evolu-tion of an older code I maintained for several years.atomic can generate both Norm-Conserving(NC)[1]and Ultrasoft(US)[2]PP’s,plus Projector Augmented Waves(PAW)[3]sets.It allows multiple projectors,full relativistic calculations,spin-splitPP’s for spin-orbit calculations.For the complete description of the input of atomic,please refer toﬁles INPUT LD1.txt and INPUT LD1.html.1.1Who needs to generate a pseudopotential?There are at least three well-known published sets of NC-PP’s:those of Bachelet,Hamann,and Schl¨u ter[4],those of Gonze,Stumpf,and Scheﬄer[5],and those of Goedecker,Teter,and Hutter[6].Moreover,all major packages for electronic-structure calculations include a downloadable table of PP’s.One could then wonder what a PPgeneration code is useful for.The problem is that sometimes available PP’s will notsuit your needs.For instance,you may want:–a better accuracy;–PP’s generated with some exotic or new exchange-correlation functional;–a diﬀerent partition of electrons into valence and core;–“softer”PP’s(i.e.PP that require a smaller cutoﬀin plane-wave calculations);–PP’s with a core-hole for calculations of X-ray Adsorption Spectra;–all-electron wavefunctions reconstruction(requires the knowledge of atomic all-electron and pseudo-orbitals used in the generation of PP’s);or you may simply want to know what is a PP,how to produce PP’s,how reliable theyare.1.2About similar workThere are other PP generation packages available on-line.Those I am aware of include:•the code by Jos´e-Lu´ıs Martins et al.[7]:http://bohr.inesc-mn.pt/~jlm/pseudo.html•the fhi98PP package[8]:http://www.fhi-berlin.mpg.de/th/fhi98md/fhi98PP•the OPIUM code by Andrew Rappe et al.[9]:/•David Vanderbilt’s US-PP package[2]:/~dhv/uspp/index.html.Other codes may be available upon request from the authors.Years ago,it occurred to me that a web-based PP generation tool would have been nice.Being too lazy and too ignorant in web-based applications,I did nothing.I recently discovered that Miguel Marques et al.have implemented something like this: see /programs/octopus/pseudo.php.1.3Pseudopotential generation,in generalIn the following I am assuming that the basic PP theory is known to the reader. Otherwise,see Refs.[1,4,7,8,9]and references quoted therein for NC-PP’s;Refs.[2,3] for US-PP’s and PAWsets.I am also assuming that the generated PP’s are to be used in separable form[10]with a plane-wave(PW)basis set.The PP generation is a three-step process.First,one generates atomic levels and orbitals with Density-functional theory(DFT).Second,from atomic results one gener-ates the PP.Third,one checks whether the reesulting PP is actually working.If not, one tries again in a diﬀerent way.Theﬁrst step is invariably done assuming a spherically symmetric self-consistent Hamiltonian,so that all elementary quantum mechanics results for the atom apply.The atomic state is deﬁned by the”electronic conﬁguration”,one-electron states are deﬁned by a principal quantum number and by the angular momentum and are obtained by solving a self-consistent radial Schr¨o dinger-like(Kohn-Sham)equation.The second step exists in many variants.One can generate“traditional”single-projector NC-PP’s;multiple-projector NC-PP’s;or US-PP’s.The crucial step is in all cases the generation of smooth“pseudo-orbitals”from atomic all-electron(AE) orbitals.Two popular pseudization methods are presently implemented:Troullier-Martins[7]and Rappe-Rabe-Kaxiras-Joannopoulos[9](RRKJ).The third step is closer to cooking than to science.There is a large arbitrariness in the preceding step that one would like to exploit in order to get the”best”PP, but there is no well-deﬁned way to do this.Moreover one is often forced to strike a compromise between transferability(thus accuracy)and hardness(puter time). This last step is the main focus of these notes.2Step-by-step Pseudopotential generationIf you want to generate a PP for a given atom,the checklist is the following:•choose the generation parameters:1.exchange-correlation functional2.valence-core partition3.electronic reference conﬁguration4.nonlinear core correction5.type of pseudization6.pseudization energies7.pseudization radii8.local potential•generate the pseudopotential•check for transferabilityIn case of trouble or of unsatisfactory results,one has to go back to theﬁrst step and change the generation parameters,usually in the last four items.2.1Choosing the generation parameters2.1.1Exchange-correlation functionalPP’s must be generated with the same exchange-correlation(XC)functional that will be later used in calculations.The use of,for instance,a GGA(Generalized Gradient Approximation)functional tegether with PP’s generated with Local-Density Approx-imation(LDA)is inconsistent.This is why the PPﬁle contains information on the DFT level used in their generation:if you or your code ignore it,you do it at your own risk.The atomic package allows PP generation for a large number of functionals,both LDA and GGA.Most of them have been extensively tested,but beware:some exotic or seldom-used functionals might contain bugs.Currently,atomic does not allow PP generation with meta-GGA(TPSS)or hybrid functionals.For the former,an old version of atomic,modiﬁed by Xiaofei Wang,is available.Work is in progress for the latter.Some functionals may present numerical problems when the charge density goes to zero.For instance,the Becke gradient correction to the exchange may diverge for ρ→0.This does not happen in a free atom if the charge density behaves as it should, that is,asρ(r)→exp(−αr)for r→∞.In a pseudoatom,however,a weird behavior may arise around the core region,r→0,because the pseudocharge in that region is very small or sometimes vanishing(if there are noﬁlled s states).As a consequence,nasty-looking“spikes”appear in the unscreened pseudopotential very close to the nucleus. This is not nice at all but it is usually harmless,because the interested region is reallyvery small.However in some unfortunate cases there can be convergence problems.If you do not want to see those horrible spikes,or if you experience problems,you have the following choices:–Use a better-behaved GGA,such as PBE–Use the nonlinear core correction,which ensures the presence of some charge close to the nucleus.A further possibility would be to cut the gradient correction for small r(it used to be implemented,but it isn’t any longer).2.1.2Valence-core partitionThis seems to be a trivial step,and often it is:valence states are those that contribute to bonding,core states are those that do not contribute.Things may sometimes be more complicated than this.For instance:–in transition metals,whose typical outer electronic conﬁguration is something like(n=main quantum number)nd i(n+1)s j(n+1)p k,it is not always evident that the ns and np states(“semicore states”)can be safely put into the core.The problem is that nd states are localized in the same spatial region as ns and np states,deeper than(n+1)s and(n+1)p states.This may lead to poor transferability.Typically,PP’s with semicore states in the core work well in solids with weak or metallic bonding,but perform poorly in compounds with a stronger(chemical)type of bonding.–Heavy alkali metals(Rb,Cs,maybe also K)have a large polarizable core.PP’s with just one electron may not always give satisfactory results.–In some II-VI and III-V semiconductors,such as ZnSe and GaN,the contribution of the d states of the cation to the bonding is not negligible and may require explicit inclusion of those d states into the valence.In all these cases,promoting the highest core states ns and np,or nd,into valence may be a computationally expensive but obliged way to improve poor transferability..You should include semicore states into valence only if really needed:their inclusion in fact makes your PP harder(unless you resort to US pseudization)and increases the number of electrons.In principle you should also use more than one projector per angular momentum,because the energy range to be covered by the PP with semicore electrons is much wider than without.If you don’t,the transferability of your PP may suﬀer(a typical phenomenon:the error on the lattice parameter of a simple metal gets worse).2.1.3Electronic reference conﬁgurationThis may be any reasonable conﬁguration not too far away from the expected conﬁgu-ration in solids or molecules.As aﬁrst choice,use the atomic ground state,unless you have a reason to do otherwise,such as for instance:–You do not want to deal with unbound states.Very often states with highest angular momentum l are not bound in the atom(an example:the3d state in Si is not bound on the ground state3s23p2,at least with LDA or GGA).In such a case one has the choice between–using one conﬁguration for s and p,another,more ionic one,for d,as inRefs.[4,5];–choosing a single,more ionic conﬁguration for which all desired states arebound;–generate PP’s on unbound states:requires to choose a suitable referenceenergy.–The results of your PP are very sensitive to the chosen conﬁguration.This is something that in principle should not happen,but I am aware of at least one case in which it does.In III-V zincblende semiconductors,the equilibrium lattice parameter is rather sensitive to the form of the d potential of the cation(due to the presence of p−d coupling between anion p states and cation d states[12]).By varying the reference conﬁguration,one can change the equilibrium lattice parameter by as much as1−2%.The problem arises if you want to calculate accurate dynamical properties of GaAs/AlAs alloys and superlattices:you need to get a good theoretical lattice matching between GaAs and AlAs,or otherwise unpleasant spurious eﬀects may arise.When I was confronted with this problem,I didn’tﬁnd any better solution than to tweak the4d reference conﬁguration forGa until I got the observed lattice-matching.–You know that for the system you are interested in,the atom will be in a giv-en conﬁguration and you try to stay close to it.This is not very elegant but sometimes it is needed.For instance,in transition metals described by a PP with semicore states in the core,it is probably wise to chose an electronic con-ﬁguration for d states that is close to what you expect in your system(as a hand-waiving argument,consider that the(n+1)s and(n+1)p PP have a hard time in reproducing the true potential if the nd state,which is much more lo-calized,changes a lot with respect to the starting conﬁguration).In Rare-Earth compounds,leaving the4f electrons in the core with the correct occupancy(if known)may be a quick and dirty way to avoid the well-known problems of DFT yielding the wrong occupancy in highly correlated materials.–You don’t manage to build a decent PP with the ground state conﬁguration,for whatever reason.NOTE1:you can calculate PP for a l as high as you want,but you are not obliged to use all of them in PW calculations.The general rule is that if your atom has states up to l=l c in the core,you need a PP with angular momenta up to l=l c+1.Angular momenta l>l c+1will feel the same potential as l=l c+1,because for all of them there is no orthogonalization to core states.As a consequence a PP should have projectors on angular momenta up to l c;l=l c+1should be the local reference state for PW calculations.This rule is not very strict and may be relaxed:high angular momentaare seldom important(but be careful if they are).Moreover separable PP pose serious constraints on local reference l(see below)and the choice is sometimes obliged.Note also that the highest the l in the PP,the more expensive the PW calculation will be.NOTE2:a completely empty conﬁguration(s0p0d0)or a conﬁguration with frac-tional occupation numbers are both acceptable.Even if fractional occupation numbers do not correspond to a physical atomic state,they correspond to a well-deﬁned math-ematical object.NOTE3:PP could in principle be generated on a spin-polarized conﬁguration,but a spin-unpolarized one is typically used.Since PP are constructed to be transferrable, they can describe spin-polarized conﬁgurations as well.The nonlinear core correction is needed if you plan to use PP in spin-polarized(magnetic)systems.2.1.4Nonlinear core correctionThe nonlinear core correction[11]accounts at least partially for the nonlinearity in the XC potential.During PP generation oneﬁrst produces a potential yielding the desired pseudo-orbitals and pseudoenergies.In order to extract a“bare”PP that can be used in a self-consistent DFT calculation,one subtracts out the screening(Hartree and XC) potential generated by the valence charge only.This introduces a trasferability error because the XC potential is not linear in the charge density.With the nonlinear core correction one keeps a pseudized core charge to be added to the valence charge both at the unscreening step and when using the PP.The nonlinear core correction must be present in one-electron PP’s for alkali atoms (especially in ionic compounds)and for PP’s to be used in spin-polarized(magnetic) systems.It is recommended whenever there is a large overlap between valence and core charge:for instance,in transition metals if the semicore states are kept into the core.Since it is never harmful,one can take the point of view that it should always be included,even in cases where it will not be very useful.The pseudized core charge used in practice is equal to the true core charge for r≥r cc,diﬀers from it for r<r cc in such a way as to be much smoother.The parameter r cc is typically chosen as the point at which the core chargeρc(r cc)is twice as big as the valence chargeρv(r cc).In fact the eﬀect of nonlinearity is important only in regions whereρc(r)∼ρv(r).Alternatively,r cc can be provided in input,Note that the smaller r cc,the more accurate the core correction,but also the harder the pseudized core charge,and vice versa.2.2Type of pseudizationThe atomic package implements two diﬀerent NC pseudization algorithms,both claim-ing to yield optimally smooth PP’s:•Troullier-Martins[7](TM)•Rappe-Rabe-Kaxiras-Joannopoulos[9](RRKJ).Both algorithms replace atomic orbitals in the core region with smooth nodeless pseudo-orbitals.The TM method uses an exponential of a polynomial(see Appendix B);theRRKJ method uses three or four Bessel functions for the pseudo-orbitals in the core region.The former is very robust.The latter may occasionally fail to produce the required nodeless pseudo-orbital.If this happens,ﬁrst try to force the usage of four Bessel functions(this is achieved by setting a small nonzero value of the charge density at the origin,variable rho0:unfortunately it works only for s states).Second-row elements N,O,F,3d transition metals,rare earths,are typically“hard”atoms,i.e.described by NC PP’s requiring a high PW cutoﬀ.These atoms are characterized by2p(N,O,F),3d(transition metals),4f(rare earths)valence states with no orthogonalization to core states of the same l and no nodes.In addition,as mentioned in Secs.2.1.2and2.1.3,there are case in which you may be forced to include semicore states in valence,thus making the PP hard(or even harder).In all such cases, one should consider ultrasoft pseudization,unless there is a good reason to stick to NC-PP’s.For the speciﬁc case of rare earths,however,remember that the problem of DFT reliability preempts the(tough)problem of generating a PP.With US-PP’s one can give up the NC requirement and get much software PP’s,at the price of introducing an augmentation charge that compensates for the missing charge.Currently,the atomic package generates US-PP’s on top of a“hard”NC-PP.In order to ensure suﬃcient transferability,at least two states per angular momentum l are required.2.2.1Pseudization energiesIf you stick to single-projector PP’s(one potential per angular momentum l,i.e.one projector per l in the separable form),the choice of the electronic conﬁguration au-tomatically determines the reference states to pseudize:for each l,the bound valence eigenstate is pseudized at the corresponding eigenvalue.If no bound valence eigenstate exists,one has to select a reference energy.The choice is rather arbitrary:you may try something between than other valence bound state energies and zero.If you have semicore states in valence,remember that for each l only the state with lowest n can be used to generate a single-projector PP.The atomic package requires that you explicitly specify the conﬁguration for unscreening in the“test”conﬁguration: see the detailed input documentation.It is possible to generate PP’s by pseudizing atomic waves,i.e.regular solutions of the radial Kohn-Sham equation,at any energy.More than one such atomic waves of diﬀerent energy can be pseudized for the same l,resulting in a PP with more than one projector per l.Note that the resulting PP is directly produced in the separable form.Such possibility considerably extends the transferability,but also the number of “degrees of freedom”in the generation of a PP.As a rule of thumb:•start with one projector per l,at the energy of the bound state;•add a second projector at a second,higher energy not too far above the former. The latter hint seems to be counterintuitive if you have semicore states in valence:the obvious choice would be to include two projectors,using both bound states energies. Unfortunately this is currently not possible with the atomic package,because the state pseudized at the upper bound-state energy will necessarily have a node(in order to be orthogonal to the one with lower energy).For US-PP pseudization,you shouldﬁrstﬁnd a suitable multi-projector NC-PP as above,than turn on the US-PP pseudization.This is done by setting diﬀerent NC and US pseudization radii(see Sec.2.2.2),2.2.2Pseudization radiiFor NC pseudization,one has to choose,for each state to be pseudized,a NC pseudiza-tion radius r c,at which the AE orbital and the corresponding NC-PP orbital match, with continuousﬁrst derivative at r=r c.For bound states,r c is typically at the outermost peak or somewhat larger.The larger the r c,the softer the potential(less PW needed in the calculations),but also the less transferable.The r c may diﬀer for diﬀerent l;as a rule,one should avoid large diﬀerences between the r c’s,but this is not always possible.Also,the r c cannot be smaller than the outermost node.A big problem in NC-PP’s is how strike a compromise between softness and trans-ferability,especially for diﬃcult elements.The basic question:“how much should I push r c outwards in order to have reasonable results with a reasonable PW cutoﬀ”. has no clear-cut answer.The choice of r c at the outermost maximum for“diﬃcult”elements(those described in Sec.2.2.1):typically0.7-0.8a.u,even less for4f electrons, yields very hard PP’s(more than100Ry needed in practical calculations).With a little bit of experience one can say that for second-row(2p)elements,r c=1.1−1.2will yield reasonably good results for50-70Ry PW kinetic energy cutoﬀ;for3d transition metals,the same r c will require>80Ry cutoﬀ(highest l have slower convergence for the same r c).The above estimates are for TM pseudization.RRKJ pseudization will yield an estimate of the required cutoﬀ.For multiple-projectors NC-PP’s,the r c of unbound states may be chosen in the same range as for bound states.If this is theﬁrst step for US-PP generation,use small r c and don’t try to push them outwards:the US pseudization will take care of softness. US pseudization radii can be chosen much larger than NC ones(e.g.1.3÷1.5a.u.for second-row2p elements,1.7÷2.2a.u.for3d transition metals),but do not forget that the sum of the r c of two atoms should not exceed the typical bond length of those atoms.Note that it is the hardest atom that determines the PW cutoﬀin a solid or molecule.Do not waste time trying toﬁnd optimally soft PP’s for element X if element Y is harder then element X.2.2.3Choosing the local potentialAs explained in Sec.2.1.3,note1,one needs in principle angular momentum channels in PP’s up to l c+1.In the semilocal form,the choice of a”local”,l-independent potential is natural and aﬀects only seldom-important PW components with l>l c. In PW calculations,however,a separable,fully nonlocal form–one in which the PP’s is written as a local potential plus pr ojectors–is used.An arbitrary function can be added to the local potential and subtracted to all l components.Generally one exploits this arbitrariness to remove one l component using it as local potential. The separable form can be either obtained by the Kleinman-Bylander projection[10] applied to single-projector PP’s,or directly produced using Vanderbilt’s procedure[2] (for single-projector PP’s the two approaches are equivalent).Unfortunately the separable form is not guaranteed to have the correct ground state (unlike the semilocal form,which,by construction,has the correct ground states):“ghost”states,having the wrong number of nodes,can appear among the occupied states or close to them,making the PP completely useless.This problem may show up in multiple-projectors NC-PP’s and in US-PP’s as well.The freedom in choosing the local part can(and usually must)be used in order to avoid the appearance of ghosts.For PW calculations it is convenient to choose as local part the highest l,because this removes more projectors(2l+1per atom)than for low l.According to Murphy’s law,this is also the choice that more often gives raise to problems,and one is forced to use a diﬀerent l.Another possibility is to generate a local potential by pseudizing the AE potential.Note that ghosts may not be visible to atomic codes based on radial integration, since the algorithm discards states with the wrong number of nodes.Diﬃcult conver-gence or mysterious errors are almost invariably a sign tha there is something wrong with our PP.A simple and safe way to check for the presence of a ghost is to diagonalize the Kohn-Sham hamiltonian in a basis set of spherical Bessel functions.This can be done together with transferability tests(see Sec.2.4)2.3Generating the pseudopotentialAs aﬁrst step,one can generate AE Kohn-Sham orbitals and one-electron levels for the reference conﬁguration.This is done by using executable ld1.x.You must specify in the input data:atomic symbol,electronic reference conﬁguration,exchange-correlation functional(default is LDA).A complete description of the input is contained in the documentation.For accurate AE results in heavy atoms,you may want to specify a denser radial grid in r-space than the default one.The default grid should however be good enough for PP generation.Before you proceed,it is a good idea to verify that the atomic data you just produced actually make sense.Some kind souls have posted on the web a complete set of reference atomic data:/PhysRefData/DFTdata/These data have been obtained with the Vosko-Wilk-Nusair functional,that for the unpolarized case is very similar to the Perdew-Zunger LDA functional(this is hte LDA default).The generation step is also done by program ld1.x.One has to supply,in addition to AE data:a list of orbitals to be pseudized,with pseudization energies and radii,theﬁlename where the newly generated PP is written,plus a number of other optional parameters,fully described in the documentation.2.4Checking for transferabilityA simple way to check for correctness and to get a feeling for the transferability of a PP,with little eﬀort,is to test the results of PP and AE atomic calculations on atomic conﬁgurations diﬀering from the starting one.The error on total energy diﬀerences between PP and AE results gives a feeling on how good the PP is.Just to give an idea:an error∼0.001Ry is very good,∼0.01Ry may still be acceptable.The code ld1.x has a“testing”mode in which it does exactly the above operation.You provide the input PPﬁle and a number of test conﬁgurations.You are advised to perform also the test with a basis set of spherical Bessel functions j l(qr).In addition to revealing the presence of“ghosts”,this test also gives an idea of the smoothness of the potential:the dependence of energy levels upon the cutoﬀin the kinetic energy is basically the same for the pseudo-atom in the basis of j l(qr)’s and for the same pseudo-atom in a solid-state calculation using PW’s.Another way to check for transferability is to compare AE and pseudo(PS)loga-rithmic derivatives,also calculated by ld1.x.Typically this comparison is done on the reference conﬁguration,but not necessarily so.You should supply on input:–the radius r d at which logarithmic derivatives are calculated(r d should be of the order of the ionic or covalent radius,and larger than any of the r c’s)–the energy range E min,E max and the number of points for the plot.The energy range should cover the typical valence one-electron energy range expected in the targeted application of the PP.Theﬁles containing logarithmic derivatives can be easily read and plotted using for instance the plotting program gnuplot or xmgrace.Sizable discrepancies between AE and PS logarithmic derivatives are a sign of trouble(unless your energy range is too large or not centered around the range of pseudization energies,of course).Note that the above checks,based on atomic calculations only,do not replace the usual checks(convergence tests,bond lengths,etc)one has to perform in at least some simple solid-state or molecular systems before starting a serious calculation.3A worked example:TiLet us consider the Ti atom:Z=22,electronic conﬁguration:1s22s22p63s23p63d24s2, with PBE XC functional.The input data for the AE calculation is simple:&inputatom=’Ti’,dft=’PBE’,config=’[Ar]3d24s24p0’/and yields the total energy and Kohn-Sham levels.Let us concentrate on the outermost states:303S1(2.00)-4.6035-2.3017-62.6334313P1(6.00)-2.8562-1.4281-38.8608323D1(2.00)-0.3130-0.1565-4.2588。

Adynamicbonedisease

Adynamic Bone Disease - Clinical Outcome of the Treatment with Different Dialysate Calcium ConcentrationG. Spasovski 1, S. Gelev 1, A. Sikole 1, J.Masin-Spasovska 1; M. Bogdanova 2, S. Subeska Stratrova 3, V. Amitov 1, N. Stojcev 1, R.Grozdanovski 1, K Zafirovska 1123IntroductionThe abnormalities in bone histology in patients with chronic renal failure (CRF), known as renal osteodystrophy (ROD), can be observed early in the course of the disease.Over the last decades the spectrum of ROD in dialysis patients has been studied thoroughly and the prevalence of the various types of renal bone disease changed over the years (1). In recent years, adynamic bone disease (ABD)has become the most prevalent bone lesion within the dialysis population. This type of ROD was first found in association with high bone aluminum accumulation (2).Other factors that might have played an important role in development of ABD consist of malnutrition, male predominance, diabetes mellitus and advanced age (3-5).Calcium-based binders, particularly when used in combination with vitamin D analogues, may result in over-suppression of PTH (6). However, it was observed that most of the cases with ABD were found in patients with "relative" hypoparathyroidism, i.e parathyroid hormone (PTH) levels that are significantly lower than those noted in renal failure patients with other types of ROD, but still higher than in subjects with normal renal function (7).Bone biopsy is considered as the gold standard for ROD diagnosis (8), but various biochemical markers have been most frequently evaluated over the last decades.Predominantly, the investigators measure intact parathyroid hormone (iPTH), total or ionized serum calcium (Ca),phosphate (P), alkaline phosphatase (AP), vitamin D status and some markers of either bone formation [bone alkaline phosphatase (BAP), osteocalcin (OC)] or bone resorption [(deoxy-) pyridinolines (DPYD, PYD)]. Most of these markers reach a high enough diagnostic performance to substitute bone histomorphometry.Disturbances of calcium-phosphate (Ca-P) metabolism in CRF play an important role not only in bone disease but also in soft tissue calcification, with an increased risk of vascular calcification, arterial stiffness, and worsening of atherosclerosis, linked to an increased mortality in a large number of dialysis patients. On the other side, the use of calcium salts for phosphate binding is complicated by the development of hypercalcemia and an increased risk of metastatic calcifications in a substantial fraction of patients particularly those taking vitamin D analogues and those with adynamic bone disease (6). Moreover, ABD patients show a reduced ability to handle an exogenous calcium load, and have a more sustained hypercalcaemia, implying a higher risk of extra-osseous calcifications. Hence, a suitable dialysate calcium concentration is important and must take into consideration the medical therapy and the calcium balance on an individual patient basis.Despite all the controversy, numerous investigators have suggested that using low-calcium dialysate (LCD) might benefit HD patients, allowing a larger dose of calcium to control hyperphosphatemia and avoiding excessive PTH suppression (9,10). Nevertheless, the information about the stimulating effect of LDC on PTH secretion is not yet clarified.The aim of the study was to compare the effects of low (LDC) and high dialysate calcium (HDC) concentration on the evolution of adynamic bone disease in dialysis patients.MethodsIn this open-label study, 52 ABD presumed patients on maintenance bicarbonate haemodialysis (HD) for 12 hours per week, with low flux polysulphone or hemophane membrane were included. The key inclusion criteria was concentration of parathyroid hormone (PTH)<100 pg/ml and bone alkaline phosphatase (BAP)<37 U/L. An equal number of patients (n=26) were randomized to LDC (1.25mM) and HDC (1.75 mM) concentration. No preset limit is applied to serum calcium and phosphate levels neither any restriction of concomitant vitamin D or erythropoetin therapy. The only phosphate binder to be used was calcium carbonate. The duration of the study was 6 months. Clinical data on the patients will be recorded at the moment of inclusion (age, type of chronic kidney disease, start of dialysis treatment and duration, gender, blood pressure (before the dialysis session), diabetes, smoker, treatment with erythropoietin and dose, type of vascular access,intake of medication). Adverse events were monitored throughout the study and 4 (HDC) patients were discontinued from the study upon investigator's decision.Blood samples were taken at the enrollment and at 3months interval for determination of a series of serum parameters relevant to bone using the appropriate kits and methodologies. Total and ionized calcium were measured monthly in serum before and after dialysis.Descriptive statistics will include mean values ± SD for continuous data, and percentage for categorical data.Between the groups comparison will be performed by Student's t - test analysis. Categorical data will be compared by the chi-square test.ResultsAfter randomized allocation to either LCD or HDC, 30patients in each group initiated the study. As a consequence of the expected side effects of the treatment with LCD (hypotension and cramps), 4 patients were excluded from the study (LCD group). Fifty-two patients completed the study. Mean patient age was 59.2 ± 11 years and they hadreceived HD for a mean period of 67.5 ± 47.6 months (range: 15-228 months).The LCD and HCD group did not differ significantly in terms of age (LCD: 61 ± 11.8 years vs HCD 57.3 ± 9.9 years), male gender (n=14 in each group) and time on HD (LCD: 74.7 ± 48.2 months vs HCD 59.3 ± 46.7 months). Fourteen patients had diabetes ((LCD: n=8, HCD: n=6). The groups didn't differ in the mean serum total calcium (tCa) before dialysis, but it was significantly increased in HDC group after dialysis (2.59 ± 0.18 vs 2.44 ± 0.19; p<0.01). Mean tCa in LCD group didn't change during dialysis, while it was markedly increased after dialysis in HDC group (2.59 ± 0.18 vs 2.41 ± 0.21; p<0.01).When compared with HDC group, patients in LDC group had significantly lower mean ionised serum calcium (iCa) before (1.08 ± 0.05 vs 1.04 ± 0.06; p=0.02) and after dialysis (1.18 ± 0.04 vs 1.04 ± 0.04; p<0.01), respectively.A significant increase in mean postdialysis iCa was observed in HDC group (1.08 ± 0.05 vs 1.18 ± 0.04; p<0.01) when compared with mean predialysis iCa. There was no modification of this parameter in LCD group. Mean serum levels of iPTH, bone and total alkaline phosphatase in LDC group were significantly increased at the end of the study compared with the baseline levels [(65.13 ± 55.74 vs 38.63 ± 22.96; p<0.05); (35.35 ± 22.46 vs 23.38 ± 7.26; p=0.01); (85.24 ± 38.14 vs 59.46 ± 18.69; p<0.01)], respectively. The bone markers in HDC group have not significantly changed over the study period. There was no difference in predialysis phosphate levels and the average dose of calcium carbonate between the groups during the study. The most common side effects of the treatment with dialysate Ca of 1.25 mM were hypotension and cramps in 16% and 17% of the dialysis sessions, respectively.DiscussionIn this randomized study on the effects of two different calcium contents in HD solutions,we found that the treatment with low-calcium dialysate showed a clear tendency to increase PTH levels. Having no differences between the groups in terms of weel known factors that might influence the production of bone markers (age, time on dialysis, male gender, basic kidney disease, calcium carbonate and vitamin D treatment), the observed effect is even more apparent.While some previous studies have reported no significant changes after using LCD (11,12), the most widely acknowledged opinion is that LCD induces a clinically significant increase in PTH levels (9,13). This goes in line with our findings.The inclusion criteria in the present study were even more restrictive than those reported to be a good marker of ABD in HD patients (PTH<100 pg/ml and BAP<37 U/L) (Coutoneye 1996 Low BAP). Thus, the design of the study aimed to assess the possibility for treatment of ABD.In contrast to some reports, the treatment with LCD was not accompained with a negative calcium balance, since there was no change in tCa and iCa during dialysis (9). However, it should be mentioned that the mean iCa levels in LCD group were continously sustained below the referent range of the lab (1.1 - 1.3 mmol/l). These findings suggest that prevention of net calcium influx, rather than its negative balance, might be responsible for the increase in PTH. The similar pattern of increased markers of bone formation (BAP and TAP) in LCD group has been observed over the whole study period. Hence, an increase in bone formation rate might improve the buffer capacity of the bone for handling of calcium influx, thus prventing extraskeletal and cardiovascular calcifications.ConclusionIn conclusion, there was an evolution towards higher bone turnover in patients treated with dialysate calcium of 1.25 mM, probably by preventing a positive calcium balance and causing repetitive stimulation of PTH secretion in each dialysis. The treatment was safe and without any major adverse effects. Hence, this might be considered a valuable treatment for ABD patients, although this rather beneficial and not harmful effect should be confirmed in a long-term evaluation.Key words: dialysis, ionised calcium, parathyroid hormone, low dialysate calcium concentration, adynamic bone disease.Reference1.Spasovski G, Bervoets A, Behets G, Ivanovski N,Sikole A, Dams G,Couttenye MM, De Broe ME,D'Haese PC. Spectrum of renal bone disease in end-stage renal failure patients not in dialysis yet. Nephrol DialTransplant 2003;18:1159-11662.D'Haese PC, Van de Vyver FL, de Wolff FA, De BroeME. Measurement of aluminum in serum, blood, urine and tissues of chronic hemodialyzed patients by use of electrothermal atomic absorption spectrometry. ClinChem 1985;31:24-293.Akizawa T, Kinugasa E, Kurihara S. Parathiroidhormone deficiency is an indicator of poor nutritionalstate and prognosis in dialysis patients. J Am SocNephrol 1999;10:616A4.Pei Y, Hercz G, Greenwood C. Risk factors for renalosteodystrophy. A multivariant analysis. J Bone Miner Res 1995;10:149-1565.Torres A, Lorenzo V, Hernandez D. Bone disease inpredialysis, hemodialysis and CAPD patients: Evidence for a better response to PTH. Kidney Int 1995; 47:1434-1442.Goodman WG, Goldin J, Kuizon BD: Coronary-artery calcification in young adults with end-stage renal disease who are undergoing dialysis. N Engl J Med2000;342:1478-14836.Couttenye MM, D'Haese PC, Van Hoof VO,Lemoniatou E, Goodman W, Verpooten GA and DeBroe ME. Low serum levels of alkaline phosphatase of bone origin: a good marker of adynamic bone disease in hemodialysis patients. Nephrol Dial Transplant1996;11:1065-10727.Spasovski GB: Bone biopsy as a diagnostic tool in theassessment of renal osteodystrophy. The Int J ArtifOrgans 2004;27(11):918-9238.Fernandez E, Borras M, Pais B, Montoliu J. Low-calcium dialysate stimulates parathormone secretionand its long-term use worsens secondaryhyperparathyroidism. J Am Soc Nephrol 1995;6:132-1359.Argiles A, Mourad G. How do we have to use thecalcium in the dialysate to optimize the management of secondary hyperparathyroidism? Nephrol DialTransplant 1998;13:( 3): 62-6410.Argiles A, Mion CM. Calcium balance and intact PTHvariations during haemodiafiltration. Nephrol DialTransplant 1995;10:2083-208911.Fabrizi F, Bacchini G, Di Filippo S, Pontoriero G,Locatelli F. Intradialytic calcium balance with different calcium dialysate levels. Effects on cardiovascularstability and parathyroid function. Nephron 1998;72:530-53512.Yokoyama K, Kagami S, Ohkido I, Kato N, YamamotoH, Shigematsu T, Nakayma M, Fukagawa M,Kawaguchi Y, Hosoya T. The negative Ca(2+) balance is involved in the stimulation of PTH secretion.Nephron 2002;92: 86-90。

Formation of the egg - Nugraha Edhi Suyatma

ovoglycoprotein (0.5%), ovomacroglobulin (0.5%),
ovoinhibitor (0.l%) and avidin (0.05%).
17
YOLK
• Less water, more protein and fat than the white egg
• Contains most of the vitamins and minerals of the egg, including Fe, vitamin A, vitamin D, phosphorus, calcium, thiamine, and riboflavin.
1. Eggshell
2. Outer membrane
3. Inner membrane
4. Chalaza
5. Exterior albumen
6. Middle albumen
7. Vitelline membrane
8. Nucleus of pander
9. Germinal disk
10.Yellow yolk
EGG CHARACTERISTICS
4th Revision, 12 Nopember 2010
Nugraha E. Suyatma and Joko Hermanianto
Department of Food Science and Technology
Bogor Agricultural University
Which came first,
the chicken or the egg?
2
Edible egg:
• Chicken egg • Quail egg • Duck egg • Goose egg • Ostrich egg • Turtle egg • Fish egg: roe and caviar

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a r X i v :c o n d -m a t /9212014v 1 9 D e c 1992DYNAMICAL PROPERTIES OF AHALDANE GAP ANTIFERROMAGNETO.Golinelli,Th.Jolicœur,*and caze ∗Service de Physique Th´e orique**C.E.SaclayF-91191Gif-sur-Yvette CEDEX,FranceABSTRACT We study the dynamic spin correlation function of a spin one antiferromagnetic chain with easy-plane single-ion anisotropy.We use exact diagonalization by the Lancz˝o s method for chains of lengths up to N=16spins.We show that a single-mode approximation is an excellent description of the dynamical properties.A variational calculation allows us to clarify the nature of the excitations.The existence of a two-particle continuum near zero wavevector is clearly seen both in ﬁnite-size eﬀects and in the dynamical structure factor.The recent neutron scattering experiments on the quasi-one-dimensional antiferromagnet NENP are fully explained by our results.Submitted to:J.Phys.C:Condensed MatterNovember 1992PACS No:75.10J,74.50M,75.50E SPhT/92-135I.INTRODUCTIONIt wasﬁrst argued by Haldane[1,2]that generic spin-S one-dimensional Heisen-berg antiferromagnets have an excitation gap for integer S.This picture is quite dif-ferent from the usual,higher-dimensional,picture of antiferromagnets with masslessGoldstone magnons.On the theoretical side,there is now convincing evidence from numerical studies[3-10]of the S=1Heisenberg chain that it has a nonzero gap inthe thermodynamic limit.Exact diagonalizations by the Lancz˝o s method have beenable to reach18spins and Monte-Carlo simulations extend the range to32spins.All these data are suggestive of a Haldane gap.This leads to a ground state spin correlation length which isﬁnite and about six lattice spacings.Such a picture is instriking contrast with the S=1/2solvable chain which is gapless and whose groundstate has algebraically decaying correlations.A spin1Heisenberg model with bi-quadratic exchange has also been discovered with an exactly solvable ground stateand a nonzero gap[11],thus reinforcing the belief in the Haldane conjecture.On the experimental side there are several candidates to exhibit this quantum gap.Theﬁrst experimental evidence came from neutron-scattering on CsNiCl3[12-15].In this compound there are chains of spin one Ni2+ions with superexchangethrough Cl−anions.There is however moderately small interchain couplings thatcomplicate the picture:this is revealed in recent experiments on the related com-pound RbNiCl3[16].The best candidate so far seems to be Ni(C2H8N2)2NO2ClO4(NENP)[17-20],as shown by inelastic neutron-scattering(INS)and magnetizationmeasurements.The ratio of the interchain to intrachain magnetic coupling is es-timated to be J′/J≈4×10−4.No transition to N´e el order is found down to1.2K which is consistent with the hypothesis of aﬁnite zero-temperature correla-tion length.Nickel ions have spin1and are described by the following anisotropicHeisenberg Hamiltonian[21]:H=J i S i· S i+1+D i(S z i)2.(1.1) Bestﬁt of INS gap values leads to J/k B=43.5K and easy-plane D/J=0.18[10].There is also evidence for a smaller in-plane anisotropy that can be described byadding to H a term E i[(S x i)2−(S y i)2].This perturbation is small and will be mostly ignored in the remainder of this paper.Its qualitative role will be discussedin section V.Theﬁrst INS measurements[17-19]have concentrated on the neighborhood of Q=π(where Q is the wavevector along the chain)and showed the existence of two gaps:one for the in-plane(IP)magneticﬂuctuations and a higher one for out-of-plane(OP)ﬂuctuations.This splitting is due to the presence of a sizable easy-plane single-ion anisotropy D.The dispersion of the magnetic excitations was then studied in the range Q/π=0.9−1.0.Recent experiments have extended our knowledge throughout the whole Brillouin zone[22].Detailed theoretical work is required to test the hypothesis that the simple model Hamiltonian(1.1)is able to reproduce the dynamical properties of NENP.Two approaches have been followed up to now:small cluster numerical studies[3-10,23]and the use of eﬀectiveﬁeldtheories[24,25].The previous numerical studies were limited to spectral calculations or have ignored the presence of in-plane anisotropy.In this paper we present the results of a study of the dynamical structure factor S(Q,ω)of chains of length up to16spins by means of an exact diagonalization method.We also apply a variational technique proposed in ref.[26]to the anisotropic chain.This physically motivated method reproduces extremely well the numerical results.The results presented are valid in the absence of an external magneticﬁeld and in the zero temperature limit,i.e.for temperatures well below the gap.In sect. II we present some general properties of the spin-1chain with easy-plane single-ion anisotropy.In sect.III we explain the methods used to obtain dynamical quantities. Sect.IV contains our results.They are extremely well reproduced in terms of a physically appealing single-mode approximation.The results of our variational calculation are presented there and we use them to understand the nature of the elementary excitations near Q=0and Q=π.We show in sect.V that they are in very good agreement with existing neutron data and we suggest an additional test of the theory.Sect.VI contains our conclusions.II.GENERAL PROPERTIESWe brieﬂy review some known results about the isotropic Heisenberg spin1 antiferromagnetic(AF)chain:H0=JNi=1 S i· S i+1.(2.1)The vectors S i are quantum spin operators satisfying the SU(2)rotation algebra with length S2i=2.They are located along a one dimensional lattice of N sites with periodic boundary conditions.The exchange integral J is positive in the AF case.For anyﬁnite lattice the ground state is a singlet and the higher-lying levels have energy increasing with increasing spin as is known rigorously[27].Above the singlet ground state oneﬁnds a triplet state presumably for all values of N.In an AF quantum magnet,in the case of broken symmetry one expects that in the thermodynamic limit the triplet becomes degenerate with the ground state as do other states with spin S=2,3,...,in order to form the degenerate ground state of the inﬁnite volume limit.This can occur only for dimension greater than2(or equal).Haldane has argued that the spin-1chain is quantum disordered and that the singlet-triplet gap remains nonzero in the thermodynamic limit.This should be true for any integer value of the spin.This argument is based on a mapping of the inﬁnite-spin,semiclassical limit of the quantum chain onto a O(3)nonlinearσmodel [1].In the spin-1case of interest,numerical studies clearly points towards a gap close to≈0.41J[3-10,23].The physics of the O(3)nonlinearσmodel is that of a triplet of massive bosons with nontrivial scattering properties.This suggests a very simple eﬀectiveﬁeld theory:a free theory of three massive bosons[25].Another route starting from an integrable model leads to an eﬀectiveﬁeld theory of three massive fermions[24].In such approaches,one has to adjust the gap values which are no longer deducible from the microscopic model but one can obtain simple and deﬁnite pre-diction on dynamical quantities.However both are approximate theories and their respective domain of validity is diﬃcult to assess.On the contrary,ﬁnite chains calculations oﬀer unbiased theoretical predictions provided one is able to carefullycontrolﬁnite-size eﬀects.Concerning the gap values this can be achieved by the use of the so-called Shanks transformation,suited to the removal of exponential tran-sients in sequences ofﬁnite-chain data[28].It has been found that the convergence towards inﬁnite-volume is very good[6,10,23]as expected since we are dealing with a massive theory.As shown with the Perron-Frobenius theorem[29],the lowest-lying triplet haswavevector Q=π,while the singlet ground state has Q=0.Most theoretical and experimental studies have concentrated on this Q=πpart of the spectrum.In the nonlinearσmodel,there are no bound states and,if we believe that it is the eﬀective theory of the spin1chain,this implies that the Q=0gap is due to two massive Q=πparticles and thus twice the Q=πgap[2].This has been checkedby a quantum Monte-Carlo simulation in the isotropic case[8]and Lancz˝o s studies [23]have shown that this property persists in the presence of anisotropy(as long as it is not too large).As a consequence,the states near Q=0should be members of a two-particle continuum contrary to the states near Q=πthat should appear as long-lived well-deﬁned excitations.INS measurements for Q=0[30]reveal avanishing structure factor in this regime.The curve of the lowest excited triplet at wavevector Q is thus bell-shaped but asymmetrical with respect to Q=π/2.Let us now discuss the inﬂuence of easy-plane single-ion anisotropy,i.e.adding to H0a term of the following form:H=H0+D i(S z i)2.(2.2) The full rotational symmetry of Hamiltonian(2.1)is broken to rotational symmetry around the z axis.Only the z component S z= i S z i of the total spin is conserved. There is also a discrete symmetry S z→−S z that is preserved in the Hamiltonian(2.2).As a consequence of the anisotropy,theﬁrst excited triplet state is split intoa higher-energy singlet S z=0and a lower-lying doublet S z=±1.These three states retain their wavevectors unchanged(Q=π)with respect to the D=0case (by continuity)since the Hamiltonian(2.2)still possesses translational symmetry. The Haldane gap is split into two components:one gap G(−)between the ground state(with S z=0)and the doublet S z=±1and one gap G(+)inside the S z=0 subspace between theﬁrst two levels.G(−)decreases while G(+)increases with increasing D as shown quantitatively in ref.[10].We expect this simple picture to be true for all wavevectors0≤Q≤πsince the triplet states with arbitrary Q will be split also by the anisotropy.There is thus two distinct magnetic modes throughout the Brillouin zone:one IP(in-plane) mode(doubly degenerate)and one OP(out-of-plane)mode.The IP mode is seen in the S z=±1sector while the OP mode appears in the S z=0sector.The dispersion of the IP mode has been obtained for various anisotropies including thatof NENP in[23].INS experiments[17-19,22]have resolved these two modes in the neighborhood of Q=π:the OP mode is found at2.5meV and the IP mode is even further resolved into two components at1.05meV and1.25meV.This splitting is due to a small in-plane anisotropy of the type E i[(S x i)2−(S y i)2]that lifts the degeneracy of the doublet states S z=±1.These values of the gaps(ignoring the in-plane anisotropy)leads to J=44K and D/J=0.18[10].Detailed interpretation of INS requires a calculation of the structure factor S(Q,ω).III.EV ALUATING DYNAMICAL QUANTITIESWe describe in this section the methods used to compute the dynamical struc-ture factor:Sαα(Q,ω)= dt e iωt<0|Sα−Q(t)SαQ(0)|0>,α=x,y,z.(3.1)Here we denote the ground state by|0>and the components of the Fourier trans-form of the spin vectors are SαQ(t)in the Heisenberg representation.Weﬁrst write the structure factor as:Sαα(Q,ω)= nδ(ω−(ǫn−ǫ0))|<n|SαQ|0>|2,(3.2)where the sum over|n>means over all excited eigenstates of the system andǫn denotes the energy of|n>.In aﬁnite system calculation,one obtains aﬁnite set of delta functions with weights given by the matrix elements appearing in Eq.(3.2). The Lancz˝o s method which is commonly used to obtain the ground state wavefunc-tion and theﬁrst few excited levels is suited to the study of the dynamical properties [31].We proceed as follows:i)One needs to knowﬁrst the vector|0>.We use the Lancz˝o s algorithm applied to the Hamiltonian H.In fact,any kind of algorithm can be used at this level.ii)One constructs the state:|Φ0>=SαQ|0>.(3.3) This state|Φ0>is then used to build a new Lancz˝o s sequence of states|Φn>by the standard procedure of applying the Hamiltonian to|Φk>and orthonormal-ization with respect to the last two vectors|Φk>and|Φk−1>.The Hamiltonian H is then tridiagonal in the basis{|Φn>}.The nonzero elements of H in this basis are directly provided by the orthonormalization procedure.We exhaust the corresponding subspace and store the tridiagonal form of the Hamiltonian.iii)One diagonalizes the tridiagonal Hamiltonian by a standard routine.This leads to a set of eigenenergiesǫn as well as the eigenvectors whoseﬁrst coordinate in the Lancz˝o s basis are precisely the overlap matrix elements<n|Φ0>that appear in the deﬁnition of the structure factor Eq.(3.2).We thus obtain the weight of each delta function peak.This has to be done separately for each Q as well as forα=x,z.In the isotropic D=0case the ground state is a singlet:SαQ=0|0>=0and thus Sαα(Q=0,ω)=0.The vanishing with Q will occur quadratically.In the pres-ence of easy-plane anisotropy the ground state is invariant only under z rotations: S z Q=0|0>=0and thus S zz(Q=0,ω)=0,while S xx(=S yy)will be nonzero at Q=0and of order O(D2).With in-plane anisotropy E i[(S x i)2−(S y i)2]even S zz(Q=0)will be nonzero and O(E2).IV.RESULTS FOR S(Q,ω)We have computed the structure factors S xx(Q,ω)and S zz(Q,ω)for chains of lengths N=4,6,8,10,12,14,16.Some Q=0and Q=πparts of the spectrum have been computed also for N=18.We have concentrated on the case D/J=0.18 quantitatively relevant to the study of NENP.Our results extend smoothly for not too large anisotropy D<J.For D=0we reproduce previousﬁndings[8] concerning the lowest excited levels.Previous Monte-Carlo measurements of the dynamical structure factor[9]for D=0are also compatible with our data.According to the deﬁnition(3.2),we will discussﬁrst the peak positions and then the corresponding weights.What we observe is that for allﬁxed wavevector Q,as a function ofωthe lowest lying peak concentrates almost all of the spectral weight.This remark will be made quantitatively precise at the end of this section. This lowest-lying peak occurs when the frequencyωmatches the energy of theﬁrst excited level with the right quantum numbers.In the correlation S xx weﬁnd the excitation spectrum from S z=0to S z=±1that we obtained previously[23].This is plotted inﬁg.1as a function of the momenta by crosses of various sizes.For Q=0and Q=πthere is enough data to allow an extrapolation to the thermodynamic limit by use of the Shanks tranformation.We have also computed the these gaps(Q=0and Q=π)for a N=18chain.The extrapolation leads to0.301J at Q=πand0.986J at Q=0.In the interval[0,π]there is only the middle of the Brillouin zone Q=π/2where we obtain several data points from N=4,8,12,16.Shanks extrapolation leads then to 2.75J for Q=π/2.In the correlation S zz weﬁnd the excitation spectrum inside the S z=0sub-space.The lowest lying excitation is plotted inﬁg.1with empty octogons.At Q=πtheﬁnite-lattice data extrapolate to0.655J.The convergence in this case Q=πis very good as expected from a massive theory yielding well-separated eigenvalues in theﬁnite systems[23].On the contrary at Q=0the convergence is extremely bad and one can only suggest a value of0.60±0.05J for this gap.This is clearly due to the presence of a continuum of states starting immediately above this gap.Such a phenomenon is expected if one describes the spectrum near Q=0as due to two particles with momenta near Q=π[8].We note that the excitations in this sector(zz)are above the in-plane excita-tions in the neighborhood of Q=πbut they cross for Q/π≈0.75and on the top of the dispersion curve it is the in-plane mode which has highest energy:2.75J against 2.65J(extrapolated value)for the out-of-plane mode.This behaviour persists in the region0≤Q≤π/2of the Brillouin zone.To gain understanding of the nature of the excitations we have performed a variational calculation along the lines proposed by G´o mez-Santos[26].One discards the states with parallel spins,either if they are nearest-neighbors or separated by any number of zeros.The typical states in this subspace are of the form:|...↑↓↑0↓00↑↓...>(4.1) There is strict N´e el ordering of the S z=±1sites but there can be any number of intermediate zeros.In this subspace the true degrees of freedom are then the”spin-zero defects”i.e.sites with S z i=0.These domain walls are then represented asfermions(which is a natural way of enforcing no double occupancy).The fermionicHamiltonian can then be treated by approximate methods.It has been shown thata simple Hartree-Fock decoupling leads to a good approximation of the spectrumfor D=0.The best results are obtained by using the variational improvementintroduced by G´o mez-Santos where one allows a small admixture of states withparallel spins.The Haldane gap,as computed by this method,is found to be0.45Jfor D=0.It is straightforward to include anisotropy of the form D i(S z i)2.We have obtained a spectrum of massive fermions E(Q)that is plotted as a continuouscurve inﬁg.1.This curve should be the excitation spectrum in the S z=0subspacedue to the restriction to the subspace(4.1).The gap at Q=πis found to be≈0.70Jwhen D/J=0.18.The single-fermion curve E(Q)reproduces extremely well the OPdispersion in the regionπ/2<Q<π.The IP dispersion will be discussed later on.Figure1Dispersion of magnetic excitations S z=0and S z=±1at D=0.18J for momentaranging from0toπ.The continuous line is the result of a variational calculation.The dashed line is the corresponding edge of two-particle excitations.We now turn to the discussion of the spectral weight associated to the peak positions.For all chain lengths studied for all wavevectors in the interval[≈0.3−1.0]×πweﬁnd that both S xx and S zz are dominated by a single peak as a function of the frequency.This peak concentrates at least98per cent of the spectral weight. Multimagnon contributions are thus extremely small in the whole range[≈0.3−1.0]×π.As typical examples we plot inﬁg.2S xx(Q=π,ω)+S zz(Q=π,ω) from the N=16chain.The peaks have been broadened for clarity.Inﬁg.3we plot the Q=π/2case showing the interchange of the two modes.A single-mode approximation will be an extremely good description of the physics in this part of the Brillouin zone.The simple picture described above breaks down for small values of Q.In the N=16chain,for Q=3π/8there is still the one-peak structure while for Q=π/4there are several peaks as a function ofω:seeﬁg.4.In the N=14chain we ﬁnd that the continuum appears already for Q=2π/7but is not there for3π/7.It is diﬃcult to give a precise value of the wavevector at which this phenomenon appears since the discretization of the momenta imposed by the chain length is coarse.As discussed below,this can be interpreted as evidence for a two-particle continuum. Our present data suggest that the continuum sets in at≈0.3πfor both IP and OP sectors.We see no reason why the continuum boundary should the same for both modes although we are unable to see any quantitative diﬀerence in our present data between IP and OP modes in this respect.Let us discuss the nature of the two-particle excitations.If a single-particle ex-citation has a dispersion E(Q),the lower edge of the continuum of two-particle exci-tations is given by E(2)(Q)=min K(E(K)+E(Q−K))in the non-interacting case. Such a free picture seems to apply to the spin1chain[1,2,24].In the anisotropic system it is possible to construct several continua since there are two distinct modes (IP and OP).In the S z=±1subspace two-particle states are obtained from one S z=±1 excitation and one S z=0excitation.The gap of this continuum at Q=0will be the sum of the IP and the OP gap at Q=πi.e.≈0.301J+0.655J in agreement with our extrapolation of0.986J.The continuum is also seen in the poor convergence of ﬁnite-size data.Its progressive build-up is seen inﬁg.4.In the S z=0subspace there are two ways of building two-particle states: either with two S z=0states or with one excitation S z=+1and one excitation S z=−1.In theﬁrst case we can obtain an approximation for the continuum boundary by using the fermionic method cited above:the curve E(2)(Q)for two fermionic excitations belonging to the S z=0sector is plotted as a dash-dotted line inﬁg.1.The two-fermion continuum is clearly above the OP(and IP)mode for 0<Q<π/2.However the second possibility which is the continuum(S z=+1) +(S z=−1)has a Q=0gap that is twice the gap at Q=πfor the IP mode i.e.≈0.6J.This agrees with our estimate≈0.6J for the gap in the OP sector at Q=0. This continuum is thus the lowest-lying one.This reasoning shows also that the OP(S z=0)mode should be below the IP mode for Q≈0since the IP gap is then given by≈0.301J+0.655J.In fact,as stressed above,we have good evidence that the crossing of the two modes occurs quite near Q/π≈0.75.Figure2,3,4The structure factor S(xx)(Q,ω)+S(zz)(Q,ω),for Q=π,π/2,π/4respectively,as a function of the frequencyω(in units of J)for chain length N=16.Inﬁg.2each of the two functions S(αα)has a single-peak structure:a single-mode approximation works very well.The IP mode is doubly degenerate and appears only in S(xx)while the OP appears in S(zz).Inﬁg.3the IP and OP modes are interchanged with respect toﬁg.2.Inﬁg.4a single-mode approximation no longer holds and the two-particle continuum is seen:spectral weight is transferred to multimagnon excitations.The agreement between the ab initio data and the variational calculation con-ﬁrms the relevance of domain walls in the whole Haldane phase,as is also pointed out in[32].The disordered-ﬂat phases obtained in the solid-on-solid picture of the spin-1chain[33]also correspond to the subspace of spin-zero defects which is so successfull in the description of the elementary excitations.Finally we quote results for the static structure factors S(αα)(Q)obtained by integration over frequency.Inﬁg.5these quantities are plotted in a logarithmic scale as a function of momentum.Due to our limited chain length,we cannot make anyﬁrm statement about the prediction[1]of square-root Lorentzian behaviour near Q=π.Our data are compatible with previous studies[34,35]concluding to a correlation length≈6lattice spacings in the D=0case:the correlation length does not change much when D/J=0.18.The behaviour of S(zz)(Q)≈Q2sets in only for very small wavevectors:for the largest part of the Brillouin zone excepting the neighborhood of Q=πit is rather close to Q3/2.Figure5The static structure factors S(xx)and S(zz)for all chain lengths as a function of momentum.The symbol sizes are the same as inﬁgs.1and6.Crosses stand for S(xx)and octogons for S(zz).PARISON WITH NEUTRON SCATTERING EXPERIMENTS The two magnetic modes in the neighborhood of Q=πhave been observed by INS in ref.[17-20].The values of the gaps lead to J≈3.8meV and D/J=0.18. These values are very close to those extracted from magnetization measurements [36].The dispersion has been studied throughout the whole Brillouin zone[22].A goodﬁt is obtained through the following formula:ω±(Q)= 2).(5.1)The parameters are∆+=2.5meV,∆−=1.2meV,v=9.6meV and A=6.1meV. Scaling by J=4meV we plotω±(Q)as continuous lines inﬁg.6.For clarity we have also plotted our Lancz˝o s points.The edges of two-particle continuum extracted from theﬁts(5.1)are also plotted inﬁg.6.The lower dashed line corresponds to the(S z=+1)+(S z=−1)continuum while the upper dashed line corresponds to (S z=+1)+(S z=0).Figure6Lancz˝o s results compared to experimentalﬁts.The two continuous curves are taken from Eq.(5.1).They reproduce theﬁndings of ref.22.The two dash-dotted lines are the two-magnon continuum boundaries obtained also from(5.1).The size of the symbols is chosen as inﬁg.1.There is very good agreement with the theoretical results in the neighborhood of Q=πwhere the IP and OP modes are separated by the experimental resolution [17-20,22].In the regionπ/2<Q<πtheﬁts(5.1)are also in agreement with the theoretical results.The two modes are no longer separated since they are very close to each other.At the top of the dispersion curve Q=π/2we estimate from the values quoted in sect.IV the gaps to be2.75J for the IP mode and2.65J for the OP.This means that the IP mode is at≈11meV and the OP mode at≈10.5meV using the value of J quoted above.The crossing(or near crossing)of the two modes for Q≈0.75πprecludes their separation in this region of Q.In the regime Q<π/2 the separation of the modes increases but the intensity of the scattering decreases strongly as is seen fromﬁg.5.The continuum will appear for Q<0.3πand is not seen in present experiments[22].We see it for Q=0.25πand below but there the structure factor will be very small.For the whole interval0.3π−1.0πour data are well reproduced by long-lived excitations as is seen experimentally[22].The asymmetry with respect toπ/2of the spectrum(ﬁgs1,6)demonstrates the absence of broken translational symmetry.The trend of the magnetic intensity versus Q in ﬁg.5is that found by INS[22].Absence of data for Q very close toπforbids us to check the square-root Lorentzian behaviour expected for each of the static functions S(xx)and S(zz).With respect to what has already been done,it would be very interesting to separate the two modes nearπ/2where intensity is not dramatically weak.The observation of the two-particle continuum on the contrary should be quite diﬃcult since it appears only for Q<0.25πwhere magnetic scattering is very weak.The observation of very long-lived modes[22]is thus in very good agreement with the physics of an anisotropic spin1chain.Finally we comment on the uncertainties in the numerical data.For the gap values there is very good convergence for Q=πand there one can use all the chain lengths at our disposal.For other values of Q it is only at the top of the spectrum that an extrapolation can be performed.Concerning the values of Q at which some-thing interesting happens(i.e.crossing of the two modes or entering the continuum) without being able to make reﬁned extrapolations we can only observe that they do not depend much on the chain length.The corresponding numbers should be regarded as tentative(i.e.0.75πfor the crossing and0.3πfor the continuum).High resolution INS experiments[30]have revealed that the IP mode is split by in-plane anisotropy E i[(S x i)2−(S y i)2].Our results neglecting this further splitting thus will apply to the description of actual experiments as long as the resolution is not very high.This eﬀect is not expected to change much the numericalﬁgures.VI.CONCLUSIONWe have studied the dynamical properties of a spin1chain with single-ion easy-plane anisotropy thought to be relevant to the magnetic behaviour of the compound NENP.The dynamical structure factor S(αα)(Q,ω)has been computed by a Lancz˝o s method on chains of lengths up to16spins while some parts of the spectrum have been obtained on a18spins chain.We have performed a variational calculation to obtain the spectrum of elementary excitations in the S z=0sector.Both ab initio and approximate methods agree very well,elucidating the role of the spin-zero defects in the Haldane phase.Weﬁnd that the magnetic excitations are described by two distinct long-lived modes throughout most of the Brillouin zone0.3−1.0πwhere the lowest excited state in each sector(S z=0and S z=±1)carries almost all of the spectral weight: a single-mode approximation is thus adequate.Weﬁnd that these modes merge into a two-particle continuum for Q<0.3πas seen in the frequency dependence of the structure factor.We have shown that these results reproduce the INS experiments on NENP.The dispersion of the magnetic modes as well as their intensity is close to that found theoretically.Our results show that in principle it should be possible to observe the crossing of the two IP and OP magnetic modes.At the top of the dispersion curve their separation and intensity should allow observation.On the contrary the edge of the two-particle continuum appear only for very small Q<0.3πwhere magnetic intensity is very weak as found in recent experiments[22].We mentionﬁnally that it would be very interesting to measure the static form factors of an anisotropic chain by a method that allows to reach the neighborhood of Q=πsince here we are limited by the coarse-graining due to our small chains.Quantum Monte-Carlo calculation that works eﬃciently for static quantities can reach this goal.ACKNOWLEDGEMENTS We thank S.Ma et al.for sending us a copy of ref.22prior to publication.Thanks are also due to L.P.Regnault for discussions about neutron scattering experiements on NENP.We also thank Th.Garel and J. Miller for reading our manuscript.Note added:while preparing this manuscript,we received a preprint by M.Taka-hashi which addresses similar questions.。