Model for fermion mass matrices and the origin of quark-lepton symmetry

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质量质心测量方法及实例分析

201 9年第4期质量质心测量方法及实例分析$刘明勇罗锋徐健(中国工程物理研究院机械制造工艺研究所，四川绵阳621900)摘要：对“三点支承称重法”质量质心测量原理、不确定数学模型进行详细阐述，结合某型质量质心测量设备的设计过程，通过分析设计输入，开展质量、质心位置U j、z方向）精度预估及关键器件选型，对建立的数学模型进行验证。

关键词：三点支承称重法;质量质心;数学模型;设计分析中图分类号:TB936 文献标识码:ADOI：10.19287/ki.1005-2402. 2019. 04. 025麵与质量Test and Quality_______________________________________________________________________Method of masscentroid measurement and case analysisLIU Mingyong,L U O Feng,X U Jian(Institute of Mechanical Manufacturer Technology,China Academy of Engineering Physics,Mianyang621900, C H N) Abstract："Three-point supporting weighing method"mass measurement principle,the mathematical model in det a i l in t h i s paper,the uncertainty,in accordance with the process of the design of a certain type of massmeasuring equipment,through the analysis of design input,t o carry out the quality,centroid position(x,j,z direction)forecast accuracy and key components selection,t o establish the mathematicalmodel for validation.Keywords：three-point support weighing method；mass center of mass；mathematical model；design and analysis在制造业领域中，常需要对产品的质量质心进行测量。

PACSnumbers1215Ff,1130Hv,1210Dm,1125Mj…

a r X i v :0803.2889v 2 [h e p -p h ] 14 J u l 2008Mapping Out SU (5)GUTs with Non-Abelian Discrete Flavor SymmetriesFlorian Plentinger ∗and Gerhart Seidl †Institut f¨u r Physik und Astrophysik,Universit¨a t W¨u rzburg,Am Hubland,D 97074W¨u rzburg,Germany(Dated:December 25,2013)We construct a class of supersymmetric SU (5)GUT models that produce nearly tribimaximal lepton mixing,the observed quark mixing matrix,and the quark and lepton masses,from discrete non-Abelian ﬂavor symmetries.The SU (5)GUTs are formulated on ﬁve-dimensional throats in the ﬂat limit and the neutrino masses become small due to the type-I seesaw mechanism.The discrete non-Abelian ﬂavor symmetries are given by semi-direct products of cyclic groups that are broken at the infrared branes at the tip of the throats.As a result,we obtain SU (5)GUTs that provide a combined description of non-Abelian ﬂavor symmetries and quark-lepton complementarity.PACS numbers:12.15.Ff,11.30.Hv,12.10.Dm,One possibility to explore the physics of grand uniﬁed theories (GUTs)[1,2]at low energies is to analyze the neutrino sector.This is due to the explanation of small neutrino masses via the seesaw mechanism [3,4],which is naturally incorporated in GUTs.In fact,from the perspective of quark-lepton uniﬁcation,it is interesting to study in GUTs the drastic diﬀerences between the masses and mixings of quarks and leptons as revealed by current neutrino oscillation data.In recent years,there have been many attempts to re-produce a tribimaximal mixing form [5]for the leptonic Pontecorvo-Maki-Nakagawa-Sakata (PMNS)[6]mixing matrix U PMNS using non-Abelian discrete ﬂavor symme-tries such as the tetrahedral [7]and double (or binary)tetrahedral [8]groupA 4≃Z 3⋉(Z 2×Z 2)and T ′≃Z 2⋉Q,(1)where Q is the quaternion group of order eight,or [9]∆(27)≃Z 3⋉(Z 3×Z 3),(2)which is a subgroup of SU (3)(for reviews see, e.g.,Ref.[10]).Existing models,however,have generally dif-ﬁculties to predict also the observed fermion mass hierar-chies as well as the Cabibbo-Kobayashi-Maskawa (CKM)quark mixing matrix V CKM [11],which applies especially to GUTs (for very recent examples,see Ref.[12]).An-other approach,on the other hand,is oﬀered by the idea of quark-lepton complementarity (QLC),where the so-lar neutrino angle is a combination of maximal mixing and the Cabibbo angle θC [13].Subsequently,this has,in an interpretation of QLC [14,15],led to a machine-aided survey of several thousand lepton ﬂavor models for nearly tribimaximal lepton mixing [16].Here,we investigate the embedding of the models found in Ref.[16]into ﬁve-dimensional (5D)supersym-metric (SUSY)SU (5)GUTs.The hierarchical pattern of quark and lepton masses,V CKM ,and nearly tribi-maximal lepton mixing,arise from the local breaking of non-Abelian discrete ﬂavor symmetries in the extra-dimensional geometry.This has the advantage that theFIG.1:SUSY SU (5)GUT on two 5D intervals or throats.The zero modes of the matter ﬁelds 10i ,5H,24H ,and the gauge supermul-tiplet,propagate freely in the two throats.scalar sector of these models is extremely simple without the need for a vacuum alignment mechanism,while of-fering an intuitive geometrical interpretation of the non-Abelian ﬂavor symmetries.As a consequence,we obtain,for the ﬁrst time,a realization of non-Abelian ﬂavor sym-metries and QLC in SU (5)GUTs.We will describe our models by considering a speciﬁc minimal realization as an example.The main features of this example model,however,should be viewed as generic and representative for a large class of possible realiza-tions.Our model is given by a SUSY SU (5)GUT in 5D ﬂat space,which is deﬁned on two 5D intervals that have been glued together at a common endpoint.The geom-etry and the location of the 5D hypermultiplets in the model is depicted in FIG.1.The two intervals consti-tute a simple example for a two-throat setup in the ﬂat limit (see,e.g.,Refs.[17,18]),where the two 5D inter-vals,or throats,have the lengths πR 1and πR 2,and the coordinates y 1∈[0,πR 1]and y 2∈[0,πR 2].The point at y 1=y 2=0is called ultraviolet (UV)brane,whereas the two endpoints at y 1=πR 1and y 2=πR 2will be referred to as infrared (IR)branes.The throats are supposed to be GUT-scale sized,i.e.1/R 1,2 M GUT ≃1016GeV,and the SU (5)gauge supermultiplet and the Higgs hy-permultiplets 5H and2neously broken to G SM by a 24H bulk Higgs hypermulti-plet propagating in the two throats that acquires a vac-uum expectation value pointing in the hypercharge direc-tion 24H ∝diag(−12,13,15i ,where i =1,2,3is the generation index.Toobtainsmall neutrino masses via the type-I seesaw mechanism [3],we introduce three right-handed SU (5)singlet neutrino superﬁelds 1i .The 5D Lagrangian for the Yukawa couplings of the zero mode fermions then readsL 5D =d 2θ δ(y 1−πR 1) ˜Y uij,R 110i 10j 5H +˜Y d ij,R 110i 5H +˜Y νij,R 15j5i 1j 5H +M R ˜Y R ij,R 21i 1j+h.c. ,(3)where ˜Y x ij,R 1and ˜Y x ij,R 2(x =u,d,ν,R )are Yukawa cou-pling matrices (with mass dimension −1/2)and M R ≃1014GeV is the B −L breaking scale.In the four-dimensional (4D)low energy eﬀective theory,L 5D gives rise to the 4D Yukawa couplingsL 4D =d 2θ Y u ij 10i 10j 5H +Y dij10i 5H +Y νij5i ∼(q i 1,q i 2,...,q i m ),(5)1i ∼(r i 1,r i 2,...,r im ),where the j th entry in each row vector denotes the Z n jcharge of the representation.In the 5D theory,we sup-pose that the group G A is spontaneously broken by singly charged ﬂavon ﬁelds located at the IR branes.The Yukawa coupling matrices of quarks and leptons are then generated by the Froggatt-Nielsen mechanism [21].Applying a straightforward generalization of the ﬂavor group space scan in Ref.[16]to the SU (5)×G A represen-tations in Eq.(5),we ﬁnd a large number of about 4×102ﬂavor models that produce the hierarchies of quark and lepton masses and yield the CKM and PMNS mixing angles in perfect agreement with current data.A distri-bution of these models as a function of the group G A for increasing group order is shown in FIG.2.The selection criteria for the ﬂavor models are as follows:First,all models have to be consistent with the quark and charged3 lepton mass ratiosm u:m c:m t=ǫ6:ǫ4:1,m d:m s:m b=ǫ4:ǫ2:1,(6)m e:mµ:mτ=ǫ4:ǫ2:1,and a normal hierarchical neutrino mass spectrumm1:m2:m3=ǫ2:ǫ:1,(7)whereǫ≃θC≃0.2is of the order of the Cabibbo angle.Second,each model has to reproduce the CKM anglesV us∼ǫ,V cb∼ǫ2,V ub∼ǫ3,(8)as well as nearly tribimaximal lepton mixing at3σCLwith an extremely small reactor angle 1◦.In perform-ing the group space scan,we have restricted ourselves togroups G A with orders roughly up to 102and FIG.2shows only groups admitting more than three valid mod-els.In FIG.2,we can observe the general trend thatwith increasing group order the number of valid modelsper group generally increases too.This rough observa-tion,however,is modiﬁed by a large“periodic”ﬂuctu-ation of the number of models,which possibly singlesout certain groups G A as particularly interesting.Thehighly populated groups would deserve further system-atic investigation,which is,however,beyond the scopeof this paper.From this large set of models,let us choose the groupG A=Z3×Z8×Z9and,in the notation of Eq.(5),thecharge assignment101∼(1,1,6),102∼(0,3,1),103∼(0,0,0),52∼(0,7,0),52↔4FIG.3:Eﬀect of the non-Abelian ﬂavor symmetry on θ23for a 10%variation of all Yukawa couplings.Shown is θ23as a function of ǫfor the ﬂavor group G A (left)and G A ⋉G B (right).The right plot illustrates the exact prediction of the zeroth order term π/4in the expansion θ23=π/4+ǫ/√2and the relation θ13≃ǫ2.The important point is that in the expression for θ23,the leading order term π/4is exactly predicted by thenon-Abelian ﬂavor symmetry G F =G A ⋉G B (see FIG.3),while θ13≃θ2C is extremely small due to a suppression by the square of the Cabibbo angle.We thus predict a devi-ation ∼ǫ/√2,which is the well-known QLC relation for the solar angle.There have been attempts in the literature to reproduce QLC in quark-lepton uniﬁed models [26],however,the model presented here is the ﬁrst realization of QLC in an SU (5)GUT.Although our analysis has been carried out for the CP conserving case,a simple numerical study shows that CP violating phases (cf.Ref.[27])relevant for neutri-noless double beta decay and leptogenesis can be easily included as well.Concerning proton decay,note that since SU (5)is bro-ken by a bulk Higgs ﬁeld,the broken gauge boson masses are ≃M GUT .Therefore,all fermion zero modes can be localized at the IR branes of the throats without intro-ducing rapid proton decay through d =6operators.To achieve doublet-triplet splitting and suppress d =5pro-ton decay,we may then,e.g.,resort to suitable extensions of the Higgs sector [28].Moreover,although the ﬂavor symmetry G F is global,quantum gravity eﬀects might require G F to be gauged [29].Anomalies can then be canceled by Chern-Simons terms in the 5D bulk.We emphasize that the above discussion is focussed on a speciﬁc minimal example realization of the model.Many SU (5)GUTs with non-Abelian ﬂavor symmetries,however,can be constructed along the same lines by varying the ﬂavor charge assignment,choosing diﬀerent groups G F ,or by modifying the throat geometry.A de-tailed analysis of these models and variations thereof will be presented in a future publication [30].To summarize,we have discussed the construction of 5D SUSY SU (5)GUTs that yield nearly tribimaximal lepton mixing,as well as the observed CKM mixing matrix,together with the hierarchy of quark and lepton masses.Small neutrino masses are generated only by the type-I seesaw mechanism.The fermion masses and mixings arise from the local breaking of non-Abelian ﬂavor symmetries at the IR branes of a ﬂat multi-throat geometry.For an example realization,we have shown that the non-Abelian ﬂavor symmetries can exactly predict the leading order term π/4in the sum rule for the atmospheric mixing angle,while strongly suppress-ing the reactor angle.This makes this class of models testable in future neutrino oscillation experiments.In addition,we arrive,for the ﬁrst time,at a combined description of QLC and non-Abelian ﬂavor symmetries in SU (5)GUTs.One main advantage of our setup with throats is that the necessary symmetry breaking can be realized with a very simple Higgs sector and that it can be applied to and generalized for a large class of uniﬁed models.We would like to thank T.Ohl for useful comments.The research of F.P.is supported by Research Train-ing Group 1147“Theoretical Astrophysics and Particle Physics ”of Deutsche Forschungsgemeinschaft.G.S.is supported by the Federal Ministry of Education and Re-search (BMBF)under contract number 05HT6WWA.∗********************************.de †**************************.de[1]H.Georgi and S.L.Glashow,Phys.Rev.Lett.32,438(1974);H.Georgi,in Proceedings of Coral Gables 1975,Theories and Experiments in High Energy Physics ,New York,1975.[2]J.C.Pati and A.Salam,Phys.Rev.D 10,275(1974)[Erratum-ibid.D 11,703(1975)].[3]P.Minkowski,Phys.Lett.B 67,421(1977);T.Yanagida,in Proceedings of the Workshop on the Uniﬁed Theory and Baryon Number in the Universe ,KEK,Tsukuba,1979;M.Gell-Mann,P.Ramond and R.Slansky,in Pro-ceedings of the Workshop on Supergravity ,Stony Brook,5New York,1979;S.L.Glashow,in Proceedings of the 1979Cargese Summer Institute on Quarks and Leptons, New York,1980.[4]M.Magg and C.Wetterich,Phys.Lett.B94,61(1980);R.N.Mohapatra and G.Senjanovi´c,Phys.Rev.Lett.44, 912(1980);Phys.Rev.D23,165(1981);J.Schechter and J.W. F.Valle,Phys.Rev.D22,2227(1980);zarides,Q.Shaﬁand C.Wetterich,Nucl.Phys.B181,287(1981).[5]P.F.Harrison,D.H.Perkins and W.G.Scott,Phys.Lett.B458,79(1999);P.F.Harrison,D.H.Perkins and W.G.Scott,Phys.Lett.B530,167(2002).[6]B.Pontecorvo,Sov.Phys.JETP6,429(1957);Z.Maki,M.Nakagawa and S.Sakata,Prog.Theor.Phys.28,870 (1962).[7]E.Ma and G.Rajasekaran,Phys.Rev.D64,113012(2001);K.S.Babu,E.Ma and J.W.F.Valle,Phys.Lett.B552,207(2003);M.Hirsch et al.,Phys.Rev.D 69,093006(2004).[8]P.H.Frampton and T.W.Kephart,Int.J.Mod.Phys.A10,4689(1995); A.Aranda, C. D.Carone and R.F.Lebed,Phys.Rev.D62,016009(2000);P.D.Carr and P.H.Frampton,arXiv:hep-ph/0701034;A.Aranda, Phys.Rev.D76,111301(2007).[9]I.de Medeiros Varzielas,S.F.King and G.G.Ross,Phys.Lett.B648,201(2007);C.Luhn,S.Nasri and P.Ramond,J.Math.Phys.48,073501(2007);Phys.Lett.B652,27(2007).[10]E.Ma,arXiv:0705.0327[hep-ph];G.Altarelli,arXiv:0705.0860[hep-ph].[11]N.Cabibbo,Phys.Rev.Lett.10,531(1963);M.Kobayashi and T.Maskawa,Prog.Theor.Phys.49, 652(1973).[12]M.-C.Chen and K.T.Mahanthappa,Phys.Lett.B652,34(2007);W.Grimus and H.Kuhbock,Phys.Rev.D77, 055008(2008);F.Bazzocchi et al.,arXiv:0802.1693[hep-ph];G.Altarelli,F.Feruglio and C.Hagedorn,J.High Energy Phys.0803,052(2008).[13]A.Y.Smirnov,arXiv:hep-ph/0402264;M.Raidal,Phys.Rev.Lett.93,161801(2004);H.Minakata andA.Y.Smirnov,Phys.Rev.D70,073009(2004).[14]F.Plentinger,G.Seidl and W.Winter,Nucl.Phys.B791,60(2008).[15]F.Plentinger,G.Seidl and W.Winter,Phys.Rev.D76,113003(2007).[16]F.Plentinger,G.Seidl and W.Winter,J.High EnergyPhys.0804,077(2008).[17]G.Cacciapaglia,C.Csaki,C.Grojean and J.Terning,Phys.Rev.D74,045019(2006).[18]K.Agashe,A.Falkowski,I.Low and G.Servant,J.HighEnergy Phys.0804,027(2008);C.D.Carone,J.Erlich and M.Sher,arXiv:0802.3702[hep-ph].[19]Y.Kawamura,Prog.Theor.Phys.105,999(2001);G.Altarelli and F.Feruglio,Phys.Lett.B511,257(2001);A.B.Kobakhidze,Phys.Lett.B514,131(2001);A.Hebecker and J.March-Russell,Nucl.Phys.B613,3(2001);L.J.Hall and Y.Nomura,Phys.Rev.D66, 075004(2002).[20]D.E.Kaplan and T.M.P.Tait,J.High Energy Phys.0111,051(2001).[21]C.D.Froggatt and H.B.Nielsen,Nucl.Phys.B147,277(1979).[22]Y.Nomura,Phys.Rev.D65,085036(2002).[23]H.Georgi and C.Jarlskog,Phys.Lett.B86,297(1979).[24]H.Arason et al.,Phys.Rev.Lett.67,2933(1991);H.Arason et al.,Phys.Rev.D47,232(1993).[25]D.S.Ayres et al.[NOνA Collaboration],arXiv:hep-ex/0503053;Y.Hayato et al.,Letter of Intent.[26]S.Antusch,S.F.King and R.N.Mohapatra,Phys.Lett.B618,150(2005).[27]W.Winter,Phys.Lett.B659,275(2008).[28]K.S.Babu and S.M.Barr,Phys.Rev.D48,5354(1993);K.Kurosawa,N.Maru and T.Yanagida,Phys.Lett.B 512,203(2001).[29]L.M.Krauss and F.Wilczek,Phys.Rev.Lett.62,1221(1989).[30]F.Plentinger and G.Seidl,in preparation.。

The Matrix Model It’s A Lot of Different Things：矩阵模型有很多不同的事情

addressed 5. Allegiance is to therapist (vs. group)
MATRIX MODEL OF TREATMENT
Different from Typical Residential Treatment
6. Nonjudgmental attitude is basis of clienttherapist bond
MATRIX MODEL OF TREATMENT
Different from General Therapy
6. Focus is on abstinence 7. Bottom line is always continued
abstinence 8. Therapist frequently pursues less
MATRIX MODEL OF TREATMENT
Organizing Principles of Matrix Treatment (cont.)
•Provide corrective feedback when necessary •Educate family regarding stimulant abuse recovery •Introduce and encourage self-help participation •Use urinalysis to monitor drug use
MATRIX MODEL OF TREATMENT
Different from General Therapy
1. Focus on behavior vs. feelings 2. Visit frequency results in strong
transference 3. Transference is encouraged 4. Transference is utilized 5. Goal is stability (vs. emotional catharsis)

czm内聚力模型ppt课件

What happens beyond that condition is the realm of ‘fracture’, ‘damage’, and ‘failure’ mechanics.
CZM offers an alternative way to view and failure in materials.
Wake of crack tip
Forward of crack tip
Fibril (MMC bridging Grain bridging
Microvoid coalescence
Plastic zone
Metallic
Cleavage fracture
Oxide bridging
Fibril(polymers) bridging
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NO MATERIAL SEPARATION
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COHESIVE CRACK TIP
Molecular force of cohesion acting near the edge of the crack at its surface (region II ). The intensity of molecular force of cohesion ‘f ’ is found to vary as shown in Fig.a. The interatomic force is initially zero when the atomic planes are separated by normal

Modeling Financial Security Returns Using Lévy Processes(Baruch College,Liuren Wu)

2 Characteristic exponent: ψ (u) = −iuµ + 1 σ . 2
s2 σ 2 . Cumulant exponent: ϕ(s) = sµ + 1 2 Probability density: f (x) =
√ 1 2πσ 2 −µ) exp − (x2 σ2
2
.
Literature: x The Black-Scholes (Merton, Garman, Kohlhagen...) model:
s
Generality : x Lévy processes can generate pretty much any return innovation distribution. x Applying stochastic time changes on Lévy processes randomizes the return innovation distribution over time ⇒ stochastic volatility, and higher moments. Explicit economic mapping by modeling returns with several time-changed Lévy components (versus models with hidden state vectors): x Each Lévy component captures shocks from each economic source. x Time change captures the time-varying intensity of its impact. ⇒ makes model design more intuitive, parsimonious, and to the point. Tractability : A model is tractable for option pricing if we have under the risk-neutral measure Q x tractable characteristic exponent for the Lévy components. x tractable Laplace transforms for the activity rates underlying the time change. ⇒ any combinations of the two generate tractable return dynamics.

Geometric Modeling

Geometric ModelingGeometric modeling is a branch of mathematics that deals with the representation of objects in space. It is a fundamental tool in computer graphics, computer-aided design (CAD), and other applications that require the creation of 3D models. Geometric modeling involves the use of mathematical equations and algorithms to create and manipulate objects in space. In this essay, we will explore the different aspects of geometric modeling, including its history, applications, and challenges.The history of geometric modeling can be traced back to the early 19th century when mathematicians began to study the properties of curves and surfaces. In the early 20th century, the development of calculus and differential geometry led to the creation of new methods for representing complex objects in space. The introduction of computers in the mid-20th century revolutionized the field of geometric modeling, making it possible to create and manipulate 3D models with greater precision and ease.Today, geometric modeling is used in a wide range of applications, including computer graphics, animation, video games, virtual reality, and CAD. In computer graphics and animation, geometric modeling is used to create realistic 3D models of objects, characters, and environments. In video games, geometric modeling is used to create the game world and characters. In virtual reality, geometric modeling is used to create immersive environments that simulate real-world experiences. In CAD, geometric modeling is used to create precise 3D models of mechanical parts and assemblies.One of the biggest challenges in geometric modeling is the representation of complex shapes and surfaces. Many real-world objects, such as cars, airplanes, and human bodies, have complex shapes that are difficult to represent using simple geometric primitives such as spheres, cylinders, and cones. To overcome this challenge, researchers have developed advanced techniques such as NURBS (non-uniform rational B-splines), which allow for the creation of complex curves and surfaces by combining simple geometric primitives.Another challenge in geometric modeling is the optimization of models for efficient rendering and simulation. As the complexity of models increases, so doesthe computational cost of rendering and simulating them. To address this challenge, researchers have developed techniques such as level-of-detail (LOD) modeling,which involves creating multiple versions of a model at different levels of detail to optimize rendering and simulation performance.In conclusion, geometric modeling is a fundamental tool in computer graphics, animation, video games, virtual reality, and CAD. Its history can be traced backto the early 19th century, and its development has been closely tied to the advancement of mathematics and computer technology. Despite its many applications and successes, geometric modeling still faces challenges in the representation of complex shapes and surfaces, as well as the optimization of models for efficient rendering and simulation. As technology continues to advance, it is likely that new techniques and approaches will emerge to overcome these challenges and pushthe field of geometric modeling forward.。

Democratic Universal Seesaw Model with Three Light Sterile Neutrinos

University of Shizuoka US-00-04R July 2000 hep-ph/0006084
arXiv:hep-ph/0006084v3 25 Jul 2000
Democratic Universal Seesaw Model with Three Light Sterile Neutrinos

(1.1)
and mL and mR are universal for all fermion sectors f . For O (MF )≫O (mR )≫O (mL), the mass matrix (1.1) leads to the well-known seesaw expression
For the up-type quark sector, the parameter bf is taken as bu = −1/3, which leads to detMU = 0, and the seesaw mechanism does not work for one of the three families, and
(1.9) (1.10)
−1 T −1 T mR ) has already been invesThe scenario corresponding to O (mLML mL )≪O (mR MR tigated by one of the authors (Y.K.) [5]. He has concluded that although either the atmospheric [6] or solar [7] neutrino data can be explained by the mixings νµ ↔ ντ or νe ↔ νµ , however, simultaneous explanation of the both data cannot be obtained in this model. −1 T −1 T In the present paper, we consider another possibility O (mL ML mL )∼O (mR MR mR ). In this case, mixings between νiL and νiR are induced. The solar neutrino data [7] are understood from a small mixing between νeL and νeR . The atmospheric [6] and the LSND [8] neutrino data are explained by the mixings νµL ↔ ντ L and νeL ↔ νµL , respectively. The vantage point of the democratic seesaw model [2] is that parameters zi in the mass matrices mL and mR are given in terms of the charged lepton masses and thereby the

Dynamic Causal Modelling (DCM) for fMRI动态因果模型(DCM)的功能磁共振成像

Visual input in the - left (LVF) - right (RVF) visual field.
z1
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z2
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u2
state changes
LVF
u1
effective connectivity system state input external parameters inputs
a21 0
a12 0
2 b21 0
green: neuronal activity red: bold response
Example: modelled BOLD signal
Underlying model
(modulatory inputs not shown)
FG left FG right
( A u j B ) z Cu z
j j 1
m
Conceptual overview
Input u(t)
c1 b23
n z F ( z , u , ) Neuronal state equation The bilinear model ( A u j B j ) z Cu z
b 0
2 21
modulatory input u2 activity through the coupling a21
Neurodynamics: reciprocal connections
u1
a11
u2
a12
z1
a21
a22
z2
1 a11 a12 z1 z 0 0 z1 c u u1 2 2 z a 2 21 a22 z2 b21 0 z2 0

yantubbs-The hardening soil model, Formulation and verification

The hardening soil model: Formulation and verificationT. SchanzLaboratory of Soil Mechanics, Bauhaus-University Weimar, GermanyP.A. VermeerInstitute of Geotechnical Engineering, University Stuttgart, GermanyP.G. BonnierP LAXIS B.V., NetherlandsKeywords: constitutive modeling, HS-model, calibration, verificationABSTRACT: A new constitutive model is introduced which is formulated in the framework of classical theory of plasticity. In the model the total strains are calculated using a stress-dependent stiffness, different for both virgin loading and un-/reloading. The plastic strains are calculated by introducing a multi-surface yield criterion. Hardening is assumed to be isotropic depending on both the plastic shear and volumetric strain. For the frictional hardening a non-associated and for the cap hardening an associated flow rule is assumed.First the model is written in its rate form. Therefor the essential equations for the stiffness mod-ules, the yield-, failure- and plastic potential surfaces are given.In the next part some remarks are given on the models incremental implementation in the P LAXIS computer code. The parameters used in the model are summarized, their physical interpre-tation and determination are explained in detail.The model is calibrated for a loose sand for which a lot of experimental data is available. With the so calibrated model undrained shear tests and pressuremeter tests are back-calculated.The paper ends with some remarks on the limitations of the model and an outlook on further de-velopments.1INTRODUCTIONDue to the considerable expense of soil testing, good quality input data for stress-strain relation-ships tend to be very limited. In many cases of daily geotechnical engineering one has good data on strength parameters but little or no data on stiffness parameters. In such a situation, it is no help to employ complex stress-strain models for calculating geotechnical boundary value problems. In-stead of using Hooke's single-stiffness model with linear elasticity in combination with an ideal plasticity according to Mohr-Coulomb a new constitutive formulation using a double-stiffness model for elasticity in combination with isotropic strain hardening is presented.Summarizing the existing double-stiffness models the most dominant type of model is the Cam-Clay model (Hashiguchi 1985, Hashiguchi 1993). To describe the non-linear stress-strain behav-iour of soils, beside the Cam-Clay model the pseudo-elastic (hypo-elastic) type of model has been developed. There an Hookean relationship is assumed between increments of stress and strain and non-linearity is achieved by means of varying Young's modulus. By far the best known model of this category ist the Duncan-Chang model, also known as the hyperbolic model (Duncan & Chang 1970). This model captures soil behaviour in a very tractable manner on the basis of only two stiff-ness parameters and is very much appreciated among consulting geotechnical engineers. The major inconsistency of this type of model which is the reason why it is not accepted by scientists is that, in contrast to the elasto-plastic type of model, a purely hypo-elastic model cannot consistently dis-tinguish between loading and unloading. In addition, the model is not suitable for collapse load computations in the fully plastic range.12These restrictions will be overcome by formulating a model in an elasto-plastic framework in this paper. Doing so the Hardening-Soil model, however, supersedes the Duncan-Chang model by far. Firstly by using the theory of plasticity rather than the theory of elasticity. Secondly by includ-ing soil dilatancy and thirdly by introducing a yield cap.In contrast to an elastic perfectly-plastic model, the yield surface of the Hardening Soil model is not fixed in principal stress space, but it can expand due to plastic straining. Distinction is made between two main types of hardening, namely shear hardening and compression hardening. Shear hardening is used to model irreversible strains due to primary deviatoric loading. Compression hardening is used to model irreversible plastic strains due to primary compression in oedometer loading and isotropic loading.For the sake of convenience, restriction is made in the following sections to triaxial loading conditions with 2σ′ = 3σ′ and 1σ′ being the effective major compressive stress.2 CONSTITUTIVE EQUATIONS FOR STANDARD DRAINED TRIAXIAL TESTA basic idea for the formulation of the Hardening-Soil model is the hyperbolic relationship be-tween the vertical strain ε1, and the deviatoric stress, q , in primary triaxial loading. When subjected to primary deviatoric loading, soil shows a decreasing stiffness and simultaneously irreversible plastic strains develop. In the special case of a drained triaxial test, the observed relationship be-tween the axial strain and the deviatoric stress can be well approximated by a hyperbola (Kondner& Zelasko 1963). Standard drained triaxial tests tend to yield curves that can be described by:The ultimate deviatoric stress, q f , and the quantity q a in Eq. 1 are defined as:The above relationship for q f is derived from the Mohr-Coulomb failure criterion, which involves the strength parameters c and ϕp . As soon as q = q f , the failure criterion is satisfied and perfectly plastic yielding occurs. The ratio between q f and q a is given by the failure ratio R f , which should obviously be smaller than 1. R f = 0.9 often is a suitable default setting. This hyperbolic relationship is plotted in Fig. 1.2.1 Stiffness for primary loadingThe stress strain behaviour for primary loading is highly nonlinear. The parameter E 50 is the con-fining stress dependent stiffness modulus for primary loading. E 50is used instead of the initial modulus E i for small strain which, as a tangent modulus, is more difficult to determine experimen-tally. It is given by the equation:ref E 50is a reference stiffness modulus corresponding to the reference stress ref p . The actual stiff-ness depends on the minor principal stress, 3σ′, which is the effective confining pressure in a tri-axial test. The amount of stress dependency is given by the power m . In order to simulate a loga-rithmic stress dependency, as observed for soft clays, the power should be taken equal to 1.0. As a3Figure 1. Hyperbolic stress-strain relation in primary loading for a standard drained triaxial test.secant modulus ref E 50 is determined from a triaxial stress-strain-curve for a mobilization of 50% ofthe maximum shear strength q f .2.2 Stiffness for un-/reloadingFor unloading and reloading stress paths, another stress-dependent stiffness modulus is used:where ref urE is the reference Young's modulus for unloading and reloading, corresponding to the reference pressure σ ref . Doing so the un-/reloading path is modeled as purely (non-linear) elastic.The elastic components of strain εe are calculated according to a Hookean type of elastic relation using Eqs. 4 + 5 and a constant value for the un-/reloading Poisson's ratio υur .For drained triaxial test stress paths with σ2 = σ3 = constant, the elastic Young's modulus E ur re-mains constant and the elastic strains are given by the equations:Here it should be realised that restriction is made to strains that develop during deviatoric loading,whilst the strains that develop during the very first stage of the test are not considered. For the first stage of isotropic compression (with consolidation), the Hardening-Soil model predicts fully elastic volume changes according to Hooke's law, but these strains are not included in Eq. 6.2.3 Yield surface, failure condition, hardening lawFor the triaxial case the two yield functions f 12 and f 13 are defined according to Eqs. 7 and 8. Here4Figure 2. Successive yield loci for various values of the hardening parameter γ p and failure surface.the measure of the plastic shear strain γ p according to Eq. 9 is used as the relevant parameter forthe frictional hardening:with the definitionIn reality, plastic volumetric strains p υε will never be precisely equal to zero, but for hard soils plastic volume changes tend to be small when compared with the axial strain, so that the approxi-mation in Eq. 9 will generally be accurate.For a given constant value of the hardening parameter, γ p , the yield condition f 12 = f 13 = 0 can be visualised in p'-q-plane by means of a yield locus. When plotting such yield loci, one has to use Eqs. 7 and 8 as well as Eqs. 3 and 4 for E 50 and E ur respectively. Because of the latter expressions,the shape of the yield loci depends on the exponent m . For m = 1.0 straight lines are obtained, but slightly curved yield loci correspond to lower values of the exponent. Fig. 2 shows the shape of successive yield loci for m = 0.5, being typical for hard soils. For increasing loading the failure sur-faces approach the linear failure condition according to Eq. 2.2.4 Flow rule, plastic potential functionsHaving presented a relationship for the plastic shear strain, γ p , attention is now focused on the plastic volumetric strain p υε. As for all plasticity models, the Hardening-Soil model involves a re-lationship between rates of plastic strain, i.e. a relationship between p υε and p γ . This flow rule hasthe linear form:5Clearly, further detail is needed by specifying the mobilized dilatancy angle m ψ. For the presentmodel, the expression:is adopted, where cv ϕ is the critical state friction angle, being a material constant independent ofdensity (Schanz & Vermeer 1996), and m ϕ is the mobilized friction angle:The above equations correspond to the well-known stress-dilatancy theory (Rowe 1962, Rowe 1971), as explained by (Schanz & Vermeer 1996). The essential property of the stress-dilatancy theory is that the material contracts for small stress ratios m ϕ < cv ϕ, whilst dilatancy occurs for high stress ratios m ϕ < cv ϕ. At failure, when the mobilized friction angle equals the failure angle,p ϕ, it is found from Eq. 11 that:Hence, the critical state angle can be computed from the failure angles p ϕand p ψ. The above defi-nition of the flow rule is equivalent to the definition of definition of the plastic potential functionsg 12 and g 13 according to:Using theKoiter-rule (Koiter 1960) for yielding depending on two yield surfaces (Multi-surface plasticity ) one finds:Calculating the different plastic strain rates by this equation, Eq. 10 directly follows.3 TIME INTEGRATIONThe model as described above has been implemented in the finite element code P LAXIS (Vermeer& Brinkgreve 1998). To do so, the model equations have to be written in incremental form. Due to this incremental formulation several assumptions and modifications have to be made, which will be explained in this section.During the global iteration process, the displacement increment follows from subsequent solu-tion of the global system of equations:where K is the global stiffness matrix in which we use the elastic Hooke's matrix D , f ext is a global load vector following from the external loads and f int is the global reaction vector following from the stresses. The stress at the end of an increment σ 1 can be calculated (for a given strain increment ∆ε) as:6whereσ0 , stress at the start of the increment,∆σ , resulting stress increment,4D , Hooke's elasticity matrix, based on the unloading-reloading stiffness,∆ε , strain increment (= B ∆u ),γ p , measure of the plastic shear strain, used as hardening parameter,∆Λ , increment of the non-negative multiplier,g , plastic potential function.The multiplier Λ has to be determined from the condition that the function f (σ1, γ p ) = 0 has to be zero for the new stress and deformation state.As during the increment of strain the stresses change, the stress dependant variables, like the elasticity matrix and the plastic potential function g , also change. The change in the stiffness during the increment is not very important as in many cases the deformations are dominated by plasticity.This is also the reason why a Hooke's matrix is used. We use the stiffness matrix 4D based on the stresses at the beginning of the step (Euler explicit ). In cases where the stress increment follows from elasticity alone, such as in unloading or reloading, we iterate on the average stiffness during the increment.The plastic potential function g also depends on the stresses and the mobilized dilation angle m ψ. The dilation angle for these derivatives is taken at the beginning of the step. The implementa-tion uses an implicit scheme for the derivatives of the plastic potential function g . The derivatives are taken at a predictor stress σtr , following from elasticity and the plastic deformation in the previ-ous iteration:The calculation of the stress increment can be performed in principal stress space. Therefore ini-tially the principal stresses and principal directions have to be calculated from the Cartesian stresses, based on the elastic prediction. To indicate this we use the subscripts 1, 2 and 3 and have 321σσσ≥≥ where compression is assumed to be positive.Principal plastic strain increments are now calculated and finally the Cartesian stresses have to be back-calculated from the resulting principal constitutive stresses. The calculation of the consti-tutive stresses can be written as:From this the deviatoric stress q (σ1 – σ3) and the asymptotic deviatoric stress q a can be expressed in the elastic prediction stresses and the multiplier ∆Λ:7whereFor these stresses the functionshould be zero. As the increment of the plastic shear strain ∆γ p also depends linearly on the multi-plier ∆Λ, the above formulae result in a (complicated) quadratic equation for the multiplier ∆Λwhich can be solved easily. Using the resulting value of ∆Λ, one can calculate (incremental)stresses and the (increment of the) plastic shear strain.In the above formulation it is assumed that there is a single yield function. In case of triaxial compression or triaxial extension states of stress there are two yield functions and two plastic po-tential functions. Following (Koiter 1960) one can write:where the subscripts indicate the principal stresses used for the yield and potential functions. At most two of the multipliers are positive. In case of triaxial compression we have σ2 = σ3, Λ23 = 0and we use two consistency conditions instead of one as above. The increment of the plastic shear strain has to be expressed in the multipliers. This again results in a quadratic equation in one of the multipliers.When the stresses are calculated one still has to check if the stress state violates the yield crite-rion q ≤ q f . When this happens the stresses have to be returned to the Mohr-Coulomb yield surface.4 ON THE CAP YIELD SURFACEShear yield surfaces as indicated in Fig. 2 do not explain the plastic volume strain that is measured in isotropic compression. A second type of yield surface must therefore be introduced to close the elastic region in the direction of the p-axis. Without such a cap type yield surface it would not be possible to formulate a model with independent input of both E 50 and E oed . The triaxial modulus largely controls the shear yield surface and the oedometer modulus controls the cap yield surface.In fact, ref E 50largely controls the magnitude of the plastic strains that are associated with the shear yield surface. Similarly, ref oedE is used to control the magnitude of plastic strains that originate from the yield cap. In this section the yield cap will be described in full detail. To this end we consider the definition of the cap yield surface (a = c cot ϕ):8where M is an auxiliary model parameter that relates to NC K 0 as will be discussed later. Further more we have p = (σ1 + σ2+ σ3) andwithq is a special stress measure for deviatoric stresses. In the special case of triaxial compression it yields q = (σ1 – σ3) and for triaxial extension reduces to q = α (σ1 –σ3). For yielding on the cap surface we use an associated flow rule with the definition of the plastic potential g c :The magnitude of the yield cap is determined by the isotropic pre-consolidation stress p c . For the case of isotropic compression the evolution ofp c can be related to the plastic volumetric strain rate p v ε:Here H is the hardening modulus according to Eq. 32, which expresses the relation between theelastic swelling modulus K s and the elasto-plastic compression modulus K c for isotropic compres-sion:From this definition follows a stress dependency of H . For the case of isotropic compression we haveq = 0 and therefor c p p=. For this reason we find Eq. 33 directly from Eq. 31:The plastic multiplier c Λ referring to the cap is determined according to Eq. 35 using the addi-tional consistency condition:Using Eqs. 33 and 35 we find the hardening law relating p c to the volumetric cap strain c v ε:9Figure 3. Representation of total yield contour of the Hardening-Soil model in principal stress space for co-hesionless soil.The volumetric cap strain is the plastic volumetric strain in isotropic compression. In addition to the well known constants m and σref there is another model constant H . Both H and M are cap pa-rameters, but they are not used as direct input parameters. Instead, we have relationships of theform NC K 0=NC K 0(..., M, H ) and ref oed E = ref oed E (..., M, H ), such that NC K 0and ref oed E can be used as in-put parameters that determine the magnitude of M and H respectively. The shape of the yield cap is an ellipse in p – q ~-plane. This ellipse has length p c + a on the p -axis and M (p c+ a ) on the q ~-axis.Hence, p c determines its magnitude and M its aspect ratio. High values of M lead to steep caps un-derneath the Mohr-Coulomb line, whereas small M -values define caps that are much more pointed around the p -axis.For understanding the yield surfaces in full detail, one should consider Fig. 3 which depicts yield surfaces in principal stress space. Both the shear locus and the yield cap have the hexagonal shape of the classical Mohr-Coulomb failure criterion. In fact, the shear yield locus can expand up to the ultimate Mohr-Coulomb failure surface. The cap yield surface expands as a function of the pre-consolidation stress p c .5 PARAMETERS OF THE HARDENING-SOIL MODELSome parameters of the present hardening model coincide with those of the classical non-hardening Mohr-Coulomb model. These are the failure parameters ϕp ,, c and ψp . Additionally we use the ba-sic parameters for the soil stiffness:ref E 50, secant stiffness in standard drained triaxial test,ref oedE , tangent stiffness for primary oedometer loading and m , power for stress-level dependency of stiffness.This set of parameters is completed by the following advanced parameters:ref urE , unloading/ reloading stiffness,10v ur , Poisson's ratio for unloading-reloading,p ref , reference stress for stiffnesses,NC K 0, K 0-value for normal consolidation andR f , failure ratio q f / q a .Experimental data on m , E 50 and E oed for granular soils is given in (Schanz & Vermeer 1998).5.1 Basic parameters for stiffnessThe advantage of the Hardening-Soil model over the Mohr-Coulomb model is not only the use of a hyperbolic stress-strain curve instead of a bi-linear curve, but also the control of stress level de-pendency. For real soils the different modules of stiffness depends on the stress level. With theHardening-Soil model a stiffness modulus ref E 50is defined for a reference minor principal stress of σ3 = σref . As some readers are familiar with the input of shear modules rather than the above stiff-ness modules, shear modules will now be discussed. Within Hooke's theory of elasticity conversion between E and G goes by the equation E = 2 (1 + v ) G . As E ur is a real elastic stiffness, one may thus write E ur = 2 (1 + v ur ) G ur , where G ur is an elastic shear modulus. In contrast to E ur , the secant modulus E 50 is not used within a concept of elasticity. As a consequence, there is no simple conver-sion from E 50 to G 50. In contrast to elasticity based models, the elasto-plastic Hardening-Soil model does not involve a fixed relationship between the (drained) triaxial stiffness E 50 and the oedometer stiffness E oed . Instead, these stiffnesses must be given independently. To define the oedometer stiff-ness we usewhere E oed is a tangent stiffness modulus for primary loading. Hence, ref oed E is a tangent stiffness ata vertical stress of σ1 = σref .5.2 Advanced parametersRealistic values of v ur are about 0.2. In contrast to the Mohr-Coulomb model, NC K 0 is not simply a function of Poisson's ratio, but a proper input parameter. As a default setting one can use the highly realistic correlation NC K 0= 1 – sin ϕp . However, one has the possibility to select different values.All possible different input values for NC K 0 cannot be accommodated for. Depending on other pa-rameters, such as E 50, E oed , E ur and v ur , there happens to be a lower bound on NC K 0. The reason for this situation will be explained in the next section.5.3 Dilatancy cut-offAfter extensive shearing, dilating materials arrive in a state of critical density where dilatancy has come to an end. This phenomenon of soil behaviour is included in the Hardening-Soil model by means of a dilatancy cut-off . In order to specify this behaviour, the initial void ratio, e 0, and the maximum void ratio, e cv , of the material are entered. As soon as the volume change results in a state of maximum void, the mobilized dilatancy angle, ψm , is automatically set back to zero, as in-dicated in Eq. 38 and Fig. 4:11Figure 4. Resulting strain curve for a standard drained triaxial test including dilatancy cut-off.The void ratio is related to the volumetric strain, εv by the relationship:where an increment of εv is negative for dilatancy. The initial void ratio, e 0, is the in-situ void ratio of the soil body. The maximum void ratio, e cv , is the void ratio of the material in a state of critical void (critical state).6 CALIBRATION OF THE MODELIn a first step the Hardening-Soil model was calibrated for a sand by back-calculating both triaxial compression and oedometer tests. Parameters for the loosely packed Hostun-sand (e 0 = 0.89), a well known granular soil in geotechnical research, are given in Tab. 1. Figs. 5 and 6 show the satis-fying comparison between the experimental (three different tests) and the numerical result. For the oedometer tests the numerical results consider the unloading loop at the maximum vertical load only.7 VERIFICATION OF THE MODEL7.1 Undrained behaviour of loose Hostun-sandIn order to verify the model in a first step two different triaxial compression tests on loose Hostun-sand under undrained conditions (Djedid 1986) were simulated using the identical parameter from the former calibration. The results of this comparison are displayed in Figs. 7 and 8.In Fig. 7 we can see that for two different confining pressures of σc = 300 and 600 kPa the stress paths in p-q-space coincide very well. For deviatoric loads of q ≈ 300 kPa excess porewater pres-sures tend to be overestimated by the calculations.Additionally in Fig. 8 the stress-strain-behaviour is compared in more detail. This diagram con-tains two different sets of curves. The first set (•, ♠) relates to the axial strain ε1 at the horizontal12Figure 5. Comparison between the numerical (•) and experimental results for the oedometer tests.Figure 6. Comparison between the numerical (•) and experimental results for the drained triaxial tests (σ3 = 300 kPa) on loose Hostun-sand.and the effective stress ratio 31/σσ′′ on the vertical (left) axis. The second set (o , a ) refers to the normalised excess pore water pressure ∆u /σc on the right vertical axis. Experimental results forboth confining stresses are marked by symbols, numerical results by straight and dotted lines.Analysing the amount of effective shear strength it can be seen that the maximum calculated stress ratio falls inside the range of values from the experiments. The variation of effective friction from both tests is from 33.8 to 35.4 degrees compared to an input value of 34 degrees. Axial stiff-ness for a range of vertical strain of ε1 < 0.05 seems to be slightly over-predicted by the model. Dif-ferences become more pronounced for the comparison of excess pore water pressure generation.Here the calculated maximum amount of ∆u is higher then the measured values. The rate of de-crease in ∆u for larger vertical strain falls in the range of the experimental data.Table 1. Parameters of loose Hostun-sand.v urm ϕp ψp ref ref s E E 50/ref ref ur E E 50/ref E 500.200.6534° 0° 0.8 3.0 20 MPa13Figure 7. Undrained behaviour of loose Hostun-sand: p-q-plane.Figure 8. Undrained behaviour of loose Hostun-sand: stress-strain relations.7.2 Pressuremeter test GrenobleThe second example to verify the Hardening-Soil model is a back-calculation of a pressuremeter test on loose Hostun-sand. This test is part of an experimental study using the calibration chamber at the IMG in Grenoble (Branque 1997). This experimental testing facility is shown in Fig. 9.The cylindrical calibration chamber has a height of 150 cm and a diameter of 120 cm. In the test considered in the following a vertical surcharge of 500 kPa is applied at the top of the soil mass by a membrane. Because of the radial deformation constraint the state of stress can be interpreted in this phase as under oedometer conditions. Inside the chamber a pressuremeter sonde of a radius r 0 of 2.75 cm and a length of 16 cm is placed. For the test considered in the following example there was loose Hostun-sand (D r ≈ 0.5) of a density according to the material parameters as shown in Tab. 1 placed around the pressuremeter by pluviation. After the installation of the device and the filling of the chamber the pressure is increased and the resulting volume change is registered.14Figure 9. Pressuremeter Grenoble .This experimental setup was modeled within a FE-simulation as shown in Fig. 10. On the left hand side the axis-symmetric mesh and its boundary conditions is displayed. The dimensions are those of the complete calibration chamber. In the left bottom corner of the geometry the mesh is finer because there the pressuremeter is modeled.In the first calculation phase the vertical surcharge load A is applied. At the same time the hori-zontal load B is increased the way practically no deformations occur at the free deformation bound-ary in the left bottom corner. In the second phase the load group A is kept constant and the load group B is increased according to the loading history in the experiment. The (horizontal) deforma-tions are analysed over the total height of the free boundary. In order to (partly) get rid of the de-formation constrains at the top of this boundary, marked point A in the detail on the right hand side of Fig. 10 two interfaces were placed crossing each other in point A . Fig. 11 shows the comparison of the experimental and numerical results for the test with a vertical surcharge of 500 kPa.On the vertical axis the pressure (relating to load group B ) is given and on the horizontal axis the volumetric deformation of the pressuremeter. Because the calculation was run taking into ac-count large deformations (updated mesh analysis ) the pressure p in the pressuremeter has to be cal-culated from load multiplier ΣLoad B according to Eq. 40, taking into account the mean radial de-formation ∆r of the free boundary:The agreement between the experimental and the numerical data is very good, both for the initial part of phase 2 and for larger deformations of up to 30%.。

量子力学英语词汇

1、microscopic world 微观世界2、macroscopic world 宏观世界3、quantum theory 量子[理]论4、quantum mechanics 量子力学5、wave mechanics 波动力学6、matrix mechanics 矩阵力学7、Planck constant 普朗克常数8、wave-particle duality 波粒二象性9、state 态10、state function 态函数11、state vector 态矢量12、superposition principle of state 态叠加原理13、orthogonal states 正交态14、antisymmetrical state 正交定理15、stationary state 对称态16、antisymmetrical state 反对称态17、stationary state 定态18、ground state 基态19、excited state 受激态20、binding state 束缚态21、unbound state 非束缚态22、degenerate state 简并态23、degenerate system 简并系24、non-deenerate state 非简并态25、non-degenerate system 非简并系26、de Broglie wave 德布罗意波27、wave function 波函数28、time-dependent wave function 含时波函数29、wave packet 波包30、probability 几率31、probability amplitude 几率幅32、probability density 几率密度33、quantum ensemble 量子系综34、wave equation 波动方程35、Schrodinger equation 薛定谔方程36、Potential well 势阱37、Potential barrien 势垒38、potential barrier penetration 势垒贯穿39、tunnel effect 隧道效应40、linear harmonic oscillator线性谐振子41、zero proint energy 零点能42、central field 辏力场43、Coulomb field 库仑场44、δ-function δ-函数45、operator 算符46、commuting operators 对易算符47、anticommuting operators 反对易算符48、complex conjugate operator 复共轭算符49、Hermitian conjugate operator 厄米共轭算符50、Hermitian operator 厄米算符51、momentum operator 动量算符52、energy operator 能量算符53、Hamiltonian operator 哈密顿算符54、angular momentum operator 角动量算符55、spin operator 自旋算符56、eigen value 本征值57、secular equation 久期方程58、observable 可观察量59、orthogonality 正交性60、completeness 完全性61、closure property 封闭性62、normalization 归一化63、orthonormalized functions 正交归一化函数64、quantum number 量子数65、principal quantum number 主量子数66、radial quantum number 径向量子数67、angular quantum number 角量子数68、magnetic quantum number 磁量子数69、uncertainty relation 测不准关系70、principle of complementarity 并协原理71、quantum Poisson bracket 量子泊松括号72、representation 表象73、coordinate representation 坐标表象74、momentum representation 动量表象75、energy representation 能量表象76、Schrodinger representation 薛定谔表象77、Heisenberg representation 海森伯表象78、interaction representation 相互作用表象79、occupation number representation 粒子数表象80、Dirac symbol 狄拉克符号81、ket vector 右矢量82、bra vector 左矢量83、basis vector 基矢量84、basis ket 基右矢85、basis bra 基左矢86、orthogonal kets 正交右矢87、orthogonal bras 正交左矢88、symmetrical kets 对称右矢89、antisymmetrical kets 反对称右矢90、Hilbert space 希耳伯空间91、perturbation theory 微扰理论92、stationary perturbation theory 定态微扰论93、time-dependent perturbation theory 含时微扰论94、Wentzel-Kramers-Brillouin method W. K. B.近似法95、elastic scattering 弹性散射96、inelastic scattering 非弹性散射97、scattering cross-section 散射截面98、partial wave method 分波法99、Born approximation 玻恩近似法100、centre-of-mass coordinates 质心坐标系101、laboratory coordinates 实验室坐标系102、transition 跃迁103、dipole transition 偶极子跃迁104、selection rule 选择定则105、spin 自旋106、electron spin 电子自旋107、spin quantum number 自旋量子数108、spin wave function 自旋波函数109、coupling 耦合110、vector-coupling coefficient 矢量耦合系数111、many-partic le system 多子体系112、exchange forece 交换力113、exchange energy 交换能114、Heitler-London approximation 海特勒-伦敦近似法115、Hartree-Fock equation 哈特里-福克方程116、self-consistent field 自洽场117、Thomas-Fermi equation 托马斯-费米方程118、second quantization 二次量子化119、identical particles全同粒子120、Pauli matrices 泡利矩阵121、Pauli equation 泡利方程122、Pauli’s exclusion principle泡利不相容原理123、Relativistic wave equation 相对论性波动方程124、Klein-Gordon equation 克莱因-戈登方程125、Dirac equation 狄拉克方程126、Dirac hole theory 狄拉克空穴理论127、negative energy state 负能态128、negative probability 负几率129、microscopic causality 微观因果性本征矢量eigenvector本征态eigenstate本征值eigenvalue本征值方程eigenvalue equation本征子空间eigensubspace (可以理解为本征矢空间)变分法variatinial method标量scalar算符operator表象representation表象变换transformation of representation表象理论theory of representation波函数wave function波恩近似Born approximation玻色子boson费米子fermion不确定关系uncertainty relation狄拉克方程Dirac equation狄拉克记号Dirac symbol定态stationary state定态微扰法time-independent perturbation定态薛定谔方程time-independent Schro(此处上面有两点)dinger equation 动量表象momentum representation角动量表象angular mommentum representation占有数表象occupation number representation坐标（位置）表象position representation角动量算符angular mommentum operator角动量耦合coupling of angular mommentum对称性symmetry对易关系commutator厄米算符hermitian operator厄米多项式Hermite polynomial分量component光的发射emission of light光的吸收absorption of light受激发射excited emission自发发射spontaneous emission轨道角动量orbital angular momentum自旋角动量spin angular momentum轨道磁矩orbital magnetic moment归一化normalization哈密顿hamiltonion黑体辐射black body radiation康普顿散射Compton scattering基矢basis vector基态ground state基右矢basis ket ‘右矢’ket基左矢basis bra简并度degenerancy精细结构fine structure径向方程radial equation久期方程secular equation量子化quantization矩阵matrix模module模方square of module内积inner product逆算符inverse operator欧拉角Eular angles泡利矩阵Pauli matrix平均值expectation value （期望值）泡利不相容原理Pauli exclusion principle氢原子hydrogen atom球鞋函数spherical harmonics全同粒子identical partic les塞曼效应Zeeman effect上升下降算符raising and lowering operator 消灭算符destruction operator产生算符creation operator矢量空间vector space守恒定律conservation law守恒量conservation quantity投影projection投影算符projection operator微扰法pertubation method希尔伯特空间Hilbert space线性算符linear operator线性无关linear independence谐振子harmonic oscillator选择定则selection rule幺正变换unitary transformation幺正算符unitary operator宇称parity跃迁transition运动方程equation of motion正交归一性orthonormalization正交性orthogonality转动rotation自旋磁矩spin magnetic monent(以上是量子力学中的主要英语词汇，有些未涉及到的可以自由组合。

Functions of Matrices-Theory and Computation(slides)

CHOL EIG FOR LONG PROD SAVE TRIU
CHOP ELSE FUN LU QR SCHU USER
CLEA END HESS MACR RAND SHOR WHAT
COND EPS HILB MAGI RANK SEMI WHIL
CONJ EXEC IF NORM RCON SIN WHO
11 / 45
Classic MATLAB
< M A T L A B > Version of 01/10/84 HELP is available <> help Type HELP followed by INTRO (To get started) NEWS (recent revisions) ABS ANS ATAN BASE CHAR DET DIAG DIAR DISP EDIT EXP EYE FILE FLOP FLPS INV KRON LINE LOAD LOG ORTH PINV PLOT POLY PRIN REAL RETU RREF ROOT ROUN SQRT STOP SUM SVD TRIL < > ( ) = . , ; \ / ’ + - * :
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Nick Higham
Functions of a Matrix
12 / 45
Classic MATLAB
<> help fun FUN For matrix arguments X , the functions SIN, COS, ATAN, SQRT, LOG, EXP and X**p are computed using eigenvalues D and eigenvectors V . If <V,D> = EIG(X) then f(X) = V*f(D)/V . This method may give inaccurate results if V is badly conditioned. Some idea of the accuracy can be obtained by comparing X**1 with X . For vector arguments, the function is applied to each component.

UPC功能说明书

Standard Features:•Advanced Linear Amplifiers Provide Very Low Voltage Distortion, no Switching Noise, Fast Voltage and Current Slew Rates, Exceptionally Low Output Impedance and High Peak Current Capability• 1, 2, or 3 Phase Output Form selectable from front panel or bus command•20 to 5,000 Hz. Full Power Bandwidth Operation – 5Hz to 50KHz small signal bandwidth, 3dB at 10% of full voltage• Precision Voltage Programming – 0.05% with Continuous Self-Calibration (CSC) engaged • True-RMS Metering of Volts, Amps, and Power • GPIB (IEEE-488.2) or RS-232 Interface • Waveform Library – Arbitrary Waveform Generator• Up to 99 Programs with Associated Transients for Static and Dynamic Test Applications •UPC Studio Software SuiteAvailable Options:• Programmable Output Impedance• Harmonic Analysis and Waveform Synthesis • Peak Inrush Capture and Waveform Analysis (Available on models with UPC3 controller)•UPC Test Manager SoftwareUPC Manager Software SuiteMaster the Power of the Wave!UPC Manager Software gives you the tools neces-sary to quickly and easily operate your AC Power Source. With our graphical interface control all areas of your AC Power Source testing with simple presets, user prompts, test sequences, test plans and custom reports.Model 312AMXFREQUENCY CONVERSION R & D MANUFACTURING AEROSPACE MILITARYCUSTOM1, 2, or 1,200VA 20-5,000 HzModel 312AMXAs a member of Pacific Power’s AMX-Series popular family of high performance Linear AC Power Sources, the 312AMX offers the same low output voltage noise and distortion, ease of installation, and high AC waveform fidelity as found in all of Pacific Power’s Linear AC Power Sources. Control and operational features provide a high degree of versatility and ease of use for applications ranging from simple,manually controlled frequency conversion to harmonic testing and sophisticated programmable transient simulation.AC TEST POWERAll 312AMX models are equipped with a powerful micro-controller with the ability to operate as a fully integrated test system. This enables a variety of power conditions and transients to be applied to the device under test while metering and analyzing all output performance parameters. For higher power requirements, refer to the AMX & ASX series catalog.FREQUENCY/ VOLTAGE CONVERSIONThe 312AMX is an excellent source of stable AC Voltage over the frequency range of 20 to 5,000 Hz when using the high-end UPC-32 controller. Also available in 1,200 Hz maximum output frequency when using UPC3 or Manual controller. The output frequency is quartz-crystal stabilized. Output voltages up to 300V L-L in split phase mode and 260V L-L in three phase mode are available on the 312AMX model.PHASE CONVERSIONWith the ability to provide either single or two phase output, the 312AMX is a good choice to convert one-phase line voltage into precisely controlled split (two-phase) or three-phase output power.UPC SERIES CONTROLLERThree controller models are available in both manual and programmable control version. All controllers provide manual operation from the front panel. Programmable Controllers may be operated from the front panel or from a remote interface via RS 232 or GPIB.The Leader in AC Power TechnologyAn early pioneer in the development solid-state power conversion equipment, Pacific Power Source continues to develop, manufacture, and market both linear and high-performance PWM AC Power Sources. Pacific Power Source’s reputation as a market and technology leader is best demonstrated by its continuing investments in both research and development and world-wide customer support. With corporate owned offices in the United States, France, the United Kingdom, and China, local personalized support is always available.1Ø42Ø43Ø40-150V L-N 0-300V L-L0-150V L-N / 0-260V L-LNOTES:1. Rated output power is based on a combination of nominal output voltage, rated current and load power factor. Values stated represent the maximum capabilities of a given model (maximum power in split phase (Form2) direct coupled mode is 800VA). Consult factory for assistance in determining specific unit capabilities as they might apply to your application.2. Unit is operable as single phase with dual range capability or 3 phase. Output voltage range and 1/2/3 conversions are selected by front panel or bus commands.3. Vmax is output voltage with nominal input and full rated load applied.4. Available current will vary with output voltage and power factor. Current shown is per phase.Output RatingsThermal and Power Factor Rating CurvesAMX Power Source Specifications (PF = 1.0, V out > 25% F.S.)Input Power Requirements (47-63 Hz)312AMXOutput Frequency Line Regulation Load Regulation Ripple and Noise OUTPUT VOLTAGE-AC VOLTS RMSShort term overloads to 150% are permitted. Operating time before thermal shutdown or circuit breaker trip varies from sec-onds to several minutes depending upon line and temperature conditions.THERMAL RATING -AC CURRENT RMSShort tem overloads to 150% of rated current are permitted.Operating time before thermal shutdown or circuit breaker trip varies from seconds to several minutes depending upon line and temperature conditions.Rated Continuous Load Current as a Function of Ambient Temperature and Power Factor and Output Voltage at Nominal Input Line.The UPC Controlleris a highly versatile one, two, or threephase oscillator/signal generator designed to control any ofPacific Power’s AC Power Sources. Three controller models,UPC-3M, UPC-3, or UPC-32 are offered. To use the full 5KHz power bandwidth of the 312AMX, the UPC-32 controller isrequired.Controller ModelsOutput Control SpecificationsTotal Control, Metering, and Analysis of AC Power- Simple, Intuitive OperationWaveform ControlExternal Inputs/OutputsOutput MeteringUsing the front panel keyboard and display , all controllermodels provide for selection of power source output mode, cou-pling, voltage, and frequency. Selecting the correct UPC controller for a given application varies with your test requirement, desired features, and price.Both the UPC-3 and UPC-32 Controllers are available witheither RS-232 or GPIB remote interface. Commands are structured in accordance with SCPI (Standard Commands for Programmable Instruments).© 2012 Pacific Power Source, Inc. Subject to change without notice. #DS312AMX101217692 Fitch, Irvine, CA 92614 USAPhone: +1 949.251.1800 Fax: +1 949.756.0756 T oll Free: 800.854.2433E-mail:**********************19" (483mm)Ordering InformationAvailable Models312AMX-UPC3M312AMX-UPC3312AMX-UPC32 General/EnvironmentalMechanical SpecificationsSoftware/Firmware OptionsProtection and SafetyOrder Example312AMX-UPC32, V IN : 120VAC • 1,200VA, 3-Phase, AC Power Source with UPC-32 programmable controller.• Standard GPIB Interface•120VAC, 1 Phase Input VoltageTypical Delivery Items• AC Power Source• English Manuals (AC Source and Controller)• UPC Studio Software - (Download)• UPC Interactive LabVIEW TM Libraries (Download)• Compliance Certificate with Test data •CE Conformity Document (CE Models)。

课程名称中英文对照参考表

外国文学作选读Selected Reading of Foreign Literature现代企业管理概论Introduction to Modern Enterprise Managerment电力电子技术课设计Power Electronics Technology Design计算机动画设计3D Animation Design中国革命史China’s Revolutionary History中国社会主义建设China Socialist Construction集散控制DCS Distributed Control计算机控制实现技术Computer Control Realization Technology计算机网络与通讯Computer Network and CommunicationERP/WEB应用开发Application ＆ Development of ERP/WEB数据仓库与挖掘Data Warehouse and Data Mining物流及供应链管理Substance and Supply Chain Management成功心理与潜能开发Success Psychology & Potential Development信息安全技术Technology of Information Security图像通信Image Communication金属材料及热加工Engineering Materials & Thermo-processing机械原理课程设计Course Design for Principles of Machine机械设计课程设计Course Design for Mechanical Design机电系统课程设计Course Design for Mechanical and Electrical System 创新成果Creative Achievements课外教育Extracurricular education。

基于磁共振脂肪定量技术IDEAL-IQ的列线图模型在预测早期骨量丢失中的价值

骨质疏松症是一种以骨量减少、骨密度减低，导致骨脆性增加、易发生骨折为特点的全身性疾病［1］。

一项以双能X 线吸收测量法（DXA ）测量骨密度（BMD ）的大样本流行病调查显示我国50岁以上人群中，男性和女性骨质疏松症患病率达6.46%和29.13%［2］，即目前我国现有男性骨质疏松症患者超过1000万，女性超过4000万。

骨质疏松性骨折是骨质疏松最严重的后果，好发于脊柱、髋部等，具有很高的致残率和致死率。

骨密度和骨质量则是反映骨强度的两个重要因素。

骨密度由骨内矿物质含量决定，DXA 测定骨密度是评估骨强度、也是诊断骨质疏松的金标准［1］。

但其测量的是面积密度，而非体积密度，并且受腰椎骨质增生、椎小关节退变及主动脉钙化的影响［3］。

研究表明BMDValue of a nomogram model based on IDEAL-IQ for predicting early bone mass lossCHENG Dongliang 1,FENG Hongmei 1,WEN Ge 2,LIU Jiangpin 1,HONG Julu 1,GAO Mingyong 11Department of Radiology,First People's Hospital of Foshan,Foshan 528000,China;2Medical Imaging Center,Nanfang Hospital,Southern Medical University,Guangzhou 510515,China摘要：目的探讨基于MRI 迭代最小二乘法水脂分离定量技术（IDEAL-IQ ）序列的列线图模型在预测早期骨量丢失中的诊断效能。

方法收集同时行双能X 线骨密度仪（DXA ）测定和腰椎MRI IDEAL-IQ 序列检查的被试59例，应用DXA 分别测定L1~4椎体的骨密度值，利用IDEAL-IQ 序列中FF 图测量相应的FF 值。

Two-dimensional Quantum Field Theory, examples and applications

Abstract The main principles of two-dimensional quantum ﬁeld theories, in particular two-dimensional QCD and gravity are reviewed. We study non-perturbative aspects of these theories which make them particularly valuable for testing ideas of four-dimensional quantum ﬁeld theory. The dynamics of conﬁnement and theta vacuum are explained by using the non-perturbative methods developed in two dimensions. We describe in detail how the eﬀective action of string theory in non-critical dimensions can be represented by Liouville gravity. By comparing the helicity amplitudes in four-dimensional QCD to those of integrable self-dual Yang-Mills theory, we extract a four dimensional version of two dimensional integrability.
2 48 49 52 54 56
5 Four-dimensional analogies and consequences 6 Conclusions and Final Remarks

Lorentz Model

Propagating Field - Exponential Form
• Interaction of light with plasmas is better analyzed by switching to exponentials with Euler identity
eiθ = cos(θ ) + i sin (θ ) Re eiθ = cos(θ )
v=
1
εµ
ε r ε 0 µ r µ0
=
ε r µr
c = ε 0 µ0 n
1
• Many optical materials are non-magnetic: µr=1, n = ε r • In optics, it is traditional to drop the “r” subscript and assume relative values are used (also in notes, hereafter) • Typical values: gold: ε = -24.9 + 1.57i; glass (pyrex): ε = 5
− iω [t − n ( w ) z c ] ˆ E( z , t ) = Re εE0e 1/ 2 ω 2 −ω 2 z i p c − iωt ˆ = Re εE0e e
[ ]
• Propagating E-field
• In optics, it is traditional to use relative values of permittivity and permeability. In physics, would write
ε = εr ε0

Gap-anisotropic model for the narrow-gap Kondo insulators

a r X i v :c o n d -m a t /9807003v 2 [c o n d -m a t .s t r -e l ] 29 S e p 1999Gap-anisotropic model for the narrow-gap Kondo insulatorsJuana Moreno 1and P.Coleman 21Dept of Physics &Astronomy,Northwestern Univ,2145Sheridan Rd,Evanston IL 60208,2Center for Materials Theory,Department of Physics and Astronomy,Rutgers University,Piscataway,NJ 08854,USA.(February 1,2008)A theory is presented which accounts for the dynamical generation of a hybridization gap with nodes in the Kondo insulating materials CeNiSn and CeRhSb .We show that Hunds interactions acting on virtual 4f 2conﬁgurations of the cerium ion can act to dynamically select the shape of the cerium ion by generating a Weiss ﬁeld which couples to the shape of the ion.In low symmetry crystals where the external crystal ﬁelds are negligible,this process selects a nodal Kondo semimetal state as the lowest energy conﬁguration.Pacs numbers:Kondo insulators share in common with the Mott insu-lators a gap which is driven by interaction eﬀects.1,2Un-like Mott insulators,they undergo a smooth cross-over into the insulating state,where a tiny charge and spin gap develops.These materials are generally regarded as a special class of heavy fermion system,where a lattice Kondo eﬀect between the localized spins and conduction electrons forms a highly renormalized band-insulator.3,4The smallest gap Kondo insulators,CeNiSn and CeRhSb ,do not naturally ﬁt into this scheme:they appear to develop gapless excitations.Early measure-ments showed a drastic increase of the electrical resistiv-ity below 6K ,5but very pure samples of CeNiSn display metallic behavior.6NMR measurements are consistent with an electronic state with a “v-shaped”component to the density of states.7These results,together with other transport properties 8–11point to the formation of a new kind of semi-metal with an anisotropic hybridization gap.Ikeda and Miyake 12(IM)recently proposed that the Kondo insulating ground-state of these materials devel-ops in a crystal ﬁeld state with an axially symmetric hy-bridization potential that vanishes along a single crystal axis.This picture accounts for the v-shaped density of states,and provides an appealing way to understand the anisotropic transport at low temperatures,but it leaves a number of puzzling questions.In CeNiSn and CeRhSb ,the Cerium ions are located at sites of minimal mono-clinic symmetry,where the low-lying f-state is a Kramers doublet|± =b 1|±1/2 +b 2|±5/2 +b 3|∓3/2(1)where ˆb =(b 1,b 2,b 3)could point anywhere on the unit sphere,depending on details of the monoclinic crystal ﬁeld.The IM model corresponds to three symmetry-related points in the space of crystal ﬁeld ground states,ˆb =(∓√4,−√4,32k ,σe −i k ·R j Y σaα(ˆk )c †k σ(6)1creates a conduction electron in a l=3,j=5/2Wannier state at site j with shape-spin quantum numbers(a,σ), N s is the number of sites andYσaα(ˆk)=Y m J−σ3(ˆk)(12m J)(7)deﬁnes the form-factors,in terms of spherical harmon-ics and the Clebsh-Gordon coeﬃcients of the j=5/2f1-state16,where m J≡m J(a,α)maps the spin-shape quantum numbers to to the original azimuthal quantumnumber of the f-scattering channel.Following previous authors,17we regard H as a low energy Hamiltonian,so that hybridization strength V is a renormalized quantity, that takes into account the high energy valence and spin ﬂuctuations.The termH f= j E f n f(j)+U2Γ2j (8)describes the residual low-energy interactions amongst the f-electrons:the second term is a Coulomb interac-tion term.The third term is a Hunds interaction which favors4f2states with maximal total angular momentum. In an isotropic environment,this interaction would take the form−g2Γ2.In general the Hund’s interaction is only invari-ant under discrete rotations so thatﬂuctuations into the f2state enable the system to sample the crystal symme-try even when the conventional crystalﬁeld splittings are absent.Suppose the crystal electricﬁeld term were un-quenched,so that H→H− α·Γj.The shape of the Cerium ion Γj =Γis determined by the condition that the energy is stationary with respect to variations inΓ,N−1sδ H o /δΓ=α+gΓ.(9) The second term is a feedback or“Weiss”contribution to the crystalline electricﬁeld,created byﬂuctuations into the4f2state.Generally,the inducedﬁeldΓwill follow the crystalline electricﬁeldsα,but in situations where the valence and spinﬂuctuations are rapid enough to quench the external crystal electricﬁeld,13thenα=0, and the Weissﬁeld becomes free to explore phase space to minimize the total energy.In such a situation,the shape of the Cerium ion is determined by the interac-tions,rather than the local conditions around each ion. To explore this process,we carry out a Hubbard-Stratonovich decoupling of the interactions,H f(j)→f†j (E f+λj)1 f j+E o[λj,∆j](10) whereE o[λj,∆j]= ∆2j2U−λj ,(11)Here∆a(j)∼−gΓa(j)is a dynamical Weissﬁeld,f j denotes the spinor f j≡f aσ(j).Note that in the path integral,theﬂuctuating part ofλj,associated with the suppression of chargeﬂuctuations,is imaginary.We now seek a mean-ﬁeld solution where the Weissﬁeldλj=λand∆j=∆,and E(λj,∆j)=E o.Such an expectation value does not break the crystal symmetry.However,the selected crystalﬁeld matrix∆·Λmust adjust to minimize the total energy.Supposing we diagonalize this matrix, writing∆·ΛU†,where∆o˜fj→b a[c†aσ(j)˜fσ(j)],(12) where˜fσ(j)≡˜f3σ(dropping the superﬂuous index“3”) describes the lowest Kramers doublet and b a≡U a3.To satisfy the constraint n f =1,the energy of the lowest Kramers doublet must be zero,i.e.E f+λ+∆3=0.We then arrive at the mean-ﬁeld HamiltonianH∗=H c+V k[φσα(k)c†kσfαk+H.c]+N s E o(13)whereφσα(k)= a b a Yσaα(ˆk)is the dynamically gener-ated form-factor of the hybridization.16The transformed hybridization is no longer rotationally invariant:all infor-mation about the anisotropic wavefunction of the Cerium ion is now encoded in the vectorˆb.The quasiparticle energies associated with this Hamil-tonian areE±k=ǫk/2±(ǫk/2)2+V2ˆk+N s E o(15)Now bothλand∆3areﬁxed independently of the direc-tion ofˆb,so that E o does not depend onˆb.To see this, write the eigenvalues of the traceless crystalﬁeld matrix as∆1,2=16∆±δ,∆3=−26∆.Since the upper two crystalﬁeld states are empty,stationarity w.r.t toδre-quiresδ=0.Since∆3couples directly to the f-charge, we obtain∂E g/∂∆=− 3 n f +(∆/g)=0,so that ∆= 2g.Thus bothλ=−∆3−E f and∆in mean-ﬁeld theory as a function of the twoﬁrst components of the unit vectorˆb(the third one is taken as positive).The darkest regions correspond to lowest values of the free-energy. Arrows point to the three global and three local minima. independently ofˆb.The selection of the crystalﬁeld con-ﬁguration is thus entirely determined by minimizing the kinetic energy of the electrons.To examine the depen-dence of the mean-ﬁeld onˆb,we replace the momentum sum in(15)by an energy and angular integral,k{...}→N(0) D−D dǫdΩˆkeD2]+F[ˆb] (17) whereF[ˆb]= dΩˆk5/4,√2T ∞−∞dωω2−∂fΓ(ω) V i V j ω,(19)where f is the Fermi function,Γ(ω)is the quasiparticlescattering rate andN(ω) V i V j ω= k V i k V j kδ(ω− E k)(20)describes the quasiparticle velocity distribution whereV k= ∇ k E k and E k is given by equation(14).For ourcalculation,we have considered quasiparticle scatteringoﬀa small,butﬁnite density of unitarilly scattering im-purities or“Kondo holes”.21We use a self-consistent T-matrix approximation,following the lines of earlier cal-culations except for one key diﬀerence.In these calcu-lations,which depend critically on the anisotropy,it isessential to include the momentum dependence of thehybridization potential in the evaluation of the quasipar-ticle current.Previous calculations12underestimated theanisotropy by neglecting these contributions.20The single node in the IM state leads to a pronouncedenhancement of the low-temperature thermal conductiv-ity along the nodalˆz axis.By contrast,in the quasi-octahedral state the distribution of minima in the gapgive rise to a modest enhancement of the thermal conduc-tivity in the basal plane.Experimental measurements19tend to favor the latter scenario,showing an enhancementin thermal conductivity that is much more pronouncedinκx than inκz orκy.Three aspects of our theory deserve more extensive ex-amination.Nodal gap formation is apparently uniqueto CeNiSn and CeRhSb;the other Kondo insulatorsSmB6,Ce3Bi4P t3and Y bB12display a well-formed gap.Curiously,these materials are cubic,leading us to specu-late that their higher symmetry prevents the dynamicallygenerated contribution to the crystalﬁeld from exploring 30.000.010.020.03T/D0.00.51.01.52.0(κ(T )/κN (D ))(D /T )−0.0250.0000.025ω/D204060N (ω)/N 00.000.010.020.03T/D0.00.20.40.60.81.01.2(κ(T )/κN (D ))(D /T )−0.0250.0000.025ω/D2040N (ω)/N 0FIG.2.Normalized thermal conductivity versus tempera-ture along the z-axis (solid line)and in the basal plane (dashed line).Top:for the Ikeda-Miyake state.Bottom:for the quasi-octahedral scenario.Insets show density of states as a function of the energy.The adjustable parameters have been chosen as V /D =0.08and an impurity scattering phase-shift of π/2.the region of parameter space where a node can develop.At present,we have not included the eﬀect of a mag-netic ﬁeld,which is known to suppress the gap nodes.6There appears to be the interesting possibility that an applied ﬁeld will actually modify the dynamically gener-ated crystal ﬁeld to eliminate the nodes.Finally,we note that since the spin-ﬂuctuation spectrum will reﬂect the nodal structure,future neutron scattering experiments 22should in principle be able to resolve the axial or octahe-dral symmetry of the low energy excitations.To conclude,we have proposed a mechanism for the dynamical generation of a hybridization gap with nodes in the Kondo insulating materials CeNiSn and CeRhSb .We have found that Hunds interactions acting on the virtual 4f 2conﬁgurations of the Cerium ions generatea Weiss ﬁeld which acts to co-operatively select a semi-metal with nodal anisotropy.Our theory predicts two stable states,one axial ,the other quasi-octahedral in symmetry.The quasi octahedral solution appears to be the most promising candidate explanation of the vari-ous transport and thermal properties of the narrow-gap Kondo insulators.We are grateful to Gabriel Aeppli,Frithjof Anders,Yoshio Kitaoka,Toshiro Takabatake and Adolfo Trumper for enlightened discussions.This research was partially supported by NSF grant DMR 96-14999and DMR 91-20000through the Science and Technology Center for Superconductivity.JM acknowledges also support by the Abdus Salam ICTP.。

swiss-model

Swiss-ModelSwiss-Model is a protein structure homology-modeling tool that helps in predicting protein structures using a template-based approach. It aims to create accurate three-dimensional models of protein structures by comparing target sequences to a library of experimentally solved structures.Introduction to Swiss-ModelSwiss-Model is a well-known platform that offers automated protein structure homology modeling. It is widely used in the scientific community for studying protein structures and their functions. Homology modeling is an effective technique for predicting the three-dimensional structure of a protein based on its sequence similarity to proteins with experimentally determined structures.The Swiss-Model platform integrates several software tools and algorithms to accurately generate protein models. It utilizes the UniProt database, which contains a vast collection of protein sequences and their annotations, as well as the Swiss-Prot database, which provides high-quality and manually curated protein sequences.Workflow of Swiss-ModelSwiss-Model follows a well-defined workflow to predict protein structures:1.Target identification: The first step is to identify the target proteinfor which the structure is to be predicted. The user provides the sequence ofthe target protein to Swiss-Model.2.Template selection: Swiss-Model searches its extensive library ofexperimentally determined protein structures to identify potential templates that share sequence similarity with the target protein.3.Alignment: The target protein sequence is aligned with the selectedtemplate sequence to establish the correspondence between equivalentresidues.4.Model building: Using the alignment information, Swiss-Model buildsa three-dimensional model of the target protein by borrowing information fromthe selected template. The model-building step involves optimizing thegeometry and stereochemistry of the model.5.Model quality assessment: Swiss-Model assesses the quality of thegenerated structure and provides a variety of statistical measures to evaluate its accuracy and reliability. This helps researchers to assess the suitability ofthe model for further analysis.6.Model visualization and analysis: The final step involves thevisualization and analysis of the generated protein model. Swiss-Modelprovides various tools and features to explore the structural details and thepotential functional sites of the protein.Features of Swiss-ModelSwiss-Model offers several features and advantages:•Ease of use: Swiss-Model has a user-friendly interface that simplifies the process of protein structure homology modeling.•Template library: It has an extensive database of experimentally determined protein structures that serve as templates for modeling. Thisincreases the accuracy of the predicted structures.•Automated workflow: Swiss-Model follows an automated workflow, reducing the manual effort required for modeling and saving time.•Model quality assessment: The platform provides an assessment of the generated structures, allowing users to evaluate their reliability andaccuracy.•Integration of databases: Swiss-Model is integrated with the UniProt and Swiss-Prot databases, enabling easy access to protein sequences andannotations.Applications of Swiss-ModelSwiss-Model has numerous applications in the field of bioinformatics and protein structure prediction:1.Structure-function relationship: Swiss-Model helps inunderstanding the relationship between protein sequence, structure, andfunction. By predicting the structure of a protein, researchers can gain insights into its potential functions.2.Drug discovery: Accurate protein structure prediction is crucial fordrug discovery. Swiss-Model aids in the identification of potential drug targets and the design of drugs that can target specific protein structures.3.Structural biology: Swiss-Model plays a significant role in structuralbiology, allowing researchers to study the three-dimensional arrangement of proteins and their interactions with other molecules.4.Protein engineering: Protein engineering involves modifying ordesigning proteins with desired properties. Swiss-Model assists in the rational design of protein variants by providing accurate protein structures as a starting point.ConclusionSwiss-Model is a powerful tool for protein structure homology modeling. Its automated workflow, extensive template library, and model quality assessment features make it a popular choice among researchers in the field of bioinformaticsand structural biology. By predicting protein structures, Swiss-Model aids in understanding protein function, drug discovery, and protein engineering.。

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and the top quark mass is nearly equal to the vacuum expectation value (VEV) of the standard model Higgs boson. Quark masses and mixings arise when quark mass matrices are diagonalized
the U (1) symmetry, where we have M22 ∼ (M23 )2 (see for example Ref. [7]). Mixings come out mainly from the down sector, where the hierarchy is less pronounced. Now we have to consider lepton masses and mixings. In uniﬁed theories, such as the SO (10) model, the charged lepton mass matrix Me is related to Md and the Dirac neutrino mass matrix Mν is related to Mu , Me ∼ Mν ∼ mτ Md , mb mτ Mu , mb (10)
ቤተ መጻሕፍቲ ባይዱ
(2)
(3)
where λ = 0.22 is the sine of the Cabibbo angle, and from Eqn.(3) we see that quark mixings are small. Moreover, the hierarchy of charged lepton masses is similar to that of down quark masses, me mµ ∼ ∼ λ2 . mµ mτ For the masses of the third generation we have mt ≫ mb ∼ mτ , 2 (5) (4)
3
(6)

√

(7)
By using Eqns.(1),(2) we get these mass matrices in terms of powers of λ and an

6

(8)

(9)
This structure for Mu and Md strongly suggests the presence of a broken U (2) horizontal symmetry [6], if we consider the zeros as approximate. In particular, for symmetric forms, the similarity M22 ∼ M23 favours the U (2) symmetry, rather than 3
(11)
where the factor mτ /mb takes into account approximate running of quark masses with respect to lepton masses, and mb ≃ mτ at the uniﬁcation scale in the supersymmetric case [8]. This is called quark-lepton symmetry. Moreover, the seesaw mechanism [9] holds, according to the formula
Several phenomenological features of fermion masses and mixings can be accounted for by a simple model for fermion mass matrices, which suggests an underlying U(2) horizontal symmetry. In this context, it is also proposed how an approximate quark-lepton symmetry can be achieved without uniﬁed gauge theories.
DSF-17/2001
MODEL FOR FERMION MASS MATRICES AND
arXiv:hep-ph/0106286v2 29 Jun 2001
THE ORIGIN OF QUARK-LEPTON SYMMETRY
D. Falcone
Dipartimento di Scienze Fisiche, Universit` a di Napoli, Complesso di Monte S. Angelo, Via Cintia, Napoli, Italy e-mail: falcone@na.infn.it
† † by means of biunitary transformations VuL Mu VuR = Du , VdL Md VdR = Dd . The
Cabibbo-Kobayashi-Maskawa (CKM) quark mixing matrix [4] is given by the for† mula VCKM = VuL VdL . In recent papers [5] a parallel structure for up and down
the running of quark mixings, which is not relevant for our analysis. In fact, also the running of quark masses is unimportant. However, we keep the factor mτ /mb to remember the presence of the running eﬀect, which is responsible for the mass diﬀerence between mb and mτ at the low scale. Quark-lepton symmetry is due to the SU (4) × SU (2) × SU (2) subgroup of SO (10) and in particular to the SU (4) component, which includes lepton number as fourth color [11]. In the SU (5) model, only relation (10) is achieved. 4
quark mass matrices has been obtained, √ 0 mu mc 0 √ √ Mu ≃ m m m m m u c c u t , √ mu mt mt 0 0 md ms 0 √ √ Md ≃ m m m m m d s s d b . √ md mb mb 0 overall mass scale, 0 λ 0 6 4 4 Mu ∼ λ λ λ mt , 4 0 λ 1 0 λ 0 3 2 2 m . Md ∼ λ λ λ b 2 0 λ 1
1
Understanding the pattern of fermion masses and mixings is a key subject in modern particle physics. Many approaches have been followed [1]. For example, discrete and continuous as well as abelian and nonabelian horizontal symmetries have been often used. Moreover, uniﬁed gauge theories, which are based on vertical symmetries, generally predict relations between quark and lepton masses [2]. Horizontal symmetries relate particles of diﬀerent generations, while vertical symmetries relate particles of the same generation. Even the SU (3) × SU (2) × U (1) symmetries of the standard model or the SU (3) × SU (2) × SU (2) × U (1) symmetries of the left-right model are vertical. In this paper we show that several phenomenological issues, among which quark-lepton symmetry, seesaw mechanism and large neutrino mixing, lead to a simple model for quark and lepton mass matrices, suggesting an underlying broken U (2) horizontal symmetry [3]. Speculations on the origin of quark-lepton symmetry, not relying on uniﬁed models, and hence not leading to proton instability, are also presented. It is well known that quark masses and mixings exhibit a hierarchical pattern, mu mc ∼ ∼ λ4 , mc mt md ms ∼ ∼ λ2 , ms mb Vus ∼ λ, Vcb ∼ λ2 , Vub ∼ λ4 , (1)