Microscopic Derivation of Ginzburg-Landau Theory
Frank, Rupert; Hainzl, Christian; Seiringer, Robert
2012-01-01
We give the first rigorous derivation of the celebrated Ginzburg-Landau (GL) theory, starting from the microscopic Bardeen-Cooper-Schrieffer (BCS) model. Close to the critical temperature, GL arises as an effective theory on the macroscopic scale. The relevant scaling limit is semiclassical...
Microscopic Derivation of Ginzburg-Landau Theory
Frank, Rupert; Hainzl, Christian; Seiringer, Robert
2012-01-01
We give the first rigorous derivation of the celebrated Ginzburg-Landau (GL) theory, starting from the microscopic Bardeen-Cooper-Schrieffer (BCS) model. Close to the critical temperature, GL arises as an effective theory on the macroscopic scale. The relevant scaling limit is semiclassical...
Ginzburg-Landau theory of noncentrosymmetric superconductors
Mukherjee, Soumya P.; Mandal, Sudhansu S.
2007-01-01
The data of temperature dependent superfluid density $n_s(T)$ in Li$_2$Pd$_3$B and Li$_2$Pt$_3$B [Yuan {\\it et al.}, \\phrl97, 017006 (2006)] show that a sudden change of the slope of $n_s (T)$ occur at slightly lower than the critical temperature. Motivated by this observation, we microscopically derive the Ginzburg-Landau (GL) equations for noncentrosymmetric superconductors with Rashba type spin orbit interaction. Cooper pairing is assumed to occur between electrons only in the same spin sp...
Ginzburg-Landau theory of a holographic superconductor
Yin, Lei; Hou, Defu; Ren, Hai-cang
2015-01-01
The general Ginzburg-Landau (GL) formulation of a holographic superconductor is developed near the transition temperature in the probe limit for two kinds of conformal dimension. elow the transition temperature, T grand canonical ensemble and the canonical ensemble are derived and the gradient term is studied. Furthermore this scaling coefficient of the order parameter takes different values in the grand canonical ensemble and the canonical ensemble, suggesting the strong coupling nature of the boundary field theory of the superconductivity.
Solution Theory of Ginzburg-Landau Theory on BCS-BEC Crossover
Shuhong Chen
2014-01-01
Full Text Available We establish strong solution theory of time-dependent Ginzburg-Landau (TDGL systems on BCS-BEC crossover. By the properties of Besov, Sobolev spaces, and Fourier functions and the method of bootstrapping argument, we deduce that the global existence of strong solutions to time-dependent Ginzburg-Landau systems on BCS-BEC crossover in various spatial dimensions.
Size effects in the Ginzburg-Landau theory
Fiolhais, Miguel C. N.; Birman, Joseph L.
2015-02-01
The Ginzburg-Landau theory is analyzed in the case of small dimension superconductors, a couple of orders of magnitude above the coherence length, where the theory is still valid but quantum fluctuations become significant. In this regime, the potential around the expectation value is approximated to a quadratic behavior, and the ground-state is derived from the Klein-Gordon solutions of the Higgs-like field. The ground-state energy is directly compared to the condensation energy, and used to extract new limits on the size of superconductors at zero Kelvin and near the critical temperature.
The Ginzburg-Landau Theory of a Holographic Superconductor
Yin, Lei; Ren, Hai-cang
2013-01-01
The Ginzburg-Landau formulation of a holographic superconductor is derived near the transition temperature in the probe limit. Below the transition temperature, $T
Self-consistent Ginzburg-Landau theory for transport currents in superconductors
Ögren, Magnus; Sørensen, Mads Peter; Pedersen, Niels Falsig
2012-01-01
We elaborate on boundary conditions for Ginzburg-Landau (GL) theory in the case of external currents. We implement a self-consistent theory within the finite element method (FEM) and present numerical results for a two-dimensional rectangular geometry. We emphasize that our approach can in princi......We elaborate on boundary conditions for Ginzburg-Landau (GL) theory in the case of external currents. We implement a self-consistent theory within the finite element method (FEM) and present numerical results for a two-dimensional rectangular geometry. We emphasize that our approach can...
Ginzburg-Landau theory of dirty two band s(+/-) superconductors.
Ng, Tai-Kai
2009-12-04
In this Letter, we study the effect of nonmagnetic impurities on two-band superconductors by deriving the corresponding Ginzburg-Landau equation. Depending on the strength of (impurity-induced) interband scattering, we find that there are two distinctive regions where the superconductors behave very differently. In the strong impurity-induced interband scattering regime T(c) band, the two-band superconductor behaves as an effective one-band dirty superconductor. In the other limit T(c) > or = tau(t)(-1), the dirty two-band superconductor is described by a network of frustrated two-band superconductor grains connected by Josephson tunneling junctions, and the Anderson theorem breaks down.
An introduction to the Ginzburg-Landau theory of phase transitions and nonequilibrium patterns
Hohenberg, P. C.; Krekhov, A. P.
2015-04-01
This paper presents an introduction to phase transitions and critical phenomena on the one hand, and nonequilibrium patterns on the other, using the Ginzburg-Landau theory as a unified language. In the first part, mean-field theory is presented, for both statics and dynamics, and its validity tested self-consistently. As is well known, the mean-field approximation breaks down below four spatial dimensions, where it can be replaced by a scaling phenomenology. The Ginzburg-Landau formalism can then be used to justify the phenomenological theory using the renormalization group, which elucidates the physical and mathematical mechanism for universality. In the second part of the paper it is shown how near pattern forming linear instabilities of dynamical systems, a formally similar Ginzburg-Landau theory can be derived for nonequilibrium macroscopic phenomena. The real and complex Ginzburg-Landau equations thus obtained yield nontrivial solutions of the original dynamical system, valid near the linear instability. Examples of such solutions are plane waves, defects such as dislocations or spirals, and states of temporal or spatiotemporal (extensive) chaos.
Why magnesium diboride is not described by anisotropic Ginzburg-Landau theory
Koshelev, A.E.; Golubov, Alexandre Avraamovitch
2004-01-01
It is well established that the superconductivity in the recently discovered superconducting compound MgB2 resides in the quasi-two-dimensional band (sigma band) and three-dimensional band (pi band). We demonstrate that, due to such band structure, the anisotropic Ginzburg-Landau theory practically
Derivation of Ginzburg-Landau theory for a one-dimensional system with contact interaction
Frank, Rupert; Hanizl, Christian; Seiringer, Robert
2013-01-01
In a recent paper we give the first rigorous derivation of the celebrated Ginzburg-Landau (GL) theory, starting from the microscopic Bardeen-Cooper-Schrieffer (BCS) model. Here we present our results in the simplified case of a one-dimensional system of particles interacting via a delta-potential....
Ginzburg-Landau theory of the superheating field anisotropy of layered superconductors
Liarte, Danilo B.; Transtrum, Mark K.; Sethna, James P.
2016-10-01
We investigate the effects of material anisotropy on the superheating field of layered superconductors. We provide an intuitive argument both for the existence of a superheating field, and its dependence on anisotropy, for κ =λ /ξ (the ratio of magnetic to superconducting healing lengths) both large and small. On the one hand, the combination of our estimates with published results using a two-gap model for MgB2 suggests high anisotropy of the superheating field near zero temperature. On the other hand, within Ginzburg-Landau theory for a single gap, we see that the superheating field shows significant anisotropy only when the crystal anisotropy is large and the Ginzburg-Landau parameter κ is small. We then conclude that only small anisotropies in the superheating field are expected for typical unconventional superconductors near the critical temperature. Using a generalized form of Ginzburg Landau theory, we do a quantitative calculation for the anisotropic superheating field by mapping the problem to the isotropic case, and present a phase diagram in terms of anisotropy and κ , showing type I, type II, or mixed behavior (within Ginzburg-Landau theory), and regions where each asymptotic solution is expected. We estimate anisotropies for a number of different materials, and discuss the importance of these results for radio-frequency cavities for particle accelerators.
Inner Structure of Statistical Gauge Potential in Chern-Simons-Ginzburg-Landau Theory
无
2005-01-01
Based on the decomposition theory of the U(1) gauge potential, the inner structure of the statistical gauge potential in the Chern-Simons-Ginzburg-Landau (CSGL) theory is studied. We give a new creation mechanism of the statistical gauge potential. Furthermore, making use of the φ-mapping topological current theory, we obtain the precise topological expression of the statistical magnetic field, which takes the topological information of the vortices.
Madhuparna Karmakar
2011-01-01
Full Text Available The electrostatic potential and the associated charge distribution in the vortices of high- superconductors involving mixed symmetry state of the order parameters have been studied. The work is carried out in the framework of an extended Ginzburg-Landau (GL theory involving the Gorter-Casimir two-fluid model and Bardeen's extension of GL theory applied to the high- superconductors. The properties are calculated using the material parameters relevant for the high- cuprate YBCO.
Multi-Component Ginzburg-Landau Theory: Microscopic Derivation and Examples
Frank, Rupert L.; Lemm, Marius
2016-09-01
This paper consists of three parts. In part I, we microscopically derive Ginzburg--Landau (GL) theory from BCS theory for translation-invariant systems in which multiple types of superconductivity may coexist. Our motivation are unconventional superconductors. We allow the ground state of the effective gap operator $K_{T_c}+V$ to be $n$-fold degenerate and the resulting GL theory then couples $n$ order parameters. In part II, we study examples of multi-component GL theories which arise from an isotropic BCS theory. We study the cases of (a) pure $d$-wave order parameters and (b) mixed $(s+d)$-wave order parameters, in two and three dimensions. In part III, we present explicit choices of spherically symmetric interactions $V$ which produce the examples in part II. In fact, we find interactions $V$ which produce ground state sectors of $K_{T_c}+V$ of arbitrary angular momentum, for open sets of of parameter values. This is in stark contrast with Schr\\"odinger operators $-\
Ginzburg-Landau theory of the bcc-liquid interface kinetic coefficient
Wu, Kuo-An; Wang, Ching-Hao; Hoyt, Jeffrey J.; Karma, Alain
2015-01-01
We extend the Ginzburg-Landau (GL) theory of atomically rough bcc-liquid interfaces [Wu et al., Phys. Rev. B 73, 094101 (2006), 10.1103/PhysRevB.73.094101] outside of equilibrium. We use this extension to derive an analytical expression for the kinetic coefficient, which is the proportionality constant μ (n ̂) between the interface velocity along a direction n ̂ normal to the interface and the interface undercooling. The kinetic coefficient is expressed as a spatial integral along the normal direction of a sum of gradient square terms corresponding to different nonlinear density wave profiles. Anisotropy arises naturally from the dependence of those profiles on the angles between the principal reciprocal lattice vectors K⃗i and n ̂. Values of the kinetic coefficient for the (100 ) ,(110 ) , and (111 ) interfaces are compared quantitatively to the prediction of linear Mikheev-Chernov (MC) theory [J. Cryst. Growth 112, 591 (1991), 10.1016/0022-0248(91)90340-B] and previous molecular dynamics (MD) simulation studies of crystallization kinetics for a classical model of Fe. Additional MD simulations are carried out here to compute the relaxation time of density waves in the liquid in order to make this comparison free of fit parameters. The GL theory predicts an expression for μ similar to the MC theory but yields a better agreement with MD simulations for both its magnitude and anisotropy due to a fully nonlinear description of density wave profiles across the solid-liquid interface. In particular, the overall magnitude of μ predicted by GL theory is an order of magnitude larger than predicted by the MC theory. GL theory is also used to derive an inverse relation between μ and the solid-liquid interfacial free energy. The general methodology used here to derive an expression for μ (n ̂) also applies to amplitude equations derived from the phase-field-crystal model, which only differ from GL theory by the choice of cubic and higher order nonlinearities in the
Attanasio, Felipe
2013-01-01
Nesta Dissertação apresentamos um estudo numéerico em uma dimensão espacial da equação de Ginzburg-Landau-Langevin (GLL), com ênfase na aplicabilidade de um método de perturbação estocástico e na mecânica estatística de defeitos topológicos em modelos de campos escalares reais. Revisamos brevemente conceitos de mecânica estatística de sistemas em equilíbrio e próximos a ele e apresentamos como a equação de GLL pode ser usada em sistemas que exibem transições de fase, na quantização estocástic...
GINZBURG-LANDAU THEORY AND VORTEX LATTICE OF HIGH-TEMPERATURE SUPERCONDUCTORS
ZHOU SHI-PING
2001-01-01
The thermodynamics of the vortex lattice of high-temperature superconductors has been studied by solving the generalized Ginzburg-Landau equations derived microscopically. Our numerical simulation indicates that the structure of the vortex lattice is oblique at the temperature far away from the transition temperature Tc, where the mixed s-dx2-ya state is expected to have the lowest energy. Whereas, very close to Tc, the dx2-ya wave is slightly lower energetically, and a triangular vortex lattice recovers. The coexistence and the coupling between the s and d waves would account for the unusual dynamic behaviours such as the upward curvature of the upper critical field curve Hc2(T), as observed in dc magnetization measurements on single-crystal YBa2Cu307 samples.
Anisotropy of Critical Fields in MgB2: Two-Band Ginzburg-Landau Theory for Layered Superconductors
I.N. Askerzade; B. Tanatar
2009-01-01
The temperature dependence of the anisotropy parameter of upper critical field γHc2 (T)= Hc2(T) / Hc2(T) and London penetration depth γλ(T) = λ(T)/λ (T) are calculated using two-band Ginzburg-Landau theory for layered superconductors. It is shown that, with decreasing temperature the anisotropy parameter γHc2 (T) is increased, while the London penetration depth anisotropy γλ (T) revea/s an opposite behavior. Results of our calculations are in agreement with experimental data for single crystal MgB2 and with other calculations. Results of an analysis of magnetic field Hc1 in a single vortex between superconducting layers are also presented.
Koma, Y
2003-01-01
The ratios between the string tensions sigma sub D of color-electric flux tubes in higher and fundamental SU(3) representations, d sub D ident to sigma sub D /sigma sub 3 , are systematically studied in a Weyl symmetric formulation of the DGL theory. The ratio is found to depend on the Ginzburg-Landau (GL) parameter, kappa ident to m subchi/m sub B , the mass ratio between the monopoles (m subchi) and the masses of the dual gauge bosons (m sub B). While the ratios d sub D follow a simple flux counting rule in the Bogomol'nyi limit, kappa=1.0, systematic deviations appear with increasing kappa due to interactions between the fundamental flux inside a higher representation flux tube. We find that in a type-II dual superconducting vacuum near kappa= 3.0 this leads to a consistent description of the ratios d sub D as observed in lattice QCD simulations. (orig.)
Koma, Y. [Institute for Theoretical Physics, Kanazawa University, Kanazawa, Ishikawa 920-1192 (Japan); Koma, M. [Research Center for Nuclear Physics (RCNP), Osaka University, Mihogaoka 10-1, Ibaraki, Osaka 567-0047 (Japan)
2003-01-01
The ratios between the string tensions {sigma}{sub D} of color-electric flux tubes in higher and fundamental SU(3) representations, d{sub D} {identical_to}{sigma}{sub D}/{sigma}{sub 3}, are systematically studied in a Weyl symmetric formulation of the DGL theory. The ratio is found to depend on the Ginzburg-Landau (GL) parameter, {kappa}{identical_to}m{sub {chi}}/m{sub B}, the mass ratio between the monopoles (m{sub {chi}}) and the masses of the dual gauge bosons (m{sub B}). While the ratios d{sub D} follow a simple flux counting rule in the Bogomol'nyi limit, {kappa}=1.0, systematic deviations appear with increasing {kappa} due to interactions between the fundamental flux inside a higher representation flux tube. We find that in a type-II dual superconducting vacuum near {kappa}= 3.0 this leads to a consistent description of the ratios d{sub D} as observed in lattice QCD simulations. (orig.)
Smiseth, Jo
2005-07-01
The critical properties of three-dimensional U(1)-symmetric lattice gauge theories have been studied. The models apply to various physical systems such as insulating phases of strongly correlated electron systems as well as superconducting and superfluid states of liquid metallic hydrogen under extreme pressures. The thesis contains an introductory part and a collection of research papers of which seven are published works and one is submitted for publication. The outline of this thesis is as follows. In Chapter 2 the theory of phase transitions is discussed with emphasis on continuous phase transitions, critical phenomena and phase transitions in gauge theories. In the next chapter the phases of the abelian Higgs model are presented, and the critical phenomena are discussed. Furthermore, the multicomponent Ginzburg-Landau theory and the applications to liquid metallic hydrogen are presented. Chapter 4 contains an overview of the Monte Carlo integration scheme, including the Metropolis algorithm, error estimates, and re weighting techniques. This chapter is followed by the papers I-VIII. Paper I: Criticality in the (2+1)-Dimensional Compact Higgs Model and Fractionalized Insulators. Paper II: Phase structure of (2+1)-dimensional compact lattice gauge theories and the transition from Mott insulator to fractionalized insulator. Paper III: Compact U(1) gauge theories in 2+1 dimensions and the physics of low dimensional insulating materials. Paper IV: Phase structure of Abelian Chern-Simons gauge theories. Paper V: Critical Properties of the N-Color London Model. Paper VI: Field- and temperature induced topological phase transitions in the three-dimensional N-component London superconductor. Paper VII: Vortex Sublattice Melting in a Two-Component Superconductor. Paper VIII: Observation of a metallic superfluid in a numerical experiment (ml)
Bethuel, Fabrice; Helein, Frederic
2017-01-01
This book is concerned with the study in two dimensions of stationary solutions of uɛ of a complex valued Ginzburg-Landau equation involving a small parameter ɛ. Such problems are related to questions occurring in physics, e.g., phase transition phenomena in superconductors and superfluids. The parameter ɛ has a dimension of a length which is usually small. Thus, it is of great interest to study the asymptotics as ɛ tends to zero. One of the main results asserts that the limit u-star of minimizers uɛ exists. Moreover, u-star is smooth except at a finite number of points called defects or vortices in physics. The number of these defects is exactly the Brouwer degree – or winding number – of the boundary condition. Each singularity has degree one – or as physicists would say, vortices are quantized. The singularities have infinite energy, but after removing the core energy we are lead to a concept of finite renormalized energy. The location of the singularities is completely determined by minimiz...
Ginzburg-Landau theory for the solid-liquid interface of bcc elements
Shih, W. H.; Wang, Z. Q.; Zeng, X. C.; Stroud, D.
1987-01-01
Consideration is given to a simple order-parameter theory for the interfacial tension of body-centered-cubic solids in which the principal order parameter is the amplitude of the density wave at the smallest nonzero reciprocal-lattice vector of the solid. The parameters included in the theory are fitted to the measured heat of fusion, melting temperature, and solid-liquid density difference, and to the liquid structure factor and its temperature derivative at freezing. Good agreement is found with experiment for Na and Fe and the calculated anisotropy of the surface tension among different crystal faces is of the order of 2 percent. On the basis of various assumptions about the universal behavior of bcc crystals at melting, the formalism predicts that the surface tension is proportional to the heat of fusion per surface atom.
Microscopic Derivation of the Ginzburg-Landau Model
Frank, Rupert; Hainzl, Christian; Seiringer, Robert
2014-01-01
We present a summary of our recent rigorous derivation of the celebrated Ginzburg-Landau (GL) theory, starting from the microscopic Bardeen-Cooper-Schrieffer (BCS) model. Close to the critical temperature, GL arises as an effective theory on the macroscopic scale. The relevant scaling limit...
Microscopic Derivation of the Ginzburg-Landau Model
Frank, Rupert; Hainzl, Christian; Seiringer, Robert
2014-01-01
We present a summary of our recent rigorous derivation of the celebrated Ginzburg-Landau (GL) theory, starting from the microscopic Bardeen-Cooper-Schrieffer (BCS) model. Close to the critical temperature, GL arises as an effective theory on the macroscopic scale. The relevant scaling limit...
Zeng, X. C.; Stroud, D.
1989-01-01
The previously developed Ginzburg-Landau theory for calculating the crystal-melt interfacial tension of bcc elements to treat the classical one-component plasma (OCP), the charged fermion system, and the Bose crystal. For the OCP, a direct application of the theory of Shih et al. (1987) yields for the surface tension 0.0012(Z-squared e-squared/a-cubed), where Ze is the ionic charge and a is the radius of the ionic sphere. Bose crystal-melt interface is treated by a quantum extension of the classical density-functional theory, using the Feynman formalism to estimate the relevant correlation functions. The theory is applied to the metastable He-4 solid-superfluid interface at T = 0, with a resulting surface tension of 0.085 erg/sq cm, in reasonable agreement with the value extrapolated from the measured surface tension of the bcc solid in the range 1.46-1.76 K. These results suggest that the density-functional approach is a satisfactory mean-field theory for estimating the equilibrium properties of liquid-solid interfaces, given knowledge of the uniform phases.
Drift of Spiral Waves in Complex Ginzburg-Landau Equation
无
2006-01-01
The spontaneous drift of the spiral wave in a finite domain in the complex Ginzburg-Landau equation is investigated numerically. By using the interactions between the spiral wave and its images, we propose a phenomenological theory to explain the observations.
The Bifurcation of Vortex Current in the Time-Dependent Ginzburg-Landau Model
XU Tao; YANG Guo-Hong; DUAN Yi-Shi
2001-01-01
By the method of φ-mapping topological current theory, the bifurcation behavior of the topological current is discussed in detail in the O(n) symmetrical time-dependent Ginzburg-Landau model at the critical points of the order parameter field. The different directions of the branch curves at the critical point have been obtained.
The attractor of the stochastic generalized Ginzburg-Landau equation
GUO BoLing; WANG GuoLian; Li DongLong
2008-01-01
The stochastic generalized Ginzburg-Landau equation with additive noise can be solved pathwise and the unique solution generates a random system. Then we prove the random system possesses a global random attractor in H01.
The attractor of the stochastic generalized Ginzburg-Landau equation
2008-01-01
The stochastic generalized Ginzburg-Landau equation with additive noise can be solved pathwise and the unique solution generates a random system.Then we prove the random system possesses a global random attractor in H01.
ATTRACTORS FOR DISCRETIZATION OF GINZBURG-LANDAU-BBM EQUATIONS
Mu-rong Jiang; Bo-ling Guo
2001-01-01
In this paper, Ginzburg-Landau equation coupled with BBM equationwith periodic initial boundary value conditions are discreted by the finite difference method in spatial direction. Existence of the attractors for the spatially discreted Ginzburg-Landau-BBM equations is proved. For each mesh size, there exist attractors for the discretized system. Moreover, finite Hausdorff and fractal dimensions of the discrete attractors are obtained and the bounds are independent of the mesh sizes.
A Ginzburg-Landau model for the expansion of a dodecahedral viral capsid
Zappa, E.; Indelicato, G.; Albano, A.; Cermelli, P.
2013-11-01
We propose a Ginzburg-Landau model for the expansion of a dodecahedral viral capsid during infection or maturation. The capsid is described as a dodecahedron whose faces, meant to model rigid capsomers, are free to move independent of each other, and has therefore twelve degrees of freedom. We assume that the energy of the system is a function of the twelve variables with icosahedral symmetry. Using techniques of the theory of invariants, we expand the energy as the sum of invariant polynomials up to fourth order, and classify its minima in dependence of the coefficients of the Ginzburg-Landau expansion. Possible conformational changes of the capsid correspond to symmetry breaking of the equilibrium closed form. The results suggest that the only generic transition from the closed state leads to icosahedral expanded form. Our approach does not allow to study the expansion pathway, which is likely to be non-icosahedral.
Gamma-convergence of 2D Ginzburg-Landau functionals with vortex concentration along curves
Alama, Stan; Millot, Vincent
2009-01-01
We study the variational convergence of a family of two-dimensional Ginzburg-Landau functionals arising in the study of superfluidity or thin-film superconductivity, as the Ginzburg-Landau parameter epsilon tends to 0. In this regime and for large enough applied rotations (for superfluids) or magnetic fields (for superconductors), the minimizers acquire quantized point singularities (vortices). We focus on situations in which an unbounded number of vortices accumulate along a prescribed Jordan curve or a simple arc in the domain. This is known to occur in a circular annulus under uniform rotation, or in a simply connected domain with an appropriately chosen rotational vector field. We prove that, suitably normalized, the energy functionals Gamma-converge to a classical energy from potential theory. Applied to global minimizers, our results describe the limiting distribution of vortices along the curve in terms of Green equilibrium measures.
Extended Ginzburg-Landau formalism for two-band superconductors.
Shanenko, A A; Milošević, M V; Peeters, F M; Vagov, A V
2011-01-28
Recent observation of unusual vortex patterns in MgB(2) single crystals raised speculations about possible "type-1.5" superconductivity in two-band materials, mixing the properties of both type-I and type-II superconductors. However, the strict application of the standard two-band Ginzburg-Landau (GL) theory results in simply proportional order parameters of the two bands-and does not support the "type-1.5" behavior. Here we derive the extended GL formalism (accounting all terms of the next order over the small τ=1-T/T(c) parameter) for a two-band clean s-wave superconductor and show that the two condensates generally have different spatial scales, with the difference disappearing only in the limit T→T(c). The extended version of the two-band GL formalism improves the validity of GL theory below T(c) and suggests revisiting the earlier calculations based on the standard model.
MODERATE DEVIATIONS FROM HYDRODYNAMIC LIMIT OF A GINZBURG-LANDAU MODEL
无
2006-01-01
The authors consider the moderate deviations of hydrodynamic limit for Ginzburg-Landau models. The moderate deviation principle of hydrodynamic limit for a specific Ginzburg-Landau model is obtained and an explicit formula of the rate function is derived.
Giant vortices in the Ginzburg-Landau model
Sørensen, Mads Peter
The time-dependent Ginzburg-Landau equation is solved in a region of two spatial dimensions and with complex geometry using the finite element method. The geometry has a marked influence on the vortex distribution and we have observed generation of giant vortices at boundary defects.......The time-dependent Ginzburg-Landau equation is solved in a region of two spatial dimensions and with complex geometry using the finite element method. The geometry has a marked influence on the vortex distribution and we have observed generation of giant vortices at boundary defects....
Numerical calculation of singularities for Ginzburg-Landau functionals
J. W. Neuberger
1997-06-01
Full Text Available We give results of numerical calculations of asymptotic behavior of critical points of a Ginzburg-Landau functional. We use both continuous and discrete steepest descent in connection with Sobolev gradients in order to study configurations of singularities.
Transition to Antispirals in the Complex Ginzburg-Landau Equation
WANG Hong-Li; OU-YANG Qi
2004-01-01
@@ We report a continuous transition from outwardly rotating spiral waves to antispirals in the complex GinzburgLandau equation. Numerical simulations demonstrate that the normal spiral to antispiral transition is fulfilled through a rest spiral wave with zero propagation speed. The propagation direction of spiral waves and the power law behaviour close to the transition boundary are examined.
Attraction properties of the Ginzburg-Landau manifold
Eckhaus, W.; Shepeleva, A.
2001-01-01
We consider solutions of weakly unstable PDE on an unbounded spatial domain. It has been shown earlier by the first author that the set of modulated solutions (called "Ginzburg-Landau manifold") is attracting. We seek to understand "how big" is the domain of attraction. Starting with general initial
Inviscid Limits of the Complex Generalized Ginzburg-Landau Equations
杨灵娥
2002-01-01
@@ 1 Introduction Derivative Ginzburg-Landau equation appeared in many physical problem. It was derived for instability waves in hydrodynamic such as the nonlinear growth of Rayleigh-Benard convective rolls, the appearance of Taylor Vortices in the couette flow between counter-rotating cylinders.
OBSTACLE PROBLEMS FOR SCALAR GINZBURG-LANDAU EQUATIONS
Ma Li; Su Ning
2004-01-01
In this note, we establish some estimates of solutions of the scalar Ginzburg-Landau equation and other nonlinear Laplacian equation Δu = f(x, u). This will give an estimate of the Hausdorff dimension for the free boundary of the obstacle problem.
On the validity of the degenerate Ginzburg-Landau equation
Shepeleva, A.
2001-01-01
The Ginzburg{Landau equation which describes nonlinear modulation of the amplitude of the basic pattern does not give a good approximation when the Landau constant (which describes the in uence of the nonlinearity) is small. In this paper a derivation of the so{called degenerate (or generalized) Gin
On the Ginzburg-Landau critical field in three dimensions
Fournais, Søren; Helffer, Bernard
2009-01-01
We study the three-dimensional Ginzburg-Landau model of superconductivity. Several natural definitions of the (third) critical field, HC3, governing the transition from the superconducting state to the normal state, are considered. We analyze the relation between these fields and give conditions...
Ginzburg-Landau vortices driven by the Landau-Lifshitz-Gilbert equation
Kurzke, Matthias; Melcher, Christof; Moser, Roger; Spirn, Daniel
2009-06-15
A simplified model for the energy of the magnetization of a thin ferromagnetic film gives rise to a version of the theory of Ginzburg-Landau vortices for sphere-valued maps. In particular we have the development of vortices as a certain parameter tends to 0. The dynamics of the magnetization is ruled by the Landau-Lifshitz-Gilbert equation, which combines characteristic properties of a nonlinear Schroedinger equation and a gradient flow. This paper studies the motion of the vortex centers under this evolution equation. (orig.)
SOLUTIONS OF GINZBURG-LANDAU EQUATIONS WITH WEIGHT AND MINIMIZERS OF THE RENORMALIZED ENERGY
Kou Yanlei; Ding Shijin
2007-01-01
In this paper, it is proved that for any given d non-degenerate local minimum points of the renormalized energy of weighted Ginzburg-Landau eqautions, one can find solutions to the Ginzburg-Landau equations whose vortices tend to these d points. This provides the connections between solutions of a class of Ginzburg-Landau equations with weight and minimizers of the renormalized energy.
Phase chaos in the anisotropic complex Ginzburg-Landau Equation
Faller, R
1998-01-01
Of the various interesting solutions found in the two-dimensional complex Ginzburg-Landau equation for anisotropic systems, the phase-chaotic states show particularly novel features. They exist in a broader parameter range than in the isotropic case, and often even broader than in one dimension. They typically represent the global attractor of the system. There exist two variants of phase chaos: a quasi-one dimensional and a two-dimensional solution. The transition to defect chaos is of intermittent type.
Landau, I. L.; Ott, H. R.
2003-11-01
We show that the scaling procedure, recently proposed for the evaluation of the temperature variation of the normalized upper critical field of type-II superconductors, may easily be modified in order to take into account a possible temperature dependence of the Ginzburg-Landau parameter κ. As an example we consider κ( T) as it follows from the microscopic theory of superconductivity.
DYNAMICS FOR VORTICES OF AN EVOLUTIONARY GINZBURG-LANDAU EQUATIONS IN 3 DIMENSIONS
刘祖汉
2002-01-01
This paper studies the asymptotic behavior of solutions to an evolutionary Ginzburg-Landau equation in 3 dimensions. It is shown that the motion of the Ginzburg-Landau vortex curves is the flow by its curvature. Away from the vortices, the author uses some measure theoretic arguments used by F. H. Lin in [16] to show the strong convergence of solutions.
GPU-advanced 3D electromagnetic simulations of superconductors in the Ginzburg-Landau formalism
Stošić, Darko; Stošić, Dušan; Ludermir, Teresa; Stošić, Borko; Milošević, Milorad V.
2016-10-01
Ginzburg-Landau theory is one of the most powerful phenomenological theories in physics, with particular predictive value in superconductivity. The formalism solves coupled nonlinear differential equations for both the electronic and magnetic responsiveness of a given superconductor to external electromagnetic excitations. With order parameter varying on the short scale of the coherence length, and the magnetic field being long-range, the numerical handling of 3D simulations becomes extremely challenging and time-consuming for realistic samples. Here we show precisely how one can employ graphics-processing units (GPUs) for this type of calculations, and obtain physics answers of interest in a reasonable time-frame - with speedup of over 100× compared to best available CPU implementations of the theory on a 2563 grid.
Eilenberger and Ginzburg-Landau models of the vortex core in high κ-superconductors
Belova, P.; Traito, K. B.; Lähderanta, E.
2011-08-01
Eilenberger approach to the cutoff parameter, ξh, of the field distribution in the mixed state of high κ-superconductors is developed. It is found that normalized value of ξh/ξc2 decreases both with temperature (due to Kramer-Pesch effect) and with impurity scattering rate Γ. Our theory explains μSR experiments in some low-field superconductors and different ξh values from the Ginzburg-Landau theory predictions in isotropic s-wave superconductors. A comparison with another characteristic length ξ1, describing the gradient of the order parameter in the vortex center, is done. They have very different Γ-dependences: monotonous suppression of ξh(B) values and crossing behavior of the ξ1(B) curves at various Γ. This is explained by the nonlocal effects in the Eilenberger theory.
Diffusive Mixing of Stable States in the Ginzburg-Landau Equation
Gallay, T; Gallay, Thierry; Mielke, Alexander
1998-01-01
For the time-dependent Ginzburg-Landau equation on the real line, we construct solutions which converge, as $x \\to \\pm\\infty$, to periodic stationary states with different wave-numbers $\\eta_\\pm$. These solutions are stable with respect to small perturbations, and approach as $t \\to +\\infty$ a universal diffusive profile depending only on the values of $\\eta_\\pm$. This extends a previous result of Bricmont and Kupiainen by removing the assumption that $\\eta_\\pm$ should be close to zero. The existence of the diffusive profile is obtained as an application of the theory of monotone operators, and the long-time behavior of our solutions is controlled by rewriting the system in scaling variables and using energy estimates involving an exponentially growing damping term.
SPATIO-TEMPORAL CHAOTIC SYNCHRONIZATION FOR MODES COUPLED TWO GINZBURG-LANDAU EQUATIONS
HU Man-feng; XU Zhen-yuan
2006-01-01
On the basis of numerical computation, the conditions of the modes coupling are proposed, and the high-frequency modes are coupled, but the low frequency modes are uncoupled. It is proved that there exist an absorbing set and a global finite dimensional attractor which is compact and connected in the function space for the high-frequency modes coupled two Ginzburg-Landau equations(MGLE). The trajectory of driver equation may be spatio-temporal chaotic. One associates with MGLE, a truncated form of the equations. The prepared equations persist in long time dynamical behavior of MGLE.MGLE possess the squeezing properties under some conditions. It is proved that the complete spatio-temporal chaotic synchronization for MGLE can occur. Synchronization phenomenon of infinite dimensional dynamical system (IFDDS) is illustrated on the mathematical theory qualitatively. The method is different from Liapunov function methods and approximate linear methods.
The time-dependent Ginzburg-Landau equation for the two-velocity difference model
Wu Shu-zhen; Cheng Rong-Jun; Ge Hong-xia
2011-01-01
A thermodynamic theory is formulated to describe the phase transition and critical phenomenon in traffic flow.Based on the two-velocity difference model,the time-dependent Ginzburg-Landau(TDGL)equation under certain condition is derived to describe the traffic flow near the critical point through the nonlinear analytical method.The corresponding two solutions,the uniform and the kink solutions,are given.The coexisting curve,spinodal line and critical point are obtained by the first and second derivatives of the thermodynamic potential.The modified Kortewegde Vries(mKdV)equation around the critical point is derived by using the reductive perturbation method and its kink-antikink solution is also obtained.The relation between the TDGL equation and the mKdV equation is shown.The simulation result is consistent with the nonlinear analytical result.
EXISTENCE OF PERIODIC SOLUTIONS OF THE BURGERS-GINZBURG-LANDAU EQUATIONS
黄海洋
2004-01-01
In this paper, the existence of the periodic solutions for a forced Burgers equation coupled to a non-homogeneous Ginzburg-Landau equation is proved by LeraySchauder fixed point theorem and Galerkin method under appropriate conditions.
Exact Traveling Wave Solutions for a Kind of Generalized Ginzburg-Landau Equation
LIU Cheng-Shi
2005-01-01
Using a complete discrimination system for polynomials, new exact traveling wave solutions for generalized Ginzburg-Landau equation are obtained. The method has general meaning for many similar problems.
Two-Dimensional Saddle Point Equation of Ginzburg-Landau Hamiltonian for the Diluted Ising Model
WU Xin-Tian
2006-01-01
@@ The saddle point equation of Ginzburg-Landau Hamiltonian for the diluted Ising model is developed. The ground state is solved numerically in two dimensions. The result is partly explained by the coarse-grained approximation.
Mauro M Doria; Antonio R de C Romaguera; Welles A M Margado
2006-01-01
A vortex line is shaped by a zigzag of pinning centers and we study here how far the stretched vortex line is able to follow this path. The pinning center is described by an insulating sphere of coherence length size such that in its surface the de Gennes boundary condition applies. We calculate the free energy density of this system in the framework of the Ginzburg-Landau theory and study the critical displacement beyond which the vortex line is detached from the pinning center.
Exact Solutions of Discrete Complex Cubic Ginzburg-Landau Equation and Their Linear Stability
张金良; 刘治国
2011-01-01
The discrete complex cubic Ginzburg-Landau equation is an important model to describe a number of physical systems such as Taylor and frustrated vortices in hydrodynamics and semiconductor laser arrays in optics. In this paper, the exact solutions of the discrete complex cubic Ginzburg-Landau equation are derived using homogeneous balance principle and the GI/G-expansion method, and the linear stability of exact solutions is discussed.
VORTEX MOTION LAW OF AN EVOLUTIONARY GINZBURG-LANDAU EQUATION IN 2 DIMENSIONS
Liu Zuhan
2001-01-01
We study the asymptotic behavior of solutions to an evolutionary Ginzburg-Landau equation. We also study the dynamical law of Ginzburg-Landau vortices of this equation under the Neuman boundary conditions. Away from the vortices,we use some measure theoretic arguments used by F.H.Lin in [1] to show the strong convergence of solutions. This is a continuation of our earlier work [2].
INHOMOGENEOUS INITIAL-BOUNDARY VALUE PROBLEM FOR GINZBURG-LANDAU EQUATIONS
杨灵娥; 郭柏灵; 徐海祥
2004-01-01
Some integral identities of smooth solution of inhomogeneous initial boundary value problem of Ginzburg-Landau equations were deduced, by which a priori estimates of the square norm on boundary of normal derivative and the square norm of partial derivatives were obtained. Then the existence of global weak solution of inhomogeneous initial-boundary value problem of Ginzburg-Landau equations was proved by the method of approximation technique and a priori estimates and making limit.
Analysis of Energy Eigenvalue in Complex Ginzburg-Landau Equation
Gao, Ji-Hua; Xiao, Qi; Xie, Ling-Ling; Zhang, Xin-Xin; Yang, Hai-Tao
2017-06-01
In this paper, we consider the two-dimensional complex Ginzburg-Landau equation (CGLE) as the spatiotemporal model, and an expression of energy eigenvalue is derived by using the phase-amplitude representation and the basic ideas from quantum mechanics. By numerical simulation, we find the energy eigenvalue in the CGLE system can be divided into two parts, corresponding to spiral wave and bulk oscillation. The energy eigenvalue of spiral wave is positive, which shows that it propagates outwardly; while the energy eigenvalue of spiral wave is negative, which shows that it propagates inwardly. There is a necessary condition for generating a spiral wave that the energy eigenvalue of spiral wave is greater than bulk oscillation. A wave with larger energy eigenvalue dominates when it competes with another wave with smaller energy eigenvalue in the space of the CGLE system. At the end of this study, a tentative discussion of the relationship between wave propagation and energy transmission is given. Supported by the Basic Research Project of Shenzhen, China under Grant Nos. JCYJ 20140418181958489 and 20160422144751573
Accessible solitons in complex Ginzburg-Landau media
He, Yingji; Malomed, Boris A.
2013-10-01
We construct dissipative spatial solitons in one- and two-dimensional (1D and 2D) complex Ginzburg-Landau (CGL) equations with spatially uniform linear gain; fully nonlocal complex nonlinearity, which is proportional to the integral power of the field times the harmonic-oscillator (HO) potential, similar to the model of “accessible solitons;” and a diffusion term. This CGL equation is a truly nonlinear one, unlike its actually linear counterpart for the accessible solitons. It supports dissipative spatial solitons, which are found in a semiexplicit analytical form, and their stability is studied semianalytically, too, by means of the Routh-Hurwitz criterion. The stability requires the presence of both the nonlocal nonlinear loss and diffusion. The results are verified by direct simulations of the nonlocal CGL equation. Unstable solitons spontaneously spread out into fuzzy modes, which remain loosely localized in the effective complex HO potential. In a narrow zone close to the instability boundary, both 1D and 2D solitons may split into robust fragmented structures, which correspond to excited modes of the 1D and 2D HOs in the complex potentials. The 1D solitons, if shifted off the center or kicked, feature persistent swinging motion.
Finding equilibrium in the spatiotemporal chaos of the complex Ginzburg-Landau equation
Ballard, Christopher C.; Esty, C. Clark; Egolf, David A.
2016-11-01
Equilibrium statistical mechanics allows the prediction of collective behaviors of large numbers of interacting objects from just a few system-wide properties; however, a similar theory does not exist for far-from-equilibrium systems exhibiting complex spatial and temporal behavior. We propose a method for predicting behaviors in a broad class of such systems and apply these ideas to an archetypal example, the spatiotemporal chaotic 1D complex Ginzburg-Landau equation in the defect chaos regime. Building on the ideas of Ruelle and of Cross and Hohenberg that a spatiotemporal chaotic system can be considered a collection of weakly interacting dynamical units of a characteristic size, the chaotic length scale, we identify underlying, mesoscale, chaotic units and effective interaction potentials between them. We find that the resulting equilibrium Takahashi model accurately predicts distributions of particle numbers. These results suggest the intriguing possibility that a class of far-from-equilibrium systems may be well described at coarse-grained scales by the well-established theory of equilibrium statistical mechanics.
YANG Ling'e; GUO Boling
2006-01-01
By the uniform a priori estimate of solution about parameters, we prove the existence of global solution and inviscid limit to a generalized Ginzburg-Landau equations in two dimensions. We also prove that the solution to the Ginzburg-Landau equations converges to the weak solution to the derivative nonlinear Schrodinger equations.
Domain Walls and Textured Vortices in a Two-Component Ginzburg-Landau Model
Madsen, Søren Peder; Gaididei, Yu. B.; Christiansen, Peter Leth
2005-01-01
We look for domain wall and textured vortex solutions in a two-component Ginzburg-Landau model inspired by two-band superconductivity. The two-dimensional two-component model, with equal coherence lengths and no magnetic field, shows some interesting properties. In the absence of a Josephson type...... coupling between the two order parameters a ''textured vortex'' is found by analytical and numerical solution of the Ginzburg-Landau equations. With a Josephson type coupling between the two order parameters we find the system to split up in two domains separated by a domain wall, where the order parameter...
Integrability and structural stability of solutions to the Ginzburg-Landau equation
Keefe, Laurence R.
1986-01-01
The integrability of the Ginzburg-Landau equation is studied to investigate if the existence of chaotic solutions found numerically could have been predicted a priori. The equation is shown not to possess the Painleveproperty, except for a special case of the coefficients that corresponds to the integrable, nonlinear Schroedinger (NLS) equation. Regarding the Ginzburg-Landau equation as a dissipative perturbation of the NLS, numerical experiments show all but one of a family of two-tori solutions, possessed by the NLS under particular conditions, to disappear under real perturbations to the NLS coefficients of O(10 to the -6th).
Random Attractors for Stochastic Ginzburg-Landau Equation on Unbounded Domains
Qiuying Lu
2014-01-01
Full Text Available We prove the existence of a pullback attractor in L2(ℝn for the stochastic Ginzburg-Landau equation with additive noise on the entire n-dimensional space ℝn. We show that the stochastic Ginzburg-Landau equation with additive noise can be recast as a random dynamical system. We demonstrate that the system possesses a unique D-random attractor, for which the asymptotic compactness is established by the method of uniform estimates on the tails of its solutions.
Domain Walls and Textured Vortices in a Two-Component Ginzburg-Landau Model
Madsen, Søren Peder; Gaididei, Yu. B.; Christiansen, Peter Leth
2005-01-01
We look for domain wall and textured vortex solutions in a two-component Ginzburg-Landau model inspired by two-band superconductivity. The two-dimensional two-component model, with equal coherence lengths and no magnetic field, shows some interesting properties. In the absence of a Josephson type...... coupling between the two order parameters a ''textured vortex'' is found by analytical and numerical solution of the Ginzburg-Landau equations. With a Josephson type coupling between the two order parameters we find the system to split up in two domains separated by a domain wall, where the order parameter...
Ginzburg-Landau expansion in BCS-BEC crossover region of disordered attractive Hubbard model
Kuchinskii, E. Z.; Kuleeva, N. A.; Sadovskii, M. V.
2017-01-01
We have studied disorder effects on the coefficients of Ginzburg-Landau expansion for attractive Hubbard model within the generalized DMFT+Σ approximation for the wide region of the values of attractive potential U—from the weak-coupling limit, where superconductivity is described by BCS model, towards the strong coupling, where superconducting transition is related to Bose-Einstein condensation (BEC) of compact Cooper pairs. For the case of semi-elliptic initial density of states disorder influence on the coefficients A and B before the square and the fourth power of the order parameter is universal for at all values of electronic correlations and is related only to the widening of the initial conduction band (density of states) by disorder. Similar universal behavior is valid for superconducting critical temperature Tc (the generalized Anderson theorem) and specific heat discontinuity at the transition. This universality is absent for the coefficient C before the gradient term, which in accordance with the standard theory of "dirty" superconductors is strongly suppressed by disorder in the weak-coupling region, but can slightly grow in BCS-BEC crossover region, becoming almost independent of disorder in the strong coupling region. This leads to rather weak disorder dependence of the penetration depth and coherence length, as well as the slope of the upper critical magnetic field at Tc, in BCS-BEC crossover and strong coupling regions.
The Ginzburg-Landau Equation Solved by the Finite Element Method
Alstrøm, Tommy Sonne; Sørensen, Mads Peter; Pedersen, Niels Falsig
2006-01-01
vortices when the magnetic field exceeds a threshold value. These superconductors are called type II supercon-ductors. In this article we solve numerically the time dependent Ginzburg-Landau equation coupled to a magnetic field for type II superconductors of complex geometry, where the finite element...
Asymptotic behavior of 2D generalized stochastic Ginzburg-Landau equation with additive noise
Dong-long LI; Bo-ling GUO
2009-01-01
The 2D generalized stochastic Ginzburg-Landau equation with additive noise is considered. The compactness of the random dynamical system is established with a priori estimate method, showing that the random dynamical system possesses a random attractor in H10.
On a Ginzburg-Landau Type Energy with Discontinuous Constraint for High Values of Applied Field
Hassen AYDI
2011-01-01
In the presence of applied magnetic fields H such that |Inε| ＜＜ H ＜＜1/ε2, the author evaluates the minimal Ginzburg-Landau energy with discontinuous constraint. Its expression is analogous to the work of Sandier and Serfaty.
Measurement of coefficients of the Ginzburg-Landau equation for patterns of Taylor spirals.
Goharzadeh, Afshin; Mutabazi, Innocent
2010-07-01
Patterns of Taylor spirals observed in the counter-rotating Couette-Taylor system are described by complex Ginzburg-Landau equations (CGLE) and have been investigated using spatiotemporal diagrams and complex demodulation technique. We have determined the real coefficients of the CGLE and their variations versus the control parameters, i.e., the rotation frequency of cylinders.
Magnetic vortices for a Ginzburg-Landau type energy with discontinuous constraint
Kachmar, Ayman
2010-01-01
This paper is devoted to an analysis of vortex-nucleation for a Ginzburg-Landau functional with discontinuous constraint. This functional has been proposed as a model for vortex-pinning, and usually accounts for the energy resulting from the interface of two superconductors. The critical applied...
Vortex-lines motion for the Ginzburg-Landau equation with impurity
Zu-han; LIU
2007-01-01
In this paper, we study the asymptotic behavior of solutions of the Ginzburg-Landau equation with impurity. We prove that, asymptotically, the vortex-lines evolve according to the mean curvature flow with a forcing term in the sense of the weak formulation.
UNIQUENESS THEOREM OF THE REGULARIZABLE RADIAL GINZBURG-LANDAU TYPE MINIMIZERS
雷雨田
2002-01-01
The author proves the uniqueness of the regularizable radial minimizers of a Ginzburg-Landau type functional in the case n - 1 ＜ p ＜ n,and the location of the zeros of the regularizable radial minimizers of this functional is discussed.
RADIAL MINIMIZER OF P-GINZBURG-LANDAU FUNCTIONAL WITH A WEIGHT
Lei Yutian
2004-01-01
The author discusses the asymptotic behavior of the radial minimizer of the p-Ginzburg-Landau functional with a weight in the case p ＞ n ≥ 2. The location of the zeros and the uniqueness of the radial minimizer are derived. Moreover, the W1,p convergence of the radial minimizer of this functional is proved.
Global solutions for 2D coupled Burgers-complex-Ginzburg-Landau equations
Hongjun Gao
2015-12-01
Full Text Available In this article, we study the periodic initial-value problem of the 2D coupled Burgers-complex-Ginzburg-Landau (Burgers-CGL equations. Applying the Brezis-Gallout inequality which is available in 2D case and establishing some prior estimates, we obtain the existence and uniqueness of a global solution under certain conditions.
杨灵娥
2003-01-01
In this paper, we prove that in the inviscid limit the solution of the gen eralized derivative Ginzburg-Landau equations converges to the solution of derivative nonlinear Schrodinger equation, we also give the convergence rates for the difference of the solution.
Ginzburg-Landau vortices with pinning functions and self-similar solutions in harmonic maps
无
2000-01-01
We obtain the H1-compactness for a system of Ginzburg-Landau equations with pinning functions and prove that the vortices of its classical solutions are attracted to the minimum points of the pinning functions. As a corollary, we construct a self-similar solution in the evolution of harmonic maps.
On solitary wave solutions of ac-driven complex Ginzburg-Landau equation
Raju, Thokala Soloman [Physics Group, Birla Institute of Technology and Science-Pilani, Goa Campus, Goa, 403 726 (India); Porsezian, Kuppuswamy [Department of Physics, Pondicherry University, Kalapet, Pondicherry, 605 014 (India)
2006-02-24
A new class of periodic solutions of modified complex Ginzburg-Landau equation phase locked to a time-dependent force, by applying a nonfeedback mechanism for chaos control, have been found. The reported solutions are necessarily of the rational form containing trigonometric and hyperbolic functions.
GAO Ji-Hua; ZHENG Zhi-Gang; TANG Jiao-Ning; PENG Jian-Hua
2003-01-01
A model of two-dimensional coupled complex Ginzburg-Landau oscillators driven by a rectificative feedbackcontroller is used to study controlling spatiotemporal chaos without gradient force items. By properly selecting the signalinjecting position with considering the maximum gap between signals and targets, and adjusting the control time interval,we have finally obtained the efficient chaos control via numerical simulations.
GAOJi-Hua; ZHENGZhi-Gang; TANGJiao-Ning; PENGJian-Hua
2003-01-01
A model of two-dimensional coupled complex Ginzburg-Landau oscillators driven by a rectificative feedback controller is used to study controlling spatiotemporal chaos without gradient force items. By properly selecting the signal injecting position with considering the maximum gap between signals and targets, and adjusting the control time interval,we have finally obtained the efficient chaos control via numerical simulations.
On the third critical field in Ginzburg-Landau theory
Fournais, S.; Helffer, B.
2005-01-01
Using recent results by the authors on the spectral asymptotics of the Neumann Laplacian with magnetic field, we give precise estimates on the critical field, $H_{C_3}$, describing the appearance of superconductivity in superconductors of type II. Furthermore, we prove that the local and global definitions of this field coincide. Near $H_{C_3}$ only a small part, near the boundary points where the curvature is maximal, of the sample carries superconductivity. We give precise estimates on the ...
Ginzburg-Landau expansion in strongly disordered attractive Anderson-Hubbard model
Kuchinskii, E. Z.; Kuleeva, N. A.; Sadovskii, M. V.
2017-07-01
We have studied disordering effects on the coefficients of Ginzburg-Landau expansion in powers of superconducting order parameter in the attractive Anderson-Hubbard model within the generalized DMFT+Σ approximation. We consider the wide region of attractive potentials U from the weak coupling region, where superconductivity is described by BCS model, to the strong coupling region, where the superconducting transition is related with Bose-Einstein condensation (BEC) of compact Cooper pairs formed at temperatures essentially larger than the temperature of superconducting transition, and a wide range of disorder—from weak to strong, where the system is in the vicinity of Anderson transition. In the case of semielliptic bare density of states, disorder's influence upon the coefficients A and B of the square and the fourth power of the order parameter is universal for any value of electron correlation and is related only to the general disorder widening of the bare band (generalized Anderson theorem). Such universality is absent for the gradient term expansion coefficient C. In the usual theory of "dirty" superconductors, the C coefficient drops with the growth of disorder. In the limit of strong disorder in BCS limit, the coefficient C is very sensitive to the effects of Anderson localization, which lead to its further drop with disorder growth up to the region of the Anderson insulator. In the region of BCS-BEC crossover and in BEC limit, the coefficient C and all related physical properties are weakly dependent on disorder. In particular, this leads to relatively weak disorder dependence of both penetration depth and coherence lengths, as well as of related slope of the upper critical magnetic field at superconducting transition, in the region of very strong coupling.
WU Lei
2009-01-01
@@ Recently, Feng et al. claimed that "they have found the asymptotic self-similar parabolic solutions in gain medium of the normal GVD", where the evolution of optical pulses is governed by the following Ginzburg-Landau equation (GLE):[1
Gui Mu
2013-01-01
Full Text Available The existence of the exponential attractors for coupled Ginzburg-Landau equations describing Bose-Einstein condensates and nonlinear optical waveguides and cavities with periodic initial boundary is obtained by showing Lipschitz continuity and the squeezing property.
Landau, I. L.; Khasanov, R.; Togano, K.; Keller, H.
2007-01-01
We present temperature dependences of the upper critical magnetic field Hc2 and the Ginzburg-Landau parameter κ for a ternary boride superconductor Li2Pd3B obtained from magnetization measurements. A specially developed scaling approach was used for the data analysis. The resulting Hc2(T) curve turns out to be surprisingly close to predictions of the BCS theory. The magnetic field penetration depth λ, evaluated in this work, is in excellent agreement with recent muon-spin-rotation experiments. We consider this agreement as an important proof of the validity of our approach.
Exact solutions of the one-dimensional generalized modified complex Ginzburg-Landau equation
Yomba, E
2003-01-01
The one-dimensional (1D) generalized modified complex Ginzburg-Landau (MCGL) equation for the traveling wave systems is analytically studied. Exact solutions of this equation are obtained using a method which combines the Painleve test for integrability in the formalism of Weiss-Tabor-Carnevale and Hirota technique of bilinearization. We show that pulses, fronts, periodic unbounded waves, sources, sinks and solution as collision between two fronts are the important coherent structures that organize much of the dynamical properties of these traveling wave systems. The degeneracies of the 1D generalized MCGL equation are examined as well as several of their solutions. These degeneracies include two important equations: the 1D generalized modified Schroedinger equation and the 1D generalized real modified Ginzburg-Landau equation. We obtain that the one parameter family of traveling localized source solutions called 'Nozaki-Bekki holes' become a subfamily of the dark soliton solutions in the 1D generalized modif...
Attractors of derivative complex Ginzburg-Landau equation in unbounded domains
GUO Boling; HAN Yongqian
2007-01-01
The Ginzburg-Landau-type complex equations are simplified mathematical models for various pattern formation systems in mechanics, physics, and chemistry. In this paper, the derivative complex Ginzburg- Landau (DCGL) equation in an unbounded domain ΩС R2 is studied. We extend the Gagliardo-Nirenberg inequality to the weighted Sobolev spaces introduced by S. V. Zelik. Applied this Gagliardo-Nirenberg inequality of the weighted Sobolev spaces and based on the technique for the semi-linear system of parabolic equations which has been developed by M. A. Efendiev and S. V. Zelik, the global attractor in the corresponding phase space is constructed, the upper bound of its Kolmogorov's ε-entropy is obtained, and the spatial chaos of the attractor for DCGL equation in R2 is detailed studied.
100 anos de supercondutividade e a teoria de Ginzburg-Landau
Pereira,S.H.; Félix,Marcelo G.
2013-01-01
Este artigo é uma proposta de ensino de supercondutividade para estudantes de nível de graduação na área de ciências exatas. Utilizando a formulação fenomenológica de Ginzburg-Landau do fenômeno, pretendemos dar uma contribuição para o aprendizado deste importante tema da física contemporânea que raramente é tratado com a devida profundidade teórica na maioria dos livros de física usualmente adotados nos cursos de engenharia, física e química. A teoria de Ginzburg-Landau é apresentada de form...
On the Shape of Meissner Solutions to a Limiting Form of Ginzburg-Landau Systems
Xiang, Xingfei
2016-12-01
In this paper we study a semilinear system involving the curl operator, which is a limiting form of the Ginzburg-Landau model for superconductors in R^3 for a large value of the Ginzburg-Landau parameter. We consider the locations of the maximum points of the magnitude of solutions, which are associated with the nucleation of instability of the Meissner state for superconductors when the applied magnetic field is increased in the transition between the Meissner state and the vortex state. For small penetration depth, we prove that the location is not only determined by the tangential component of the applied magnetic field, but also by the normal curvatures of the boundary in some directions. This improves the result obtained by Bates and Pan in Commun. Math. Phys. 276, 571-610 (2007). We also show that the solutions decay exponentially in the normal direction away from the boundary if the penetration depth is small.
LIHua-Mei; LINJi; XUYou-Sheng
2005-01-01
In this paper, we extend the hyperbolic function approach for constructing the exact solutions of nonlinear differential-difference equation (NDDE) in a unified way. Applying the extended approach and with the aid of Maple,we have studied the discrete complex Ginzburg-Landau equation (dCGLE). As a result, we find a set of exact solutions which include bright and dark soliton solutions.
FENG Jie; XU WenCheng; LI ShuXian; LIU SongHao
2008-01-01
Based on the constant coefficients of Ginzburg-Landau equation that considers the influence of the doped fiber retarded time on the evolution of self-similar pulse, the parabolic asymptotic self-similar solutions were obtained by the symmetry reduc-tion algorithm.The parabolic asymptotic amplitude function, phase function, strict linear chirp function and the effective temporal pulse width of self-similar pulse are given in this paper.And these theoretical results are consistent with the numerical simulations.
Hernández-García, E; Colet, P; Montagne, R; Miguel, M S; Hernandez-Garcia, Emilio; Hoyuelos, Miguel; Colet, Pere; Montagne, Raul; Miguel, Maxi San
1999-01-01
We study the spatiotemporal dynamics, in one and two spatial dimensions, of two complex fields which are the two components of a vector field satisfying a vector form of the complex Ginzburg-Landau equation. We find synchronization and generalized synchronization of the spatiotemporally chaotic dynamics. The two kinds of synchronization can coexist simultaneously in different regions of the space, and they are mediated by localized structures. A quantitative characterization of the degree of synchronization is given in terms of mutual information measures.
Raza, Nauman; Sial, Sultan; Siddiqi, Shahid S.
2009-04-01
The Sobolev gradient technique has been discussed previously in this journal as an efficient method for finding energy minima of certain Ginzburg-Landau type functionals [S. Sial, J. Neuberger, T. Lookman, A. Saxena, Energy minimization using Sobolev gradients: application to phase separation and ordering, J. Comput. Phys. 189 (2003) 88-97]. In this article a Sobolev gradient method for the related time evolution is discussed.
Localized Pulsating Solutions of the Generalized Complex Cubic-Quintic Ginzburg-Landau Equation
Ivan M. Uzunov; Georgiev, Zhivko D.
2014-01-01
We study the dynamics of the localized pulsating solutions of generalized complex cubic-quintic Ginzburg-Landau equation (CCQGLE) in the presence of intrapulse Raman scattering (IRS). We present an approach for identification of periodic attractors of the generalized CCQGLE. Using ansatz of the travelling wave and fixing some relations between the material parameters, we derive the strongly nonlinear Lienard-Van der Pol equation for the amplitude of the nonlinear wave. Next, we apply the Meln...
Phase Space Compression in One-Dimensional Complex Ginzburg-Landau Dquation
GAO Ji-Hua; PENG Jian-Hua
2007-01-01
The transition from stationary to oscillatory states in dynamical systems under phase space compression is investigated. By considering the model for the spatially one-dimensional complex Ginzburg-Landau equation, we find that defect turbulence can be substituted with stationary and oscillatory signals by applying system perturbation and confining variable into various ranges. The transition procedure described by the oscillatory frequency is studied via numerical simulations in detail.
The Existence of Exponential Attractor for Discrete Ginzburg-Landau Equation
Guangyin Du
2015-01-01
Full Text Available This paper studies the following discrete systems of the complex Ginzburg-Landau equation: iu˙m-(α-iε(2um-um+1-um-1+iκum+βum2σum=gm, m∈Z. Under some conditions on the parameters α, ε, κ, β, and σ, we prove the existence of exponential attractor for the semigroup associated with these discrete systems.
Ginzburg-Landau vortex dynamics with pinning and strong applied currents
Serfaty, Sylvia
2010-01-01
We study a mixed heat and Schr\\"odinger Ginzburg-Landau evolution equation on a bounded two-dimensional domain with an electric current applied on the boundary and a pinning potential term. This is meant to model a superconductor subjected to an applied electric current and electromagnetic field and containing impurities. Such a current is expected to set the vortices in motion, while the pinning term drives them toward minima of the pinning potential and "pins" them there. We derive the limiting dynamics of a finite number of vortices in the limit of a large Ginzburg-Landau parameter, or $\\ep \\to 0$, when the intensity of the electric current and applied magnetic field on the boundary scale like $\\lep$. We show that the limiting velocity of the vortices is the sum of a Lorentz force, due to the current, and a pinning force. We state an analogous result for a model Ginzburg-Landau equation without magnetic field but with forcing terms. Our proof provides a unified approach to various proofs of dynamics of Gin...
Nonstationary Superconductivity: Quantum Dissipation and Time-Dependent Ginzburg-Landau Equation
Anatoly A. Barybin
2011-01-01
Full Text Available Transport equations of the macroscopic superfluid dynamics are revised on the basis of a combination of the conventional (stationary Ginzburg-Landau equation and Schrödinger's equation for the macroscopic wave function (often called the order parameter by using the well-known Madelung-Feynman approach to representation of the quantum-mechanical equations in hydrodynamic form. Such an approach has given (a three different contributions to the resulting chemical potential for the superfluid component, (b a general hydrodynamic equation of superfluid motion, (c the continuity equation for superfluid flow with a relaxation term involving the phenomenological parameters GL and GL, (d a new version of the time-dependent Ginzburg-Landau equation for the modulus of the order parameter which takes into account dissipation effects and reflects the charge conservation property for the superfluid component. The conventional Ginzburg-Landau equation also follows from our continuity equation as a particular case of stationarity. All the results obtained are mutually consistent within the scope of the chosen phenomenological description and, being model-neutral, applicable to both the low-c and high-c superconductors.
Ginzburg-Landau equation as a heuristic model for generating rogue waves
Lechuga, Antonio
2016-04-01
Envelope equations have many applications in the study of physical systems. Particularly interesting is the case 0f surface water waves. In steady conditions, laboratory experiments are carried out for multiple purposes either for researches or for practical problems. In both cases envelope equations are useful for understanding qualitative and quantitative results. The Ginzburg-Landau equation provides an excellent model for systems of that kind with remarkable patterns. Taking into account the above paragraph the main aim of our work is to generate waves in a water tank with almost a symmetric spectrum according to Akhmediev (2011) and thus, to produce a succession of rogue waves. The envelope of these waves gives us some patterns whose model is a type of Ginzburg-Landau equation, Danilov et al (1988). From a heuristic point of view the link between the experiment and the model is achieved. Further, the next step consists of changing generating parameters on the water tank and also the coefficients of the Ginzburg-Landau equation, Lechuga (2013) in order to reach a sufficient good approach.
Winding number instability in the phase-turbulence regime of the complex Ginzburg-Landau equation
Montagne, R; San Miguel, M
1996-01-01
We give a statistical characterization of states with nonzero winding number in the Phase Turbulence (PT) regime of the one-dimensional Complex Ginzburg-Landau equation. We find that states with winding number larger than a critical one are unstable, in the sense that they decay to states with smaller winding number. The transition from Phase to Defect Turbulence is interpreted as an ergodicity breaking transition which occurs when the range of stable winding numbers vanishes. Asymptotically stable states which are not spatio-temporally chaotic are described within the PT regime of nonzero winding number.
Spectrum of the linearized operator for the Ginzburg-Landau equation
Tai-Chia Lin
2000-06-01
Full Text Available We study the spectrum of the linearized operator for the Ginzburg-Landau equation about a symmetric vortex solution with degree one. We show that the smallest eigenvalue of the linearized operator has multiplicity two, and then we describe its behavior as a small parameter approaches zero. We also find a positive lower bound for all the other eigenvalues, and find estimates of the first eigenfunction. Then using these results, we give partial results on the dynamics of vortices in the nonlinear heat and Schrodinger equations.
Relation between the complex Ginzburg-Landau equation and reaction-diffusion System
Shao Xin; Ren Yi; Ouyang Qi
2006-01-01
The complex Ginzburg-Landau equation(CGLE)has been used to describe the travelling wave behaviour in reaction-diffusion (RD) systems. We argue that this description is valid only when the RD system is close to the Hopf bifurcation,and is not valid when a RD system is away from the onset.To test this,we study spirals and anti-spirals in the chlorite-iodide-malonic acid (CIMA) reaction and the corresponding CGLE.Numerical simulations confirm that the CGLE can only be applied to the CIMA reaction when it is very near the Hopf onset.
Ginzburg-Landau-type multiphase field model for competing fcc and bcc nucleation.
Tóth, G I; Morris, J R; Gránásy, L
2011-01-28
We address crystal nucleation and fcc-bcc phase selection in alloys using a multiphase field model that relies on Ginzburg-Landau free energies of the liquid-fcc, liquid-bcc, and fcc-bcc subsystems, and determine the properties of the nuclei as a function of composition, temperature, and structure. With a realistic choice for the free energy of the fcc-bcc interface, the model predicts well the fcc-bcc phase-selection boundary in the Fe-Ni system.
Local times for solutions of the complex Ginzburg-Landau equation and the inviscid limit
Shirikyan, Armen
2010-01-01
We consider the behaviour of the distribution for stationary solutions of the complex Ginzburg-Landau equation perturbed by a random force. It was proved earlier that if the random force is proportional to the square root of the viscosity, then the family of stationary measures possesses an accumulation point as the viscosity goes to zero. We show that if $\\mu$ is such point, then the distributions of the L^2 norm and of the energy possess a density with respect to the Lebesgue measure. The proofs are based on It\\^o's formula and some properties of local time for semimartingales.
Thin film limits for Ginzburg--Landau with strong applied magnetic fields
Alama, Stan; Galvão-Sousa, Bernardo
2009-01-01
In this work, we study thin-film limits of the full three-dimensional Ginzburg-Landau model for a superconductor in an applied magnetic field oriented obliquely to the film surface. We obtain Gamma-convergence results in several regimes, determined by the asymptotic ratio between the magnitude of the parallel applied magnetic field and the thickness of the film. Depending on the regime, we show that there may be a decrease in the density of Cooper pairs. We also show that in the case of variable thickness of the film, its geometry will affect the effective applied magnetic field, thus influencing the position of vortices.
WANG Xin; TIAN Xu; WANG Hong-Li; OUYANG Qi; LI Hao
2004-01-01
@@ The effect of additive coloured noises, which are correlated in time, on one-dimensional travelling waves in the complex Ginzburg-Landau equation is studied by numerical simulations. We found that a small coloured noise with temporal correlation could considerably influence the stability of one-dimensional wave trains. There exists an optimal temporal correlation of noise where travelling waves are the most vulnerable. To elucidate the phenomena, we statistically calculated the convective velocities Va of the wave packets, and found that the coloured noise with an appropriate temporal correlation can decrease Va, making the system convectively more unstable.
Incompatibility of Time-Dependent Bogoliubov-de-Gennes and Ginzburg-Landau Equations
Frank, Rupert L.; Hainzl, Christian; Schlein, Benjamin; Seiringer, Robert
2016-07-01
We study the time-dependent Bogoliubov-de-Gennes equations for generic translation-invariant fermionic many-body systems. For initial states that are close to thermal equilibrium states at temperatures near the critical temperature, we show that the magnitude of the order parameter stays approximately constant in time and, in particular, does not follow a time-dependent Ginzburg-Landau equation, which is often employed as a phenomenological description and predicts a decay of the order parameter in time. The full non-linear structure of the equations is necessary to understand this behavior.
Noise-induced synchronization of spatiotemporal chaos in the Ginzburg-Landau equation
Koronovskiĭ, A. A.; Popov, P. V.; Hramov, A. E.
2008-11-01
We have studied noise-induced synchronization in a distributed autooscillatory system described by the Ginzburg-Landau equations, which occur in a regime of chaotic spatiotemporal oscillations. A new regime of synchronous behavior, called incomplete noise-induced synchronization (INIS), is revealed, which can arise only in spatially distributed systems. The mechanism leading to the development of INIS in a distributed medium under the action of a distributed source of noise is analytically described. Good coincidence of analytical and numerical results is demonstrated.
Ginzburg-Landau free energy for molecular fluids: Determination and coarse-graining
Desgranges, Caroline; Delhommelle, Jerome
2017-02-01
Using molecular simulation, we determine Ginzburg-Landau free energy functions for molecular fluids. To this aim, we extend the Expanded Wang-Landau method to calculate the partition functions, number distributions and Landau free energies for Ar,CO2 and H2O . We then parametrize a coarse-grained free energy function of the density order parameter and assess the performance of this free energy function on its ability to model the onset of criticality in these systems. The resulting parameters can be readily used in hybrid atomistic/continuum simulations that connect the microscopic and mesoscopic length scales.
Spatiotemporal chaos control with a target wave in the complex Ginzburg-Landau equation system.
Jiang, Minxi; Wang, Xiaonan; Ouyang, Qi; Zhang, Hong
2004-05-01
An effective method for controlling spiral turbulence in spatially extended systems is realized by introducing a spatially localized inhomogeneity into a two-dimensional system described by the complex Ginzburg-Landau equation. Our numerical simulations show that with the introduction of the inhomogeneity, a target wave can be produced, which will sweep all spiral defects out of the boundary of the system. The effects exist in certain parameter regions where the spiral waves are absolutely unstable. A theoretical explanation is given to reveal the underlying mechanism.
Gaididei, Yu. B.; Christiansen, Peter Leth
2008-01-01
We study a parametrically driven Ginzburg-Landau equation model with nonlinear management. The system is made of laterally coupled long active waveguides placed along a circumference. Stationary solutions of three kinds are found: periodic Ising states and two types of Bloch states, staggered...... and unstaggered. The stability of these states is investigated analytically and numerically. The nonlinear dynamics of the Bloch states are described by a complex Ginzburg-Landau equation with linear and nonlinear parametric driving. The switching between the staggered and unstaggered Bloch states under...
Lijun Song; Lu Li; Guosheng Zhou
2005-01-01
The effect of third-order dispersion on breathing localized solutions in the quintic complex GinzburgLandau (CGL) equation is investigated. It is found that even small third-order dispersion can cause dramatic changes in the behavior of the solutions, such as breathing solution asymmetrically and travelling slowly towards the right for the positive third-order dispersion.
Alstrøm, Tommy Sonne; Sørensen, Mads Peter; Pedersen, Niels Falsig
2010-01-01
The time-dependent Ginzburg-Landau equation is solved numerically for type-II superconductors of complex geometry using the finite element method. The geometry has a marked influence on the magnetic vortex distribution and the vortex dynamics. We have observed generation of giant vortices...
Ginzburg-Landau vortex dynamics driven by an applied boundary current
Tice, Ian
2009-01-01
In this paper we study the time-dependent Ginzburg-Landau equations on a smooth, bounded domain $\\Omega \\subset \\Rn{2}$, subject to both an applied magnetic field and an applied boundary current. We model the boundary current by a gauge invariant inhomogeneous Neumann boundary condition. After proving well-posedness of the equations with this boundary condition, we study the evolution of the energy of the solutions, deriving an upper bound for the energy growth. We then turn to the study of the dynamics of the vortices of the solutions in the limit $\\ep \\to 0$. We first consider the original time scale, in which the vortices do not move and the solutions undergo a ``phase relaxation.'' Then we study an accelerated time scale in which the vortices move according to a derived dynamical law. In the dynamical law, we identify a novel Lorentz force term induced by the applied boundary current.
Wound-up phase turbulence in the Complex Ginzburg-Landau equation
Montagne, R; Amengual, A; Miguel, M S
1997-01-01
We consider phase turbulent regimes with nonzero winding number in the one-dimensional Complex Ginzburg-Landau equation. We find that phase turbulent states with winding number larger than a critical one are only transients and decay to states within a range of allowed winding numbers. The analogy with the Eckhaus instability for non-turbulent waves is stressed. The transition from phase to defect turbulence is interpreted as an ergodicity breaking transition which occurs when the range of allowed winding numbers vanishes. We explain the states reached at long times in terms of three basic states, namely quasiperiodic states, frozen turbulence states, and riding turbulence states. Justification and some insight into them is obtained from an analysis of a phase equation for nonzero winding number: rigidly moving solutions of this equation, which correspond to quasiperiodic and frozen turbulence states, are understood in terms of periodic and chaotic solutions of an associated system of ordinary differential eq...
Novel asymmetric representation method for solving the higher-order Ginzburg-Landau equation.
Wong, Pring; Pang, Lihui; Wu, Ye; Lei, Ming; Liu, Wenjun
2016-04-18
In ultrafast optics, optical pulses are generated to be of shorter pulse duration, which has enormous significance to industrial applications and scientific research. The ultrashort pulse evolution in fiber lasers can be described by the higher-order Ginzburg-Landau (GL) equation. However, analytic soliton solutions for this equation have not been obtained by use of existing methods. In this paper, a novel method is proposed to deal with this equation. The analytic soliton solution is obtained for the first time, and is proved to be stable against amplitude perturbations. Through the split-step Fourier method, the bright soliton solution is studied numerically. The analytic results here may extend the integrable methods, and could be used to study soliton dynamics for some equations in other disciplines. It may also provide the other way to obtain two-soliton solutions for higher-order GL equations.
Ginzburg-Landau方程的齐次化%Homogenization of Ginzburg-Landau Equations
Abdellatif Messaoudi
2005-01-01
This paper deals with the asymptotic behavior of solutions of the Ginzburg-Landau boundary value problem with respect to two parameters ε and δ. We discuss the existence and uniqueness of solutions and their asymptotic behavior asε→0, as well as the homogenization of problems Pδε and Pδ as δ→ 0.%本文研究了Ginzburg-Landau边值问题加罚齐次化方程解的存在唯一性,文中通过引入两个参数ε和δ,分别研究ε→0和δ→0时,上述方程解的渐近性态得到的.
Existence and decay estimates of solutions to complex Ginzburg-Landau type equations
Shimotsuma, Daisuke; Yokota, Tomomi; Yoshii, Kentarou
2016-02-01
This paper deals with the initial-boundary value problem (denoted by (CGL)) for the complex Ginzburg-Landau type equation ∂u/∂t - (λ + iα) Δu + (κ + iβ)| u | q - 1 u - γu = 0 with initial data u0 ∈Lp (Ω) in the case 1 0, α , β , γ , κ ∈ R. There are a lot of studies on local and global existence of solutions to (CGL) including the physically relevant case q = 3 and κ > 0. This paper gives existence results with precise properties of solutions and rigorous proof from a mathematical point of view. The physically relevant case can be considered as a special case of the results. Moreover, in the case κ inequality with Re .
Attractors of the Derivative Complex Ginzburg-Landau Equation in Unbounded Domains
GUO Bo-ling; HAN Yong-qian
2005-01-01
@@ We consider the following initial boundary problem of derivative complex Ginzburg-Landau (DCGL) equation ut-(a1+ia2)△u-X0u+(b1+ib2)|u|2σu+|u|2λ·▽u+u2μ·▽u=g(x), (1) u(x,t = 0) = u0(x), u| Ω = 0 (2) in an unbounded domain Ω R2. Here u is a complex valued function of (x, t) ∈Ω× R +,a1 ＞ 0, b1 ＞ 0, σ＞ 0, a2, b2 ∈ R, λ = (λ1, λ2) and μ = (μ1,μ2) are complex constant vector.
Subharmonic phase clusters in the complex Ginzburg-Landau equation with nonlinear global coupling.
García-Morales, Vladimir; Orlov, Alexander; Krischer, Katharina
2010-12-01
A wide variety of subharmonic n -phase cluster patterns was observed in experiments with spatially extended chemical and electrochemical oscillators. These patterns cannot be captured with a phase model. We demonstrate that the introduction of a nonlinear global coupling (NGC) in the complex Ginzburg-Landau equation has subharmonic cluster pattern solutions in wide parameter ranges. The NGC introduces a conservation law for the oscillatory state of the homogeneous mode, which describes the strong oscillations of the mean field in the experiments. We show that the NGC causes a pronounced 2:1 self-resonance on any spatial inhomogeneity, leading to two-phase subharmonic clustering, as well as additional higher resonances. Nonequilibrium Ising-Bloch transitions occur as the coupling strength is varied.
Freeman, W J; Obinata, M; Vitiello, G
2011-01-01
The formation of amplitude modulated and phase modulated assemblies of neurons is observed in the brain functional activity. The study of the formation of such structures requires that the analysis has to be organized in hierarchical levels, microscopic, mesoscopic, macroscopic, each with its characteristic space-time scales and the various forms of energy, electric, chemical, thermal produced and used by the brain. In this paper, we discuss the microscopic dynamics underlying the mesoscopic and the macroscopic levels and focus our attention on the thermodynamics of the non-equilibrium phase transitions. We obtain the time-dependent Ginzburg-Landau equation for the non-stationary regime and consider the formation of topologically non-trivial structures such as the vortex solution. The power laws observed in functional activities of the brain is also discussed and related to coherent states characterizing the many-body dissipative model of brain.
Koshelev, A. E.; Sadovskyy, I. A.; Phillips, C. L.; Glatz, A.
2016-02-29
Introducing nanoparticles into superconducting materials has emerged as an efficient route to enhance their current-carrying capability. We address the problem of optimizing vortex pinning landscape for randomly distributed metallic spherical inclusions using large-scale numerical simulations of time- dependent Ginzburg-Landau equations. We found the size and density of particles for which the highest critical current is realized in a fixed magnetic field. For each particle size and magnetic field, the critical current reaches a maximum value at a certain particle density, which typically corresponds to 15{23% of the total volume being replaced by nonsuperconducting material. For fixed diameter, this optimal particle density increases with the magnetic field. Moreover, we found that the optimal particle diameter slowly decreases with the magnetic field from 4.5 to 2.5 coherence lengths at a given temperature. This result shows that pinning landscapes have to be designed for specific applications taking into account relevant magnetic field scales.
Coarse graining from variationally enhanced sampling applied to the Ginzburg-Landau model.
Invernizzi, Michele; Valsson, Omar; Parrinello, Michele
2017-03-28
A powerful way to deal with a complex system is to build a coarse-grained model capable of catching its main physical features, while being computationally affordable. Inevitably, such coarse-grained models introduce a set of phenomenological parameters, which are often not easily deducible from the underlying atomistic system. We present a unique approach to the calculation of these parameters, based on the recently introduced variationally enhanced sampling method. It allows us to obtain the parameters from atomistic simulations, providing thus a direct connection between the microscopic and the mesoscopic scale. The coarse-grained model we consider is that of Ginzburg-Landau, valid around a second-order critical point. In particular, we use it to describe a Lennard-Jones fluid in the region close to the liquid-vapor critical point. The procedure is general and can be adapted to other coarse-grained models.
Limiting Motion for the Parabolic Ginzburg-Landau Equation with Infinite Energy Data
Côte, Delphine; Côte, Raphaël
2017-03-01
We study a class of solutions to the parabolic Ginzburg-Landau equation in dimension 2 or higher, with ill-prepared infinite energy initial data. We show that, asymptotically, the vorticity evolves according to motion by mean curvature in Brakke's weak formulation. Then, we prove that in the plane, point vortices do not move in the original time scale. These results extend the works of Bethuel, Orlandi and Smets (Ann Math (2) 163(1):37-163, 2006; Duke Math J 130(3):523-614, 2005) to infinite energy data; they allow us to consider point vortices on a lattice (in dimension 2), or filament vortices of infinite length (in dimension 3).
Amplitude wave in one-dimensional complex Ginzburg-Landau equation
Xie Ling-Ling; Gao Jia-Zhen; Xie Wei-Miao; Gao Ji-Hua
2011-01-01
The wave propagation in the one-dimensional complex Ginzburg-Landau equation (CGLE) is studied by considering a wave source at the system boundary.A special propagation region,which is an island-shaped zone surrounded by the defect turbulence in the system parameter space,is observed in our numerical experiment.The wave signal spreads in the whole space with a novel amplitude wave pattern in the area.The relevant factors of the pattern formation,such as the wave speed,the maximum propagating distance and the oscillatory frequency,are studied in detail.The stability and the generality of the region are testified by adopting various initial conditions.This finding of the amplitude pattern extends the wave propagation region in the parameter space and presents a new signal transmission mode,and is therefore expected to be of much importance.
Critical initial-slip scaling for the noisy complex Ginzburg-Landau equation
Liu, Weigang; Täuber, Uwe C.
2016-10-01
We employ the perturbative fieldtheoretic renormalization group method to investigate the universal critical behavior near the continuous non-equilibrium phase transition in the complex Ginzburg-Landau equation with additive white noise. This stochastic partial differential describes a remarkably wide range of physical systems: coupled nonlinear oscillators subject to external noise near a Hopf bifurcation instability; spontaneous structure formation in non-equilibrium systems, e.g., in cyclically competing populations; and driven-dissipative Bose-Einstein condensation, realized in open systems on the interface of quantum optics and many-body physics, such as cold atomic gases and exciton-polaritons in pumped semiconductor quantum wells in optical cavities. Our starting point is a noisy, dissipative Gross-Pitaevski or nonlinear Schrödinger equation, or equivalently purely relaxational kinetics originating from a complex-valued Landau-Ginzburg functional, which generalizes the standard equilibrium model A critical dynamics of a non-conserved complex order parameter field. We study the universal critical behavior of this system in the early stages of its relaxation from a Gaussian-weighted fully randomized initial state. In this critical aging regime, time translation invariance is broken, and the dynamics is characterized by the stationary static and dynamic critical exponents, as well as an independent ‘initial-slip’ exponent. We show that to first order in the dimensional expansion about the upper critical dimension, this initial-slip exponent in the complex Ginzburg-Landau equation is identical to its equilibrium model A counterpart. We furthermore employ the renormalization group flow equations as well as construct a suitable complex spherical model extension to argue that this conclusion likely remains true to all orders in the perturbation expansion.
王保祥
2003-01-01
Considering the Cauchy problem for the critical complex Ginzburg-Landau equation in H1(Rn), weshall show the asymptotic behavior for its solutions in C(0, ∞; H1 (Rn)) ∩ L2(0, ∞; H1,2n/(n-2)(Rn )), n≥ 3.Analogous results also hold in the case that the nonlinearity has the subcritical power in H1(Rn), n≥ 1.
Instabilities and splitting of pulses in coupled Ginzburg-Landau equations
Sakaguchi, H
2001-01-01
We introduce a general system of two coupled cubic complex Ginzburg- Landau (GL) equations that admits exact solitary-pulse (SP) solutions with a stable zero background. Besides representing a class of systems of the GL type, it also describes a dual-core nonlinear optical fiber with gain in one core and losses in the other. By means of systematic simulations, we study generic transformations of SPs in this system, which turn out to be: cascading multiplication of pulses through a subcritical Hopf bifurcation, which eventually leads to a spatio-temporal chaos; splitting of SP into stable traveling pulses; and a symmetry-breaking bifurcation transforming a standing SP into a traveling one. In some parameter region, the Hopf bifurcation is found to be supercritical, which gives rise to stable breathers. Travelling breathers are also possible in the system considered. In a certain parameter region, stable standing SPs, moving permanent-shape ones, and traveling breathers all coexist. In that case, we study colli...
Localized Pulsating Solutions of the Generalized Complex Cubic-Quintic Ginzburg-Landau Equation
Ivan M. Uzunov
2014-01-01
Full Text Available We study the dynamics of the localized pulsating solutions of generalized complex cubic-quintic Ginzburg-Landau equation (CCQGLE in the presence of intrapulse Raman scattering (IRS. We present an approach for identification of periodic attractors of the generalized CCQGLE. Using ansatz of the travelling wave and fixing some relations between the material parameters, we derive the strongly nonlinear Lienard-Van der Pol equation for the amplitude of the nonlinear wave. Next, we apply the Melnikov method to this equation to analyze the possibility of existence of limit cycles. For a set of fixed parameters we show the existence of limit cycle that arises around a closed phase trajectory of the unperturbed system and prove its stability. We apply the Melnikov method also to the equation of Duffing-Van der Pol oscillator used for the investigation of the influence of the IRS on the bandwidth limited amplification. We prove the existence and stability of a limit cycle that arises in a neighborhood of a homoclinic trajectory of the corresponding unperturbed system. The condition of existence of the limit cycle derived here coincides with the relation between the critical value of velocity and the amplitude of the solitary wave solution (Uzunov, 2011.
Vortices with scalar condensates in two-component Ginzburg-Landau systems
Forgacs, Peter
2016-01-01
In a class of two-component Ginzburg-Landau models (TCGL) with a U(1)$\\times$U(1) symmetric potential, vortices with a condensate at their core may have significantly lower energies than the Abrikosov-Nielsen-Olesen (ANO) ones. On the example of liquid metallic hydrogen (LMH) above the critical temperature for protons we show that the ANO vortices become unstable against core-condensation, while condensate-core (CC) vortices are stable. For LMH the ratio of the masses of the two types of condensates, $M=m_2/m_1$ is large, and then as a consequence the energy per flux quantum of the vortices, $E_n/n$ becomes a non-monotonous function of the number of flux quanta, $n$. This leads to yet another manifestation of neither type 1 nor type 2, (type 1.5) superconductivity: superconducting and normal domains coexist while various "giant" vortices form. We note that LMH provides a particularly clean example of type 1.5 state as the interband coupling between electronic and protonic Cooper-pairs is forbidden.
Ergodicity of stochastic real Ginzburg-Landau equation driven by $\\alpha$-stable noises
Xu, Lihu
2012-01-01
We study the ergodicity of stochastic real Ginzburg-Landau equation driven by additive $\\alpha$-stable noises, showing that as $\\alpha \\in (3/2,2)$, this stochastic system admits a unique invariant measure. After establishing the existence of invariant measures by the same method as in [9], we prove that the system is strong Feller and accessible to zero. These two properties imply the ergodicity by a simple but useful criterion in [16]. To establish the strong Feller property, we need to truncate the nonlinearity and apply a gradient estimate established in [26] (or see [24]} for a general version for the finite dimension systems). Because the solution has discontinuous trajectories and the nonlinearity is not Lipschitz, we can not solve a control problem to get irreducibility. Alternatively, we use a replacement, i.e., the fact that the system is accessible to zero. In section 3, we establish a maximal inequality for stochastic $\\alpha$-stable convolution, which is crucial for studying the well-posedness, s...
Infrared behavior and fixed-point structure in the compactified Ginzburg--Landau model
Linhares, C A; Souza, M L
2011-01-01
We consider the Euclidean $N$-component Ginzburg--Landau model in $D$ dimensions, of which $d$ ($d\\leq D$) of them are compactified. As usual, temperature is introduced through the mass term in the Hamiltonian. This model can be interpreted as describing a system in a region of the $D$-dimensional space, limited by $d$ pairs of parallel planes, orthogonal to the coordinates axis $x_1,\\,x_2,\\,...,\\,x_d$. The planes in each pair are separated by distances $L_1,\\;L_2,\\; ...,\\,L_d$. For $D=3$, from a physical point of view, the system can be supposed to describe, in the cases of $d=1$, $d=2$, and $d=3$, respectively, a superconducting material in the form of a film, of an infinitely long wire having a retangular cross-section and of a brick-shaped grain. We investigate in the large-$N$ limit the fixed-point structure of the model, in the absence or presence of an external magnetic field. An infrared-stable fixed point is found, whether of not an external magnetic field is applied, but for different ranges of valu...
Stable topological modes in two-dimensional Ginzburg-Landau models with trapping potentials
Mihalache, D; Skarka, V; Malomed, B A; Leblond, H; Aleksić, N B; Lederer, F
2010-01-01
Complex Ginzburg-Landau (CGL) models of laser media (with the cubic-quintic nonlinearity) do not contain an effective diffusion term, which makes all vortex solitons unstable in these models. Recently, it has been demonstrated that the addition of a two-dimensional periodic potential, which may be induced by a transverse grating in the laser cavity, to the CGL equation stabilizes compound (four-peak) vortices, but the most fundamental "crater-shaped" vortices (CSVs), alias vortex rings, which are, essentially, squeezed into a single cell of the potential, have not been found before in a stable form. In this work we report families of stable compact CSVs with vorticity S=1 in the CGL model with the external potential of two different types: an axisymmetric parabolic trap, and the periodic potential. In both cases, we identify stability region for the CSVs and for the fundamental solitons (S=0). Those CSVs which are unstable in the axisymmetric potential break up into robust dipoles. All the vortices with S=2 a...
Pressure Dependence of the Ginzburg-Landau Parameter in Superconducting YB6
Gabáni, S.; Orendáč, Mat.; Kušnír, J.; Gažo, E.; Pristáš, G.; Mori, T.; Flachbart, K.
2016-12-01
We present measurements of the superconducting critical temperature T_c , the upper critical field H_{c2} and the third critical field H_{c3} as a function of pressure in BCS type-II superconductor YB6 (T_c = 7.5 K, H_{c2}(0) = 270 mT and H_{c3}(0) = 450 mT at ambient pressure) up to 3 GPa. Magnetic susceptibility measurements down to 2 K have shown a negative pressure effect on T_c as well as on H_{c2} with slopes dT_c/dp = -0.531 K/GPa (d ln T_c/{dp} = -7.1 %/GPa) and dH_{c2}(0)/dp = -37 mT/GPa (d ln H_{c2}/{dp} = -14 %/GPa) , respectively. Parallel magnetoresistance measurements evidenced nearly the same slopes of d ln T_c/{dp} = -5.9 %/GPa (d ln H_{c3}/{dp} = -11 %/GPa) in the equal pressure range. From these results, the estimated pressure effect on the coherence length dξ (0)/{dp} = 2.05 nm/GPa together with the supposed zero pressure effect on the magnetic penetration depth (dλ (0)/{dp} ≈ 0 ) implies that the Ginzburg-Landau parameter κ (0) = {λ }(0)/{ξ }(0) decreases with pressure as dκ (0)/d{p} = -0.31/GPa. According to this decrease, a transition from type-II to type-I superconductor should be observed in YB6 at a critical pressure p_c ≈ 10 GPa.
Lee, Jeehye
2010-01-01
We present the first systematic {\\em ab initio} study of anti-ferrodistortive (AFD) order in Ruddlesden-Popper (RP) phases of strontium titanate, Sr$_{1+n}$Ti$_n$O$_{3n+1}$, as a function of both compressive epitaxial strain and phase number $n$. We find all RP phases to exhibit AFD order under a significant range of strains, recovering the bulk AFD order as $\\sim 1/n^2$. A Ginzburg-Landau Hamiltonian generalized to include inter-octahedral interactions reproduces our {\\em ab initio} results well, opening a pathway to understanding other nanostructured perovskite systems.
Aguirre, C. A.; González, J. D.; Barba-Ortega, J.
2016-01-01
The magnetic signature of a nanoscopic superconductor immersed in a magnetic applied field H_e is calculated numerically. The calculated magnetic susceptibility partial M / partial H_e of a superconducting nanoprism shows discontinuities and a quasiperiodic modulation at the vortex transition fields H_T (fields for which one or several vortices enter/leave the sample). In this contribution, we studied the influence of the sample size, the Ginzburg-Landau parameter κ and the deGennes parameter b on the magnetic susceptibility in a type-II isotropic superconductor. We found distinct signatures of the magnetic susceptibility when superconducting samples of two and three dimensions are considered.
雷雨田
2002-01-01
The behavior of radial minimizers for a Ginzburg-Landau type functional is considered. The weak convergence of minimizers in W1'n is improved to the strong convergence in W1,n. Some estimates of the rate of the convergence for the module of minimizers are presented.
Shokri, Ali; Afshari, Fatemeh
2015-12-01
In this article, a high-order compact alternating direction implicit (HOC-ADI) finite difference scheme is applied to numerical solution of the complex Ginzburg-Landau (GL) equation in two spatial dimensions with periodical boundary conditions. The GL equation has been used as a mathematical model for various pattern formation systems in mechanics, physics, and chemistry. The proposed HOC-ADI method has fourth-order accuracy in space and second-order accuracy in time. To avoid solving the nonlinear system and to increase the accuracy and efficiency of the method, we proposed the predictor-corrector scheme. Validation of the present numerical solutions has been conducted by comparing with the exact and other methods results and evidenced a good agreement.
Mvogo, Alain; Tambue, Antoine; Ben-Bolie, Germain H.; Kofané, Timoléon C.
2016-10-01
We investigate localized wave solutions in a network of Hindmarsh-Rose neural model taking into account the long-range diffusive couplings. We show by a specific analytical technique that the model equations in the infrared limit (wave number k → 0) can be governed by the complex fractional Ginzburg-Landau (CFGL) equation. According to the stiffness of the system, we propose both the semi and the linearly implicit Riesz fractional finite-difference schemes to solve efficiently the CFGL equation. The obtained fractional numerical solutions for the nerve impulse reveal localized short impulse properties. We also show the equivalence between the continuous CFGL and the discrete Hindmarsh-Rose models for relatively large network.
Reigada, Ramon; Buceta, Javier; Gómez, Jordi; Sagués, Francesc; Lindenberg, Katja
2008-01-14
Preferential affinity of cholesterol for saturated rather than unsaturated lipids underlies the thermodynamic process of the formation of lipid nanostructures in cell membranes, that is, of rafts. In this context, phase segregation of two-dimensional ternary lipid mixtures is formally studied from two different perspectives. The simplest approach is based on Monte Carlo simulations of an Ising model corresponding to two interconnected lattices, from which the basic features of the phenomenon are investigated. Then, the coarse-graining mean field procedure of the discrete Hamiltonian is adapted and a Ginzburg-Landau-like free energy expression is obtained. From this latter description, we construct kinetic equations that enable us to perform numerical simulations and to establish analytical phase separation criteria. Application of our formalism in the biological context is also discussed.
Merkurjev, Ekaterina; Bertozzi, Andrea; Yan, Xiaoran; Lerman, Kristina
2017-07-01
Recent advances in clustering have included continuous relaxations of the Cheeger cut problem and those which address its linear approximation using the graph Laplacian. In this paper, we show how to use the graph Laplacian to solve the fully nonlinear Cheeger cut problem, as well as the ratio cut optimization task. Both problems are connected to total variation minimization, and the related Ginzburg-Landau functional is used in the derivation of the methods. The graph framework discussed in this paper is undirected. The resulting algorithms are efficient ways to cluster the data into two classes, and they can be easily extended to the case of multiple classes, or used on a multiclass data set via recursive bipartitioning. In addition to showing results on benchmark data sets, we also show an application of the algorithm to hyperspectral video data.
Ge, Hong-xia; Meng, Xiang-pei; Cheng, Rong-jun; Lo, Siu-Ming
2011-10-01
In this paper, an extended car-following model considering the delay of the driver's response in sensing headway is proposed to describe the traffic jam. It is shown that the stability region decreases when the driver's physical delay in sensing headway increases. The phase transition among the freely moving phase, the coexisting phase, and the uniformly congested phase occurs below the critical point. By applying the reductive perturbation method, we get the time-dependent Ginzburg-Landau (TDGL) equation from the car-following model to describe the transition and critical phenomenon in traffic flow. We show the connection between the TDGL equation and the mKdV equation describing the traffic jam.
Facão, M; Carvalho, M I
2015-08-01
We found two stationary solutions of the cubic complex Ginzburg-Landau equation (CGLE) with an additional term modeling the delayed Raman scattering. Both solutions propagate with nonzero velocity. The solution that has lower peak amplitude is the continuation of the chirped soliton of the cubic CGLE and is unstable in all the parameter space of existence. The other solution is stable for values of nonlinear gain below a certain threshold. The solutions were found using a shooting method to integrate the ordinary differential equation that results from the evolution equation through a change of variables, and their stability was studied using the Evans function method. Additional integration of the evolution equation revealed the basis of attraction of the stable solutions. Furthermore, we have investigated the existence and stability of the high amplitude branch of solutions in the presence of other higher order terms originating from complex Raman, self-steepening, and imaginary group velocity.
Uzunov, Ivan M.; Georgiev, Zhivko D.
2014-10-01
We study the dynamics of the localized pulsating solutions of generalized complex cubic- quintic Ginzburg-Landau equation (CCQGLE) in the presence of intrapulse Raman scattering (IRS). We present an approach for identification of periodic attractors of the generalized CCQGLE. At first using ansatz of the travelling wave, and fixing some relations between the material parameters, we derive the strongly nonlinear Lienard - Van der Pol equation for the amplitude of the nonlinear wave. Next, we apply the Melnikov method to this equation to analyze the possibility of existence of limit cycles. For a set of fixed material parameters we show the existence of limit cycle that arises around a closed phase trajectory of the unperturbed system and prove its stability.
A note on the infrared behavior of the compactified Ginzburg--Landau model in a magnetic field
Linhares, C A; Souza, M L; 10.1209/0295-5075/96/31002
2011-01-01
We consider the Euclidean large-$N$ Ginzburg--Landau model in $D$ dimensions, $d$ ($d\\leq D$) of them being compactified. For D=3, the system can be supposed to describe, in the cases of d=1, d=2, and d=3, respectively, a superconducting material in the form of a film, of an infinitely long wire having a rectangular cross-section and of a brick-shaped grain. We investigate the fixed-point structure of the model, in the presence of an external magnetic field. An infrared-stable fixed points is found, which is independent of the number of compactified dimensions. This generalizes previous work for type-II superconducting films
Besse, Valentin; Leblond, Hervé; Mihalache, Dumitru; Malomed, Boris A
2013-01-01
We consider the kick- (tilt-) induced mobility of two-dimensional (2D) fundamental dissipative solitons in models of bulk lasing media based on the 2D complex Ginzburg-Landau equation including a spatially periodic potential (transverse grating). The depinning threshold, which depends on the orientation of the kick, is identified by means of systematic simulations and estimated by means of an analytical approximation. Various pattern-formation scenarios are found above the threshold. Most typically, the soliton, hopping between potential cells, leaves arrayed patterns of different sizes in its wake. In the single-pass-amplifier setup, this effect may be used as a mechanism for the selective pattern formation controlled by the tilt of the input beam. Freely moving solitons feature two distinct values of the established velocity. Elastic and inelastic collisions between free solitons and pinned arrayed patterns are studied too.
二带超导体中的扩展京兹堡-朗道方程%EXTENDED GINZBURG-LANDAU EQUATIONS FOR TWO-BAND SUPERCONDUCTORS
公丕锋; 张金锋; 路洪艳; 尹新国
2013-01-01
Recent observation of unusual vortex patterns in MgP2 single crystals raised speculations about possible "type-1.5" superconductivity in two-band materials,mixing the properties of both type-Ⅰ and type-Ⅱ superconductors.However,the strict application of the standard two-band Ginzburg-Landau(G-L) theory results in order pararneters of the two bands,and does not support the "type-1.5" behavior.So that we derive the extended GL formalism for a two-band s-wave superconductor and show that the two condensates have different spatial scales,with difference disappearing only in the limit T→ Tc.The extended version of the two-band GL formalism improves the validity of GL theory below Tc.%通过研究MgB2单晶体的非常规涡旋分布图,认为二带材料中可能有1.5型超导电性同时伴随着第一类超导体和第二类超导体的一些特性.但把二带京兹堡-朗道理论结果严格应用到二带序参量上,并不支持1.5型超导体行为.为此对于二带s-波超导体扩展了京兹堡-朗道形式,并发现这两种凝聚态有存在不同空间尺度,当T→Tc时有不同的衰减形式.通过二带京兹堡-朗道扩展形式扩展了京兹堡-朗道理论在T＜Tc时的有效性.
王雪琴; 高洪俊
2004-01-01
@@ 0 Introduction The Ginzburg-Landau type equations are simplified mathematical models for non-linear systems in mechanics, physics, and other areas. The time-dependent complex Ginzburg-Landau partial differential equation has been used to model phenomena in a number of different areas in physics, including phase transitions in non-equilibrium systems, instabilities in hydrodynamic systems, chemical turbulence, and thermodynamics([1]).
Koshelev, A. E.; Sadovskyy, I. A.; Phillips, C. L.; Glatz, A.
2016-02-01
Incorporating nanoparticles into superconducting materials has emerged as an efficient route to enhance their current-carrying capability. However, a thorough understanding of how these inclusions can be used in the most efficient way is still lacking. We address this problem of optimizing the vortex pinning landscape for randomly distributed metallic spherical inclusions using systematic large-scale numerical simulations of time-dependent Ginzburg-Landau equations. This approach allows us to predict the size and density of particles for which the highest critical current is realized. For a given particle size and magnetic field, the critical current reaches a maximum value at a particle density, which typically corresponds to 15%-23% of the total volume being replaced by the nonsuperconducting material. For a fixed diameter, this optimal particle density increases with the magnetic field. Moreover, we found that, as the magnetic field increased, the optimal particle diameter slowly decreases from 4.5 to 2.5 coherence lengths. This result shows that pinning landscapes have to be designed for specific applications taking into account relevant magnetic field scales.
随机Ginzburg-Landau方程的数值模拟%Numerical Simulation of Stochastic Ginzburg-Landau Equation
王廷春; 郭柏灵
2010-01-01
对随机Ginzburg-Landau方程进行数值研究,构造一个非线性差分格式和一个线性化差分格式.通过对确定性和随机Ginzburg-Landau方程的计算,表明所构造的格式具有较高的精度和较快的计算效率.对随机Ginzburg-Landau方程就噪声振幅的不同取值进行了数值模拟,并对由此引发的各种行为进行了描述.%Stochastic Ginzburg-Landau equation is numerically studied.A nonlinear difference scheme and a linearized scheme which avoid iteration in implementation are constructed.Numerical solutions of both deterministic equation and stochastic equation show accuracy and efficiency of the difference schemes.Numerical experiments with different noise amplitudes are presented and different types of behaviors are described.
Landau, I. L.; Ott, H. R.; Bilusic, A.; Smontara, A.; Berger, H.
2004-05-01
We present the results of magnetization measurements made on a NbSe2 single crystal for magnetic-field orientations both along and perpendicular to the c-axis of the crystal. The data were analyzed using a recently developed scaling procedure. We show that in the case of NbSe2, in addition to evaluating Hc2(T), the temperature dependence of the Ginzburg-Landau parameter may be extracted from the reversible-magnetization data. NbSe2, whose properties were extensively studied in the past, is used as a test case for the above-mentioned scaling procedure.
Val'kov, V. V.; Zlotnikov, A. O.
2016-12-01
On the basis of the periodic Anderson model, the microscopic Ginzburg-Landau equations for heavy-fermion superconductors in the coexistence phase of superconductivity and antiferromagnetism have been derived. The obtained expressions are valid in the vicinity of quantum critical point of heavy-fermion superconductors when the onset temperatures of antiferromagnetism and superconductivity are sufficiently close to each other. It is shown that the formation of antiferromagnetic ordering causes a decrease of the critical temperature of superconducting transition and order parameter in the phase of coexisting superconductivity and antiferromagnetism.
A time-dependent Ginzburg-Landau phase field formalism for shock-induced phase transitions
Haxhimali, Tomorr; Belof, Jonathan L.; Benedict, Lorin X.
2017-01-01
Phase-field models have become popular in the last two decades to describe a host of free-boundary problems. The strength of the method relies on implicitly describing the dynamics of surfaces and interfaces by a continuous scalar field that enters the global grand free energy functional of the system. Here we explore the potential utility of this method in order to describe shock-induced phase transitions. To this end we make use of the Multiphase Field Theory (MFT) to account for the existence of multiple phases during the transition, and we couple MFT to a hydrodynamic model in the context of a new LLNL code for phase transitions, SAMSA. As a demonstration of this approach, we apply our code to the α - ɛ-Fe phase transition under shock wave loading conditions and compare our results with experiments of Jensen et. al. [J. Appl. Phys., 105:103502 (2009)] and Barker and Hollenbach [J. Appl. Phys., 45:4872 (1974)].
Leconte, M; Jeon, Y M
2016-01-01
We derive and study a simple 1D nonlinear model for Edge Localized Mode (ELM) cycles. The nonlinear dynamics of a resistive ballooning mode is modeled via a single nonlinear equation of the Ginzburg-Landau type with a radial frequency gradient due to a prescribed ExB shear layer of finite extent. The nonlinearity is due to the feedback of the mode on the profile. We identify a novel mechanism, whereby the ELM only crosses the linear stability boundary once, and subsequently stays in the nonlinear regime for the full duration of the cycles. This is made possible by the shearing and merging of filaments by the ExB flow, which forces the system to oscillate between a radially-uniform solution and a non-uniform solitary - wave like solution. The model predicts a 'phase-jump' correlated with the ELM bursts.
Golubov, Alexandre Avraamovitch; Koshelev, A.E.
2003-01-01
We investigate the upper critical field in a dirty two-band superconductor within quasiclassical Usadel equations. The regime of very high anisotropy in the quasi-2D band, relevant for MgB2, is considered. We show that strong disparities in pairing interactions and diffusion constant anisotropies fo
Achilleos, V; Bishop, A R; Diamantidis, S; Frantzeskakis, D J; Horikis, T P; Karachalios, N I; Kevrekidis, P G
2016-07-01
The dynamical behavior of a higher-order cubic Ginzburg-Landau equation is found to include a wide range of scenarios due to the interplay of higher-order physically relevant terms. We find that the competition between the third-order dispersion and stimulated Raman scattering effects gives rise to rich dynamics: this extends from Poincaré-Bendixson-type scenarios, in the sense that bounded solutions may converge either to distinct equilibria via orbital connections or to space-time periodic solutions, to the emergence of almost periodic and chaotic behavior. One of our main results is that third-order dispersion has a dominant role in the development of such complex dynamics, since it can be chiefly responsible (even in the absence of other higher-order effects) for the existence of periodic, quasiperiodic, and chaotic spatiotemporal structures. Suitable low-dimensional phase-space diagnostics are devised and used to illustrate the different possibilities and identify their respective parametric intervals over multiple parameters of the model.
Configuración de Vórtices en Películas Finas: Teoría Ginzburg-Landau No Lineal
José J. Barba-Ortega
2011-12-01
Full Text Available En este trabajo investigamos teóricamente el estado de Shubnikov en una película superconductora con sección transversal cuadrada con un defecto inserido en su centro. La muestra está inmersa en un campo magnético uniforme y homogéneo aplicado perpendicularmente a su plano. Asumimos que el defecto interno está lleno de un material metálico. La presencia de dicho material se simula mediante las condiciones de contorno de de Gennes, vía la longitud de extrapolación, parámetro b>0. Utilizando la teoría Ginzburg-Landau dependiente del tiempo con el método de variables de unión, estudiamos el número de vórtices, supercorrientes, curvas de magnetización y energía libre en función del campo magnético aplicado. Espontáneamente una interacción de un par vórtice-antivórtice (V-AV dentro de la muestra puede aparecer. Esta interacción puede ocurrir dentro o fuera del defecto metálico. Podemos apreciar que la aniquilación del par VAV ocurre cada vez más cerca del defecto a medida que b→0 (materiales más metálicos.
Achilleos, V.; Bishop, A. R.; Diamantidis, S.; Frantzeskakis, D. J.; Horikis, T. P.; Karachalios, N. I.; Kevrekidis, P. G.
2016-07-01
The dynamical behavior of a higher-order cubic Ginzburg-Landau equation is found to include a wide range of scenarios due to the interplay of higher-order physically relevant terms. We find that the competition between the third-order dispersion and stimulated Raman scattering effects gives rise to rich dynamics: this extends from Poincaré-Bendixson-type scenarios, in the sense that bounded solutions may converge either to distinct equilibria via orbital connections or to space-time periodic solutions, to the emergence of almost periodic and chaotic behavior. One of our main results is that third-order dispersion has a dominant role in the development of such complex dynamics, since it can be chiefly responsible (even in the absence of other higher-order effects) for the existence of periodic, quasiperiodic, and chaotic spatiotemporal structures. Suitable low-dimensional phase-space diagnostics are devised and used to illustrate the different possibilities and identify their respective parametric intervals over multiple parameters of the model.
Kengne, E.; Lakhssassi, A.; Vaillancourt, R.; Liu, Wu-Ming
2012-12-01
We present a double-mapping method (D-MM), a natural combination of a similarity with F-expansion methods, for obtaining general solvable nonlinear evolution equations. We focus on variable-coefficients complex Ginzburg-Landau equations (VCCGLE) with multi-body interactions. We show that it is easy by this method to find a large class of exact solutions of Gross-Pitaevskii and Gross-Pitaevskii-Ginzburg equations. We apply the D-MM to investigate the dynamics of Bose-Einstein condensation with two- and three-body interactions. As a surprising result, we obtained that it is very easy to use the built D-MM to obtain a large class of exact solutions of VCCGLE with two-body interactions via a generalized VCCGLE with two- and three-body interactions containing cubic-derivative terms. The results show that the proposed method is direct, concise, elementary, and effective, and can be a very effective and powerful mathematical tool for solving many other nonlinear evolution equations in physics.
Haxhimali, Tomorr; Belof, Jonathan; Benedict, Lorin
2015-06-01
Phase-field models have become popular in last two decades to describe a host of free-boundary problems. The strength of the method relies on implicitly describing the dynamics of surfaces and interfaces by continuous scalar field that enter in the global grand free energy functional of the system. We adapt this method in order to describe shock-induced phase transition. To this end we make use of the Multiphase Field Theory (MFT) to account for the existence of multiple phases during the transition. In this talk I will initially describe the constitutive equations that couple the dynamic of the phase field with that of the thermodynamic fields like T, P, c etc. I will then give details on developing a thermodynamically consistent phase-field interpolation function for multiple-phase system in the context of shock-induced phase-transition. At the end I will briefly comment on relating the dynamics of the interfaces in the shock/ramp compression to the Kardar-Parisi-Zhang equation. This work is performed under the auspices of the U. S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.
戴振祥; 徐园芬
2011-01-01
Some exact traveling wave solutions were found of generalized Zakharov equation and Ginzburg-Landau equation. What are the dynamical behavior of these traveling wave solutions and how do they depend on the parameters of the systems? These questions by using the method of dynamical systems were answered. Six exact explicit parametric representations of the traveling wave solutions for two equations were given.%获得了广义的Zakharov方程和Ginzburg-Landau方程的一些精确行波解,这些行波解有什么样的动力学行为,它们怎样依赖系统的参数?该文将利用动力系统方法回答这些问题,给出了两个方程的6个行波解的精确参数表达式.
Ginzburg-Landau型泛函极小元的W1,p收敛性%W1，p Convergence of the Minimizers for a Ginzburg-Landau Type Function
雷雨田
2001-01-01
Let uε be minimizers for the Ginzburg-Landau type function Eε(u,G) in W1，pg(G,Rn). It is proved that as ε→0, uε→up in W1，p, where up is a map such that 「G｜ u｜p is a least p-energy on W1，pg(G,Sn-1).%证明当ε→0时，一类Ginzburg-Landau型泛函Eε(u，G)于集合W1，pg(G，Rn)中的极小元uε在W1，p下收敛到以g为边值的p能量极小up.
Coskun, E. [Northern Illinois Univ., DeKalb, IL (United States). Dept. of Mathematical Sciences; Kwong, M.K. [Argonne National Lab., IL (United States)
1995-09-01
Time-dependent Ginzburg-Landau (TDGL) equations are considered for modeling a thin-film finite size superconductor placed under magnetic field. The problem then leads to the use of so-called natural boundary conditions. Computational domain is partitioned into subdomains and bond variables are used in obtaining the corresponding discrete system of equations. An efficient time-differencing method based on the Forward Euler method is developed. Finally, a variable strength magnetic field resulting in a vortex motion in Type II High {Tc} superconducting films is introduced. The authors tackled the problem using two different state-of-the-art parallel computing tools: BlockComm/Chameleon and PCN. They had access to two high-performance distributed memory supercomputers: the Intel iPSC/860 and IBM SP1. They also tested the codes using, as a parallel computing environment, a cluster of Sun Sparc workstations.
Fink, H.J. (Department of Electrical Engineering and Computer Science, University of California, Davis, Davis, California 95616 (USA)); Buisson, O.; Pannetier, B. (Centre de Recherches sur les Tres Basses Temperature, Centre National de la Recherche Scientifique, Boite Postale 166X, 38042 Grenoble CEDEX, France (FR))
1991-05-01
The largest supercurrent which can be injected into a superconducting microladder was calculated as a function of nodal spacing {ital scrL} and temperature for zero magnetic flux using (i) exact solutions of the Ginzburg-Landau equation in terms of Jacobian elliptic functions and (ii) approximate solutions in terms of hyperbolic functions. The agreement is good for {ital scrL}/{xi}({ital T}){lt}3, where {xi}({ital T}) is the temperature-dependent coherence length. Since solution (ii) is much simpler than solution (i), it is of considerable value when calculating critical currents of micronets with nodal spacings comparable to {xi}({ital T}). We find that the temperature-dependent critical current deviates significantly from the classical 3/2 power law of the Ginzburg-Landau theory. Preliminary experiments on a submicrometer ladder confirm such deviations.
On field theory quantization around instantons
Anselmi, D
2009-01-01
With the perspective of looking for experimentally detectable physical applications of the so-called topological embedding, a procedure recently proposed by the author for quantizing a field theory around a non-discrete space of classical minima (instantons, for example), the physical implications are discussed in a ``theoretical'' framework, the ideas are collected in a simple logical scheme and the topological version of the Ginzburg-Landau theory of superconductivity is solved in the intermediate situation between type I and type II superconductors.
Murray, James M; Tesanović, Zlatko
2010-07-16
A Ginzburg-Landau approach to fluctuations of a layered superconductor in a magnetic field is used to show that the interlayer coupling can be incorporated within an interacting self-consistent theory of a single layer, in the limit of a large number of neighboring layers. The theory exhibits two phase transitions-a vortex liquid-to-solid transition is followed by a Bose-Einstein condensation into the Abrikosov lattice-illustrating the essential role of interlayer coupling. By using this theory, explicit expressions for magnetization, specific heat, and fluctuation conductivity are derived. We compare our results with recent experimental data on the iron-pnictide superconductors.
Schauder-Tychonoff Fixed-Point Theorem in Theory of Superconductivity
Mariusz Gil
2013-01-01
Full Text Available We study the existence of mild solutions to the time-dependent Ginzburg-Landau ((TDGL, for short equations on an unbounded interval. The rapidity of the growth of those solutions is characterized. We investigate the local and global attractivity of solutions of TDGL equations and we describe their asymptotic behaviour. The TDGL equations model the state of a superconducting sample in a magnetic field near critical temperature. This paper is based on the theory of Banach space, Fréchet space, and Sobolew space.
Theory of specific heat of vortex liquid of high T c superconductors
Bai, Chen; Chi, Cheng; Wang, Jiangfan
2016-10-01
Superconducting thermal fluctuation (STF) plays an important role in both thermodynamic and transport properties in the vortex liquid phase of high T c superconductors. It was widely observed in the vicinity of the critical transition temperature. In the framework of Ginzburg-Landau-Lawrence-Doniach theory in magnetic field, a self-consistent analysis of STF including all Landau levels is given. Besides that, we calculate the contribution of STF to specific heat in vortex liquid phase for high T c cuprate superconductors, and the fitting results are in good agreement with experimental data. Project supported by the National Natural Science Foundation of China (Grant No. 11274018).
On Ginzburg-Landau Vortices of Superconducting Thin Films
Shi Jin DING; Qiang DU
2006-01-01
In this paper, we discuss the vortex structure of the superconducting thin films placed in a magnetic field. We show that the global minimizer of the functional modelling the superconducting thin films has a bounded number of vortices when the applied magnetic field hex ＜ Hc1 + K log |log ε|where Hc1 is the lower critical field of the film obtained by Ding and Du in SIAM J. Math. Anal.,2002. The locations of the vortices are also given.
The radial-hedgehog solution in Landau–de Gennes' theory for nematic liquid crystals
MAJUMDAR, APALA
2011-09-06
We study the radial-hedgehog solution in a three-dimensional spherical droplet, with homeotropic boundary conditions, within the Landau-de Gennes theory for nematic liquid crystals. The radial-hedgehog solution is a candidate for a global Landau-de Gennes minimiser in this model framework and is also a prototype configuration for studying isolated point defects in condensed matter physics. The static properties of the radial-hedgehog solution are governed by a non-linear singular ordinary differential equation. We study the analogies between Ginzburg-Landau vortices and the radial-hedgehog solution and demonstrate a Ginzburg-Landau limit for the Landau-de Gennes theory. We prove that the radial-hedgehog solution is not the global Landau-de Gennes minimiser for droplets of finite radius and sufficiently low temperatures and prove the stability of the radial-hedgehog solution in other parameter regimes. These results contain quantitative information about the effect of geometry and temperature on the properties of the radial-hedgehog solution and the associated biaxial instabilities. © Copyright Cambridge University Press 2011.
Kim, Ki-Seok; Kim, Youngman; Ko, Yumi
2011-01-01
It is beyond the present techniques based on perturbation theory to reveal the nature of phase transitions in strongly interacting field theories. Recently, the holographic approach has provided us with an effective dual description, mapping strongly coupled conformal field theories to classical gravity theories. Resorting to the holographic superconductor model, we propose a general criterion for the nature of the superconducting phase transition based on effective interactions between vortices. We find "tricritical" points in terms of the chemical potential for U(1) charges and an effective Ginzburg-Landau parameter, where vortices do not interact to separate the second order (repulsive) from the first order (attractive) transitions. We interpret the first order transition as the Coleman-Weinberg mechanism, arguing that it is relevant to superconducting instabilities around quantum criticality.
Phase structure and critical properties of an abelian gauge theory
Mo, Sjur
2001-12-01
The main new results are presented in the form of three papers at the end of this thesis. The main topic is Monte-Carlo studies of the phase structure and critical properties of the phenomenological Ginzburg-Landau model, i.e. an abelian gauge theory. However, the first paper is totally different and deals with microscopic theory for lattice-fermions in a magnetic field. Paper I is about ''Fermion-pairing on a square lattice in extreme magnetic fields''. We consider the Cooper-problem on a two-dimensional, square lattice with a uniform, perpendicular magnetic field. Only rational flux fractions are considered. An extended (real-space) Hubbard model including nearest and next nearest neighbor interactions is transformed to ''k-space'', or more precisely, to the space of eigenfunctions of Harper's equation, which constitute basis functions of the magnetic translation group for the lattice. A BCS-like truncation of the interaction term is performed. Expanding the interactions in the basis functions of the irreducible representations of the point group C{sub 4{nu}} of the square lattice simplify calculations. The numerical results indicate enhanced binding compared to zero magnetic field, and thus re-entrant superconducting pairing at extreme magnetic fields, well beyond the point where the usual semi-classical treatment of the magnetic field breaks down. Paper II is about the ''Hausdorff dimension of critical fluctuations in abelian gauge theories''. Here we analyze the geometric properties of the line-like critical fluctuations (vortex loops) in the Ginzburg-Landau model in zero magnetic background field. By using a dual description, we obtain scaling relations between exponents of geometric arid thermodynamic nature. In particular we connect the anomalous scaling dimension {eta} of the dual matter field to the Hausdorff or fractal dimension D{sub H} of the critical fluctuations, in the original model
The Landau-de Gennes theory of nematic liquid crystals: Uniaxiality versus Biaxiality
Majumdar, Apala
2011-12-01
We study small energy solutions within the Landau-de Gennes theory for nematic liquid crystals, subject to Dirichlet boundary conditions. We consider two-dimensional and three-dimensional domains separately. In the two-dimensional case, we establish the equivalence of the Landau-de Gennes and Ginzburg-Landau theory. In the three-dimensional case, we give a new definition of the defect set based on the normalized energy. In the threedimensional uniaxial case, we demonstrate the equivalence between the defect set and the isotropic set and prove the C 1,α-convergence of uniaxial small energy solutions to a limiting harmonic map, away from the defect set, for some 0 < a < 1, in the vanishing core limit. Generalizations for biaxial small energy solutions are also discussed, which include physically relevant estimates for the solution and its scalar order parameters. This work is motivated by the study of defects in liquid crystalline systems and their applications.
Symmetry of Uniaxial Global Landau--de Gennes Minimizers in the Theory of Nematic Liquid Crystals
Henao, Duvan
2012-01-01
We extend the recent radial symmetry results by Pisante [J. Funct. Anal., 260 (2011), pp. 892-905] and Millot and Pisante [J. Eur. Math. Soc. (JEMS), 12 (2010), pp. 1069- 1096] (who show that the equivariant solutions are the only entire solutions of the three-dimensional Ginzburg-Landau equations in superconductivity theory) to the Landau-de Gennes framework in the theory of nematic liquid crystals. In the low temperature limit, we obtain a characterization of global Landau-de Gennes minimizers, in the restricted class of uniaxial tensors, in terms of the well-known radial-hedgehog solution. We use this characterization to prove that global Landau-de Gennes minimizers cannot be purely uniaxial for sufficiently low temperatures. Copyright © by SIAM.
Microscopic and macroscopic theories for the dynamics of polar liquid crystals.
Wittkowski, Raphael; Löwen, Hartmut; Brand, Helmut R
2011-10-01
We derive and analyze the dynamic equations for polar liquid crystals in two spatial dimensions in the framework of classical dynamical density functional theory (DDFT). Translational density variations, polarization, and quadrupolar order are used as order-parameter fields. The results are critically compared with those obtained using the macroscopic approach of time-dependent Ginzburg-Landau (GL) equations for the analogous order-parameter fields. We demonstrate that, for both the microscopic DDFT and the macroscopic GL approach, the resulting dissipative dynamics can be derived from a dissipation function. We obtain microscopic expressions for all diagonal contributions and for many of the cross-coupling terms emerging from a GL approach. Thus, we establish a bridge between molecular correlations and macroscopic modeling for the dissipative dynamics of polar liquid crystals.
Quantitative theory of thermal fluctuations and disorder in the vortex matter
Dingping Li; Rosenstein Baruch; P Lin
2006-01-01
A metastable supercooled homogeneous vortex liquid state exists down to zero fluctuation temperature in systems of mutually repelling objects. The zero-temperature liquid state therefore serves as a (pseudo) `fixed point' controlling the properties of vortex liquid below and even around the melting point. Based on this picture, a quantitative theory of vortex melting and glass transition in Type II superconductors in the framework of Ginzburg-Landau approach is presented. The melting line location is determined and magnetization and specific heat jumps are calculated. The point-like disorder shifts the line downwards and joins the order{disorder transition line. On the other hand, the disorder induces irreversible effects via replica symmetry breaking. The irreversibility line can be calculated within the Gaussian variational method. Therefore, the generic phase diagram contains four phases divided by the irreversibility line and melting line: liquid, solid, vortex glass and Bragg glass. We compare various experimental results with the theoretical formula.
Coupled multiple-mode theory for s± pairing mechanism in iron based superconductors.
Kiselev, M N; Efremov, D V; Drechsler, S L; van den Brink, Jeroen; Kikoin, K
2016-11-29
We investigate the interplay between the magnetic and the superconducting degrees of freedom in unconventional multi-band superconductors such as iron pnictides. For this purpose a dynamical mode-mode coupling theory is developed based on the coupled Bethe-Salpeter equations. In order to investigate the region of the phase diagram not too far from the tetracritical point where the magnetic spin density wave, (SDW) and superconducting (SC) transition temperatures coincide, we also construct a Ginzburg-Landau functional including both SC and SDW fluctuations in a critical region above the transition temperatures. The fluctuation corrections tend to suppress the magnetic transition, but in the superconducting channel the intraband and interband contribution of the fluctuations nearly compensate each other.
Belova, P., E-mail: Polina.Belova@lut.fi [Lappeenranta University of Technology, P.O. Box 20, FI-53851 Lappeenranta (Finland); Petrozavodsk State University, Lenin Str. 33, RU-185640 Petrozavodsk (Russian Federation); Zakharchuk, I. [Lappeenranta University of Technology, P.O. Box 20, FI-53851 Lappeenranta (Finland); Saint-Petersburg Electrotechnical University, Popov Str. 5, RU-197376 St. Petersburg (Russian Federation); Safonchik, M. [Lappeenranta University of Technology, P.O. Box 20, FI-53851 Lappeenranta (Finland); A.F. Ioffe Physico-Technical Institute, St. Petersburg 194021 (Russian Federation); Traito, K.B.; Laehderanta, E. [Lappeenranta University of Technology, P.O. Box 20, FI-53851 Lappeenranta (Finland)
2012-06-15
The generalized London equation in the mixed state of high-{kappa} s-wave pairing superconductors with impurities is considered as a projection of the quasiclassical nonlocal nonlinear Eilenberger theory. Only one fitting parameter - the cutoff parameter {xi}{sub h} - is used in the theory. The distribution of the magnetic field is calculated self-consistently. Both nonlocal effects originated from extended states between the vortices and bound Andreev states in the vortex are taken into account. Comparison with different analytical nonlocal linear approaches (the Kogan-Gurevich, Amin-Franz-Affleck, Kogan-Zhelezina models) including only extended states is done. The importance of the Kramer-Pesch nonlinear effect and the field dependence of the cutoff parameter is emphasized and their strong influence on the variance of the magnetic field is found. The influence of the impurities on the ratio of the cutoff parameter {xi}{sub h} and the Ginzburg-Landau coherence length {xi}{sub c2} is considered. Quasiparticle scattering by impurities and lowering of the temperature reduces the value of {xi}{sub h} to the values much less than {xi}{sub c2}. This is different from the prediction of the local Ginzburg-Landau theory where {xi}{sub h} is scaled by {xi}{sub c2}. It is found that impurities influence by different way on the cutoff parameter {xi}{sub h} and the order parameter coherence length {xi}{sub 1}. The {xi}{sub h} decreases monotonously with the impurity scattering time in contrast to the nonmonotonous behavior of {xi}{sub 1}. The results can be used for analysis of the {mu}SR experimental data.
G-L theory of phase transitions of synergy analysis of concrete damage%基于G-L理论的混凝土损伤相变协同分析
赵文彦; 于广明; 李杏; 荆昱; 路世豹
2012-01-01
Based on the Ginzburg-Landau phase transitions theory and within the framework of continuum mechanics and phenomenological theory,a new method which uses analog phase-change idea of synergy theory is proposed to the study of the phase transitions of concrete damage.This paper employs Ginzburg-Landau phase transition theory to the research of phase transition of concrete damage and achieves a good result.Firstly it deduces the model which describes phase change of concrete damage,and then analyzes the linear and nonlinear solutions of damage model and relative functions.Finally,a large numerical simulation software named RFPA is used to verify the correctness of the theory.%基于Ginzburg-Landau相变理论,在连续介质力学与唯象理论的框架内,利用协同学系统相变类比的思想,提出了一种新的研究混凝土损伤相变的思路,即将超导相变的Ginzburg-Landau理论类比到混凝土损伤相变过程中来,并且取得了良好的研究成果.首先推导出了混凝土损伤相变的本构模型表达式,并计算出了损伤模型的线性解和非线性解及其相关函数,然后用大型数值模拟软件RFPA进行模拟验算,验证了该研究成果的正确性.
Weak crystallization theory of metallic alloys
Martin, Ivar; Gopalakrishnan, Sarang; Demler, Eugene A.
2016-06-01
Crystallization is one of the most familiar, but hardest to analyze, phase transitions. The principal reason is that crystallization typically occurs via a strongly first-order phase transition, and thus rigorous treatment would require comparing energies of an infinite number of possible crystalline states with the energy of liquid. A great simplification occurs when crystallization transition happens to be weakly first order. In this case, weak crystallization theory, based on unbiased Ginzburg-Landau expansion, can be applied. Even beyond its strict range of validity, it has been a useful qualitative tool for understanding crystallization. In its standard form, however, weak crystallization theory cannot explain the existence of a majority of observed crystalline and quasicrystalline states. Here we extend the weak crystallization theory to the case of metallic alloys. We identify a singular effect of itinerant electrons on the form of weak crystallization free energy. It is geometric in nature, generating strong dependence of free energy on the angles between ordering wave vectors of ionic density. That leads to stabilization of fcc, rhombohedral, and icosahedral quasicrystalline (iQC) phases, which are absent in the generic theory with only local interactions. As an application, we find the condition for stability of iQC that is consistent with the Hume-Rothery rules known empirically for the majority of stable iQC; namely, the length of the primary Bragg-peak wave vector is approximately equal to the diameter of the Fermi sphere.
Stochastic properties of a one-dimensional discrete Ginzburg-Landau field
Jaspers, M.; Schattke, W.
1981-01-01
Starting from a master equation for a discrete order parameter a dynamical model is set up via mean-field approximation in the Fokker-Planck equation. The time evolution of some mean values is calculated numerically, showing two transitions with characteristic slowing down of the relaxation time.
Xu, Guanglong
2016-01-01
Las transformaciones martensíticas (MT) se definen como un cambio en la estructura del cristal para formar una fase coherente o estructuras de dominio multivariante, a partir de la fase inicial con la misma composición, debido a pequeños intercambios o movimientos atómicos cooperativos. En el siglo pasado se han descubierto MT en diferentes materiales partiendo desde los aceros hasta las aleaciones con memoria de forma, materiales cerámicos y materiales inteligentes. Todos muestran propiedade...
Multiclass Semi-Supervised Learning on Graphs using Ginzburg-Landau Functional Minimization
Garcia-Cardona, Cristina; Percus, Allon G
2013-01-01
We present a graph-based variational algorithm for classification of high-dimensional data, generalizing the binary diffuse interface model to the case of multiple classes. Motivated by total variation techniques, the method involves minimizing an energy functional made up of three terms. The first two terms promote a stepwise continuous classification function with sharp transitions between classes, while preserving symmetry among the class labels. The third term is a data fidelity term, allowing us to incorporate prior information into the model in a semi-supervised framework. The performance of the algorithm on synthetic data, as well as on the COIL and MNIST benchmark datasets, is competitive with state-of-the-art graph-based multiclass segmentation methods.
A non-existence result for the Ginzburg-Landau equations
Kachmar, Ayman; Persson, Mikael
2009-01-01
We consider the stationary Ginzburg–Landau equations in , d=2,3 . We exhibit a class of applied magnetic fields (including constant fields) such that the Ginzburg–Landau equations do not admit finite energy solutions....
Dissecting zero modes and bound states on BPS vortices in Ginzburg-Landau superconductors
Izquierdo, A. Alonso [Departamento de Matematica Aplicada, Universidad de Salamanca,Facultad de Ciencias Agrarias y Ambientales,Av. Filiberto Villalobos 119, E-37008 Salamanca (Spain); Fuertes, W. Garcia [Departamento de Fisica, Universidad de Oviedo, Facultad de Ciencias,Calle Calvo Sotelo s/n, E-33007 Oviedo (Spain); Guilarte, J. Mateos [Departamento de Fisica Fundamental, Universidad de Salamanca, Facultad de Ciencias,Plaza de la Merced, E-37008 Salamanca (Spain)
2016-05-12
In this paper the zero modes of fluctuation of cylindrically symmetric self-dual vortices are analyzed and described in full detail. These BPS topological defects arise at the critical point between Type II and Type I superconductors, or, equivalently, when the masses of the Higgs particle and the vector boson in the Abelian Higgs model are equal. In addition, novel bound states of Higss and vector bosons trapped by the self-dual vortices at their core are found and investigated.
Dissecting zero modes and bound states on BPS vortices in Ginzburg-Landau superconductors
Alonso-Izquierdo, Alberto; Guilarte, Juan Mateos
2016-01-01
In this paper the zero modes of fluctuation of cylindrically symmetric self-dual vortices are analyzed and described in full detail. These BPS topological defects arise at the critical point between Type II and Type I superconductors, or, equivalently, when the masses of the Higgs particle and the vector boson in the Abelian Higgs model are equal. In addition, novel bound states of Higss and vector bosons trapped by the self-dual vortices at their core are found and investigated.
Varieties of stable vortical solitons in Ginzburg-Landau media with radially inhomogeneous losses.
Skarka, V; Aleksić, N B; Leblond, H; Malomed, B A; Mihalache, D
2010-11-19
Using a combination of the variation approximation and direct simulations, we consider the model of the light transmission in nonlinearly amplified bulk media, taking into account the localization of the gain, i.e., the linear loss shaped as a parabolic function of the transverse radius, with a minimum at the center. The balance of the transverse diffraction, self-focusing, gain, and the inhomogeneous loss provides for the hitherto elusive stabilization of vortex solitons, in a large zone of the parameter space. Adjacent to it, stability domains are found for several novel kinds of localized vortices, including spinning elliptically shaped ones, eccentric elliptic vortices which feature double rotation, spinning crescents, and breathing vortices.
The variety of stable vortical solitons in Ginzburg-Landau media with radially inhomogeneous losses
Skarka, V; Leblond, H; Malomed, B A; Mihalache, D
2010-01-01
Using a combination of the variation approximation (VA) and direct simulations, we consider the light transmission in nonlinearly amplified bulk media, taking into account the localization of the gain, i.e., the linear loss shaped as a parabolic function of the transverse radius, with a minimum at the center. The balance of the transverse diffraction, self-focusing, gain, and the inhomogeneous loss provide for the hitherto elusive stabilization of vortex solitons in a large zone of the parameter space. Adjacent to it, stability domains are found for several novel kinds of localized vortices, including spinning elliptically shaped ones, eccentric elliptic vortices which feature double rotation, spinning crescents, and breathing vortices.
Theory of superconductivity of gravitation and the dark matter enigma
Santiago-Germán, Wenceslao
2011-01-01
In this article, the question of the nature of cold dark matter is approached from a new angle. By invoking the Cauchy problem of relativity it is shown how, under very precise astrophysical conditions, the Einstein general theory of relativity is formally equivalent to the Ginzburg-Landau theory of superconductivity. This fact lead us to suspect that the superconductivity of gravitation ought to be a real physical process occurring in the outskirts of galaxies. It is found that quantum mechanically gravity can achieve a type-II superconductor state characterised by the Gizburg-Landau parameter $\\kappa=1.5$, and it is suggested that a probability flux of Cooper pairs (quantum gravitational geons charged with vacuum energy) are directly responsible for the flatness exhibited by the rotation curves in spiral galaxies, as well as the exotic behaviour observed in galactic cluster collisions. If this hypothesis proves correct, the whole phenomenon of dark matter may count, after all, as another triumph for Einstei...
Nodal Liquid Theory of the Pseudo-Gap Phase of High-Tc Superconductors
Balents, Leon; Fisher, Matthew P. A.; Nayak, Chetan
We introduce and study the nodal liquid, a novel zero-temperature quantum phase obtained by quantum-disordering a d-wave superconductor. It has numerous remarkable properties which lead us to suggest it as an explanation of the pseudo-gap state in underdoped high-temperature superconductors. In the absence of impurities, these include power-law magnetic order, a T-linear spin susceptibility, nontrivial thermal conductivity, and two- and one-particle charge gaps, the latter evidenced, e.g. in transport and electron photoemission (which exhibits pronounced fourfold anisotropy inherited from the d-wave quasiparticles). We use a (2+1)-dimensional duality transformation to derive an effective field theory for this phase. The theory is comprised of gapless neutral Dirac particles living at the former d-wave nodes, weakly coupled to the fluctuating gauge field of a dual Ginzburg-Landau theory. The nodal liquid interpolates naturally between the d-wave superconductor and the insulating antiferromagnet, and our effective field theory is powerful enough to permit a detailed analysis of a panoply of interesting phenomena, including charge ordering, antiferromagnetism, and d-wave superconductivity. We also discuss the zero-temperature quantum phase transitions which separate the nodal liquid from various ordered phases.
Atomically flat superconducting nanofilms: multiband properties and mean-field theory
Shanenko, A. A.; Aguiar, J. Albino; Vagov, A.; Croitoru, M. D.; Milošević, M. V.
2015-05-01
Recent progress in materials synthesis enabled fabrication of superconducting atomically flat single-crystalline metallic nanofilms with thicknesses down to a few monolayers. Interest in such nano-thin systems is attracted by the dimensional 3D-2D crossover in their coherent properties which occurs with decreasing the film thickness. The first fundamental aspect of this crossover is dictated by the Mermin-Wagner-Hohenberg theorem and concerns frustration of the long-range order due to superconductive fluctuations and the possibility to track its impact with an unprecedented level of control. The second important aspect is related to the Fabri-Pérot modes of the electronic motion strongly bound in the direction perpendicular to the nanofilm. The formation of such modes results in a pronounced multiband structure that changes with the nanofilm thickness and affects both the mean-field behavior and superconductive fluctuations. Though the subject is very rich in physics, it is scarcely investigated to date. The main obstacle is that there are no manageable models to study a complex magnetic response in this case. Full microscopic consideration is rather time consuming, if practicable at all, while the standard Ginzburg-Landau theory is not applicable. In the present work we review the main achievements in the subject to date, and construct and justify an efficient multiband mean-field formalism which allows for numerical and even analytical treatment of nano-thin superconductors in applied magnetic fields.
Wang, Juven; Gu, Zheng-Cheng; Wen, Xiao-Gang
The challenge of identifying symmetry-protected topological states (SPTs) is due to their lack of symmetry-breaking order parameters and intrinsic topological orders. For this reason, it is impossible to formulate SPTs under Ginzburg-Landau theory or probe SPTs via fractionalized bulk excitations and topology-dependent ground state degeneracy. However, the partition functions from path integrals with various symmetry twists are universal SPT invariants, fully characterizing SPTs. In this work, we use gauge fields to represent those symmetry twists in closed spacetimes of any dimensionality and arbitrary topology. This allows us to express the SPT invariants in terms of continuum field theory. We show that SPT invariants of pure gauge actions describe the SPTs predicted by group cohomology, while the mixed gauge-gravity actions describe the beyond-group-cohomology SPTs, recently observed by Kapustin. We find new examples of mixed gauge-gravity actions for U(1) SPTs in 3+1D and 4+1D via the Stiefel-Whitney class and the gravitational Chern-Simons term. [Work based on Phys. Rev. Lett. 114, 031601 (2015) arXiv:1405.7689
Tóth, Gyula I; Gránásy, László
2007-08-21
The phase field theory (PFT) has been applied to predict equilibrium interfacial properties and nucleation barrier in the binary eutectic system Ag-Cu using double well and interpolation functions deduced from a Ginzburg-Landau expansion that considers fcc (face centered cubic) crystal symmetries. The temperature and composition dependent free energies of the liquid and solid phases are taken from CALculation of PHAse Diagrams-type calculations. The model parameters of PFT are fixed so as to recover an interface thickness of approximately 1 nm from molecular dynamics simulations and the interfacial free energies from the experimental dihedral angles available for the pure components. A nontrivial temperature and composition dependence for the equilibrium interfacial free energy is observed. Mapping the possible nucleation pathways, we find that the Ag and Cu rich critical fluctuations compete against each other in the neighborhood of the eutectic composition. The Tolman length is positive and shows a maximum as a function of undercooling. The PFT predictions for the critical undercooling are found to be consistent with experimental results. These results support the view that heterogeneous nucleation took place in the undercooling experiments available at present. We also present calculations using the classical droplet model [classical nucleation theory (CNT)] and a phenomenological diffuse interface theory (DIT). While the predictions of the CNT with a purely entropic interfacial free energy underestimate the critical undercooling, the DIT results appear to be in a reasonable agreement with the PFT predictions.
姚锋平
2004-01-01
讨论导体材料在中间、超导材料在两边的一维Ginzburg-Landau超导方程组的渐近性态,并证明了当Ginzburg-Landau参数趋于无穷大时方程组的解趋向于一个非线性常微分方程组的解.
2016-02-01
vertices it is connecting are similar and a small weight otherwise. One popular choice for the weight function is the Gaussian w(x, y) = e− M(x,y)2...undirected graph with the set of vertices V and set of edges E, and consider a target set X of size n embedded in a graph G. A weight function is defined on...containing the weight function values. The minimum cut problem is to find the set S ⊂ V such that the following value is minimized: cut(S, S̄) = ∑ x∈S,y
A. Doelman; P. Takác; P. Bollerman; A. van Harten; E.S. Titi
1996-01-01
Some analytic smoothing properties of a general strongly coupled, strongly parabolic semilinear system of order $2m$ in $realnos^D times (0,T)$ with analytic entries are investigated. These properties are expressed in terms of holomorphic continuation in space and time of essentially bounded global
无
2007-01-01
Temperature dependence of the magnetization M(T) of two-band superconductors is studied in the vicinity of upper critical field Hc2 by using a two-band Ginzburg-Landau (GL) theory. It is shown that magnetization M(T) has a nonlinear character due to positive curvature of upper critical field Hc2(T) and temperature dependence of effective Ginzburg-Landau parameter (n)eff(T). The results are shown to be in qualitative agreement with experimental data for the superconducting magnesium diboride, MgB2.
Topological Aspects of Superconductors at Dual Point
REN Ji-Rong; XU Dong-Hui; ZHANG Xin-Hui; DUAN Yi-Shi
2008-01-01
We study the properties of the Ginzburg-Landau model at the dual point for the superconductors. By making use of the U(1) gauge potential decomposition and the C-mapping theory, we investigate the topological inner structure of the Bogomol'nyi equations and deduce a modified deeoupled Bogomol'nyi equation with a nontrivial topo-logical term, which is ignored in conventional model. We find that the nontrivial topological term is closely related tothe N-vortex, which arises from the zero points of the complex scalar field. Furthermore, we establish a relationship between Ginzburg-Landau free energy and the winding number.
Milovanov, A.V.; Juul Rasmussen, J.
2005-01-01
class of critical phenomena when the organization of the system near the phase transition point is influenced by a competing nonlocal ordering. Fractional modifications of the free energy functional at criticality and of the widely known Ginzburg-Landau equation central to the classical Landau theory...... of second-type phase transitions are discussed in some detail. An implication of the fractional Ginzburg-Landau equation is a renormalization of the transition temperature owing to the nonlocality present. (c) 2005 Elsevier B.V. All rights reserved....
Stability of Travelling Wave Solutions of the Derivative Ginzburg—Landau Equations
BolingGuo; BainianLU; 等
1997-01-01
The existence of travelling wave solution of the quinitic Ginzburg-Landau equation with derivatives is proved by the geometric singular perturbation theory.The stability of the wave solution is presented by topological methods which are proposed in Alexander,Gardner and Jones[6].The Chern number of the unstable augmented bundle is used to count the number of the linearizing operator L.For derivative Ginzburg-Landau equations,the Chern number of the unstable augmented bundle is equal to zero.I.e.c1（ε）=0,then the wave solution is stable.
Mean Curvature, Threshold Dynamics, and Phase Field Theory on Finite Graphs
2013-06-28
BK91] Lia Bronsard and Robert V. Kohn, Motion by mean curvature as the singular limit of Ginzburg-Landau dynamics, J. Differential Equations 90 (1991...Proceedings of the IEEE 95 (2007), no. 1, 215–233. [Peg89] Robert L. Pego, Front migration in the nonlinear cahn-hilliard equation, Proceedings of the Royal...625. [SB10] Arthur Szlam and Xavier Bresson , Total variation and cheeger cuts, Proceedings of the 27th International Conference on Machine Learning
Langevin simulation of scalar fields: Additive and multiplicative noises and lattice renormalization
Cassol-Seewald, N. C.; Farias, R. L. S.; Fraga, E. S.; Krein, G.; Ramos, Rudnei O.
2012-08-01
We consider the Langevin lattice dynamics for a spontaneously broken λϕ4 scalar field theory where both additive and multiplicative noise terms are incorporated. The lattice renormalization for the corresponding stochastic Ginzburg-Landau-Langevin and the subtleties related to the multiplicative noise are investigated.
High Temperature Superconducting State in Metallic Nanoclusters and Nano-Based Systems
2013-12-01
the Nonlinear Schrodinger Equation” JETP 112, 469-478 (2011) The nonlinear Schrodinger equation, known in low-temperature physics as Gross...paper we study the Gross-Pitaevskii equation of the theory of superfluidity, i.e. the nonlinear Schrodinger equation of the Ginzburg-Landau type. We
Maurits, N.M; Fraaije, J.G E M
1997-01-01
In this paper we apply nonlocal kinetic coupling to the dynamic mean-field density functional method, which is derived from generalized time-dependent Ginzburg-Landau theory. The method is applied to the mesoscopic dynamics of copolymer melts, which was previously simulated using a local coupling ap
Energy minimization using Sobolev gradients application to phase separation and ordering
Sial, S; Lookman, T; Saxena, A
2003-01-01
A common problem in physics and engineering is the calculation of the minima of energy functionals. The theory of Sobolev gradients provides an efficient method for seeking the critical points of such a functional. We apply the method to functionals describing coarse-grained Ginzburg-Landau models commonly used in pattern formation and ordering processes.
Fraaije, JGEM; vanVlimmeren, BAC; Maurits, NM; Postma, M; Evers, OA; Hoffmann, C; Altevogt, P; GoldbeckWood, G
1997-01-01
In this paper we discuss a new generalized time-dependent Ginzburg-Landau theory for the numerical calculation of polymer phase separation kinetics in 3D. The thermodynamic forces are obtained by a mean-field density functional method, using a Gaussian chain as a molecular model. The method is
Maurits, NM; Fraaije, JGEM
1997-01-01
In this paper we apply nonlocal kinetic coupling to the dynamic mean-field density functional method, which is derived from generalized time-dependent Ginzburg-Landau theory. The method is applied to the mesoscopic dynamics of copolymer melts, which was previously simulated using a local coupling ap
Ginzburg deserved Nobel prize 50 years back
Golovchansky, V
2003-01-01
"Vitali Ginzburg deserved a Nobel prize fifty years back, Leonid Keldysh, academician of the Russian Academy of Sciences, who was Ginzburg's disciple, told Tass. "The Ginzburg-Landau phenomenal theory of superconductivity deserved a Nobel prize right upon being produced. It was a work of intransient importance" (1/2 page).
杨灵娥; 郭柏灵; 徐海祥
2004-01-01
研究具非线性边界条件的一类广义Ginzburg-Landau方程解的整体存在性.推导了Ginzburg-Landau方程的非齐次初边值问题光滑解的几个积分恒等式,由此得到了解的法向导数在边界上的平方模以及解的平方模和导数的平方模估计;通过逼近技巧、先验估计和取极限方法证明了Ginzburg-Landau方程的非齐次初边值问题整体弱解的存在性.
Zharkov, G. F.
2001-06-01
Based on self-consistent solution of nonlinear GL equations, the phase boundary is found, which divides the regions of first- and second-order phase transitions to normal state of a superconducting cylinder of radius R, placed in magnetic field and remaining in the state of fixed vorticity m. This boundary is a complicated function of the parameters (m,R,{kappa}) ({kappa} is the GL parameter), which does not coincide with the simple phase boundary {kappa}=1/{radical}2, dividing the regions of first- and second-order phase transitions in infinite (open) superconducting systems.
Rolland, Joran; Bouchet, Freddy; Simonnet, Eric
2016-01-01
In this article we compute and analyse the transition rates and duration of reactive trajectories of the stochastic 1-D Allen-Cahn equations for both the Freidlin-Wentzell regime (weak noise or temperature limit) and finite-amplitude white noise, as well as for small and large domain. We demonstrate that extremely rare reactive trajectories corresponding to direct transitions between two metastable states are efficiently computed using an algorithm called adaptive multilevel splitting. This algorithm is dedicated to the computation of rare events and is able to provide ensembles of reactive trajectories in a very efficient way. In the small noise limit, our numerical results are in agreement with large-deviation predictions such as instanton-like solutions, mean first passages and escape probabilities. We show that the duration of reactive trajectories follows a Gumbel distribution like for one degree of freedom systems. Moreover, the mean duration growths logarithmically with the inverse temperature. The prefactor given by the potential curvature grows exponentially with size. The main novelty of our work is that we also perform an analysis of reactive trajectories for large noises and large domains. In this case, we show that the position of the reactive front is essentially a random walk. This time, the mean duration grows linearly with the inverse temperature and quadratically with the size. Using a phenomenological description of the system, we are able to calculate the transition rate, although the dynamics is described by neither Freidlin-Wentzell or Eyring-Kramers type of results. Numerical results confirm our analysis.
Rolland, J; Simonnet, E
2015-01-01
In this paper we compute and analyse the transition rates and duration of reactive trajectories of the stochastic 1-D Allen-Cahn equations for both the Freidlin-Wentzell regime (weak noise or temperature limit) and finite-amplitude white noise, as well as for small and large domain. We demonstrate that extremely rare reactive trajectories corresponding to direct transitions between two metastable states are efficiently computed using an algorithm called adaptive multilevel splitting. This algorithm is dedicated to the computation of rare events and is able to provide ensembles of reactive trajectories in a very efficient way. In the small noise limit, our numerical results are in agreement with large-deviation predictions such as instanton-like solutions, mean first passages and escape probabilities. We show that the duration of reactive trajectories follows a Gumbel distribution like for one degree of freedom systems. Moreover, the mean duration growths logarithmically with the inverse temperature. The prefa...
Global Attractor for Complex Ginzburg Landau Equation in Whole R3%三维全空间上Ginzburg-Landau方程的整体吸引子
李栋龙; 郭柏灵
2004-01-01
作者在三维全空间中考虑研究复Ginzburg-Landau方程(CGL)的解的长时间行为.通过引入权空间,应用内插不等式和在权空间的先验估计,获得复 Ginzburg-Landau方程整体解的存在性,进一步建立了整体吸引子的存在性.
Strong-coupling and the Stripe phase of $^3$He
Wiman, Joshua J.; Sauls, J. A.
2016-01-01
Thin films of superfluid $^3$He were predicted, based on weak-coupling BCS theory, to have a stable phase which spontaneously breaks translational symmetry in the plane of the film. This crystalline superfluid, or "stripe" phase, develops as a one dimensional periodic array of domain walls separating degenerate B phase domains. We report calculations of the phases and phase diagram for superfluid $^3$He in thin films using a strong-coupling Ginzburg-Landau theory that accurately reproduces th...
The emergence of superconducting systems in Anti-de Sitter space
Wu, W. M.; Pierpoint, M. P.; Forrester, D. M.; Kusmartsev, F. V.
2016-10-01
In this article, we investigate the mathematical relationship between a (3+1) dimensional gravity model inside Anti-de Sitter space AdS4, and a (2+1) dimensional superconducting system on the asymptotically flat boundary of AdS4 (in the absence of gravity). We consider a simple case of the Type II superconducting model (in terms of Ginzburg-Landau theory) with an external perpendicular magnetic field H. An interaction potential V ( r, ψ) = α( T)| ψ|2 /r 2 + χ| ψ|2 /L 2 + β| ψ|4 /(2 r k ) is introduced within the Lagrangian system. This provides more flexibility within the model, when the superconducting system is close to the transition temperature T c. Overall, our result demonstrates that the Ginzburg-Landau differential equations can be directly deduced from Einstein's theory of general relativity.
The Emergence of Superconducting Systems in Anti-de Sitter Space
Wu, W M; Forrester, D M; Kusmartsev, F V
2016-01-01
In this article, we investigate the mathematical relationship between a (3+1) dimensional gravity model inside Anti-de Sitter space $\\rm AdS_4$, and a (2+1) dimensional superconducting system on the asymptotically flat boundary of $\\rm AdS_4$ (in the absence of gravity). We consider a simple case of the Type II superconducting model (in terms of Ginzburg-Landau theory) with an external perpendicular magnetic field ${\\bf H}$. An interaction potential $V(r,\\psi) = \\alpha(T)|\\psi|^2/r^2+\\chi|\\psi|^2/L^2+\\beta|\\psi|^4/(2 r^k )$ is introduced within the Lagrangian system. This provides more flexibility within the model, when the superconducting system is close to the transition temperature $T_c$. Overall, our result demonstrates that the two Ginzburg-Landau differential equations can be directly deduced from Einstein's theory of general relativity.
Spinor bose gases in cubic optical lattice
Mobarak, Mohamed Saidan Sayed Mohamed
2014-01-27
In recent years the quantum simulation of condensed-matter physics problems has resulted from exciting experimental progress in the realm of ultracold atoms and molecules in optical lattices. In this thesis we analyze theoretically a spinor Bose gas loaded into a three-dimensional cubic optical lattice. In order to account for different superfluid phases of spin-1 bosons with a linear Zeeman effect, we work out a Ginzburg-Landau theory for the underlying spin-1 Bose-Hubbard model. To this end we add artificial symmetry-breaking currents to the spin-1 Bose-Hubbard Hamiltonian in order to break the global U (1) symmetry. With this we determine a diagrammatic expansion of the grand-canonical free energy up to fourth order in the symmetry-breaking currents and up to the leading non-trivial order in the hopping strength which is of first order. As a cross-check we demonstrate that the resulting grand-canonical free energy allows to recover the mean-field theory. Applying a Legendre transformation to the grand-canonical free energy, where the symmetry-breaking currents are transformed to order parameters, we obtain the effective Ginzburg-Landau action. With this we calculate in detail at zero temperature the Mott insulator-superfluid quantum phase boundary as well as condensate and particle number density in the superfluid phase. We find that both mean-field and Ginzburg-Landau theory yield the same quantum phase transition between the Mott insulator and superfluid phases, but the range of validity of the mean-field theory turns out to be smaller than that of the Ginzburg-Landau theory. Due to this finding we expect that the Ginzburg-Landau theory gives better results for the superfluid phase and, thus, we restrict ourselves to extremize only the effective Ginzburg-Landau action with respect to the order parameters. Without external magnetic field the superfluid phase is a polar (ferromagnetic) state for anti-ferromagnetic (ferromagnetic) interactions, i.e. only the
Langevin Simulation of Scalar Fields: Additive and Multiplicative Noises and Lattice Renormalization
Cassol-Seewald, N C; Fraga, E S; Krein, G; Ramos, R O
2007-01-01
We consider the nonequilibrium dynamics of the formation of a condensate in a spontaneously broken lambda phi4 scalar field theory, incorporating additive and multiplicative noise terms to study the role of fluctuation and dissipation. The corresponding stochastic Ginzburg-Landau-Langevin (GLL) equation is derived from the effective action, and solved on a (3+1)-dimensional lattice. Particular attention is devoted to the renormalization of the stochastic GLL equation in order to obtain lattice-independent equilibrium results.
Theoretical study on the two-band degenerate-gaps superconductors: Application to SrPt3P
Huang, Hai; Hou, Li-Chao; Zhao, Bin-Peng
2016-09-01
We study the magnetic properties of two-band degenerate-gaps superconductors with two-band isotropic Ginzburg-Landau theory. The exact solutions of upper critical field and London penetration depth are obtained, and the calculations reproduce the experimental data of the recently observed superconducting crystal SrPt3P in a broad temperature range. It directly underlies that SrPt3P is a multi-band superconductor with equal gaps in two Fermi surface sheets.
Umurhan, O M; Spiegel, E A
1998-01-01
We study the weakly nonlinear evolution of acoustic instability of a plane- parallel polytrope with thermal dissipation in the form of Newton's law of cooling. The most unstable horizontal wavenumbers form a band around zero and this permits the development of a nonlinear pattern theory leading to a complex Ginzburg-Landau equation (CGLE). Numerical solutions for a subcritical, quintic CGLE produce vertically oscillating, localized structures that resemble the oscillons observed in recent experiments of vibrated granular material.
Umurhan, O M; Tao, L; Spiegel, E A
1998-12-30
We study the weakly nonlinear evolution of acoustic instability of a plane-parallel polytrope with thermal dissipation in the form of Newton's law of cooling. The most unstable horizontal wavenumbers form a band around zero and this permits the development of a nonlinear pattern theory leading to a complex Ginzburg-Landau equation (CGLE). Numerical solutions for a subcritical, quintic CGLE produce vertically oscillating, localized structures that resemble the oscillons observed in recent experiments of vibrated granular material.
Holographic superconductors with Lifshitz scaling in external magnetic field
Zhao, Zixu; Jing, Jiliang
2014-01-01
We analytically study the holographic superconductors with Lifshitz scaling in presence of an external magnetic field. We observe that Lifshitz scaling can hinder the condensation to be formed, which can be used to back up the existing numerical results. Moreover, we find that the dynamical exponent $z$ does have effects on the upper critical magnetic field. However, we note that Lifshitz scaling does not modify the well-known relation obtained from the Ginzburg-Landau theory for the upper critical magnetic field.
Poole, Charles P; Farach, Horacio A
1995-01-01
Superconductivity covers the nature of the phenomenon of superconductivity. The book discusses the fundamental principles of superconductivity; the essential features of the superconducting state-the phenomena of zero resistance and perfect diamagnetism; and the properties of the various classes of superconductors, including the organics, the buckministerfullerenes, and the precursors to the cuprates. The text also describes superconductivity from the viewpoint of thermodynamics and provides expressions for the free energy; the Ginzburg-Landau and BCS theories; and the structures of the high
Fluctuation sound absorption in quark matter
Kerbikov, B O
2016-01-01
We investigate the sound absorption in quark matter due to the interaction of the sound wave with the precritical fluctuations of the diquark-pair field above $T_c$. The soft collective mode of the pair field is derived using the time dependent Ginzburg-Landau functional with random Langevin forces. The strong absorption near the phase transition line may be viewed as a manifestation of the Mandelshtam-Leontovich slow relaxation time theory.
The weakly nonlinear magnetorotational instability in a thin-gap Taylor-Couette flow
Clark, S E
2016-01-01
The magnetorotational instability (MRI) is a fundamental process of accretion disk physics, but its saturation mechanism remains poorly understood despite considerable theoretical and computational effort. We present a multiple scales analysis of the non-ideal MRI in the weakly nonlinear regime -- that is, when the most unstable MRI mode has a growth rate asymptotically approaching zero from above. Here, we develop our theory in a thin-gap, Cartesian channel. Our results confirm the finding by Umurhan et al. (2007) that the perturbation amplitude follows a Ginzburg-Landau equation. We extend these results by performing a detailed force balance for the saturated azimuthal velocity and vertical magnetic field, demonstrating that even when diffusive effects are important, the bulk flow saturates via the combined processes of reducing the background shear and rearranging and strengthening the background vertical magnetic field. We directly simulate the Ginzburg-Landau amplitude evolution for our system and demons...
Landau, I. L.
2008-07-01
By comparison of recent direct measurements of the temperature dependence of the upper critical field Hc2 of an YBa2Cu3O7-x high-Tc superconductor with the scaling analysis of magnetization data, collected in fields H \\ll H_{\\mathrm {c2}} , we demonstrate that the temperature dependence of the Ginzburg-Landau parameter κ is negligible. Another conclusion is that the normalized temperature dependence of Hc2 is independent of the orientation of the magnetic field with respect to the crystallographic axes of the sample. We also discuss the fact that isotropy of the temperature dependence of Hc2 straightforwardly follows from the Ginzburg-Landau theory if κ does not depend on the temperature.
胡满峰; 徐振源
2006-01-01
根据数值计算的结果提出了模态耦合的条件,两个方程在高频模态上是耦合的,而在低频模态上是不耦合的.利用了无穷维动力系统理论,证明了两个高频模态耦合的Ginzburg-Landau方程在函数空间中存在吸引域,因而存在连通的、有限维的紧的整体吸引子.驱动方程存在时空混沌.将方程组联系一个截断形式,得到的修正方程组将保持原方程组的动力学行为.高频模态耦合的两个方程在一定的条件下具有挤压性质,证明了可达到完全的时空混沌同步化.在数学上定性解释了无穷维动力系统的同步化现象.研究方法不同于有限维动力系统中通常使用的Liapunov函数方法与近似线性方法.
李栋龙; 郭柏灵
2009-01-01
考虑带附加噪声的随机广义2D Ginzburg-Landau方程.通过先验估计的方法,随机动力系统的紧性得到证明,进一步验证了该随机动力系统在础存在随机整体吸引子.
刘红胚
2010-01-01
文章考虑含有导数项的一维复Ginzburg-Landau方程,证明了含有导数项的一维复Ginzburg-Landau方程的初边值问题的局部解在一定的条件下,收敛于满足同样初边值问题的Schr(o)dinger方程的解的速度.
杨丽英
2010-01-01
通过对Ginzburg-Landau方程系数的分析,给出其包络波解存在的一个必要条件.利用两类辅助椭圆方程,求得Ginzburg-Landau方程的多种椭圆函数解,其极限情形可以还原为经典的包络孤立波解.
余王辉
2000-01-01
本文讨论了一维Ginzburg-Landau超导方程组的渐近性态. 确定了当 Ginzburg-Landau参数趋于无穷大时, 稳态Ginzburg-Landau超导方程组以及发展型Ginzburg-Landau超导方程组的解列的极限, 并证明了当时间和Ginzburg-Landau参数均趋于无穷大时,发展型Ginzburg-Landau超导方程组的不对称的极限函数是渐近稳定的, 而对称的极限函数是非渐近稳定的.
Theory of director precession and nonlinear waves in nematic liquid crystals under elliptical shear.
Krekhov, A P; Kramer, L
2005-09-01
We study theoretically the slow director precession and nonlinear waves observed in homeotropically oriented nematic liquid crystals subjected to circular or elliptical Couette and Poiseuille flow and an electric field. From a linear analysis of the nematodynamic equations it is found that in the presence of the flow the electric bend Fréedericksz transition is transformed into a Hopf-type bifurcation. In the framework of an approximate weakly nonlinear analysis we have calculated the coefficients of the modified complex Ginzburg-Landau equation, which slightly above onset describes nonlinear waves with strong nonlinear dispersion. We also derive the equation describing the precession and waves well above the Fréedericksz transition and for small flow amplitudes. Then the nonlinear waves are of diffusive nature. The results are compared with full numerical simulations and with experimental data.
Pereira, Paulo J; Moshchalkov, Victor V; Chibotaru, Liviu F
2012-11-01
We present a method for finding the condensate distribution at the nucleation of superconductivity for arbitrary polygons. The method is based on conformal mapping of the analytical solution of the linearized Ginzburg-Landau problem for the disk and uses the superconducting gauge for the magnetic potential proposed earlier. As a demonstration of the method's accuracy, we calculate the distribution of the order parameter in regular polygons and compare the obtained solutions with available numerical results. As an example of an irregular polygon, we consider a deformed hexagon and prove that its calculation with the proposed method requires the same level of computational efforts as the regular ones. Finally, we extend the method over samples with arbitrary smooth boundaries. With this, we have made simulations for an experimental sample. They have shown perfect agreement with experimental data.
Theory of the vortex matter transformations in high-Tc superconductor YBCO.
Li, Dingping; Rosenstein, Baruch
2003-04-25
Flux line lattice in type II superconductors undergoes a transition into a "disordered" phase such as vortex liquid or vortex glass, due to thermal fluctuations and random quenched disorder. We quantitatively describe the competition between the thermal fluctuations and the disorder using the Ginzburg-Landau approach. The following T-H phase diagram of YBCO emerges. There are just two distinct thermodynamical phases, the homogeneous and the crystalline one, separated by a single first order transition line. The line, however, makes a wiggle near the experimentally claimed critical point at 12 T. The "critical point" is reinterpreted as a (noncritical) Kauzmann point in which the latent heat vanishes and the line is parallel to the T axis. The magnetization, the entropy, and the specific heat discontinuities at melting compare well with experiments.
Theory for electric dipole superconductivity with an application for bilayer excitons.
Jiang, Qing-Dong; Bao, Zhi-qiang; Sun, Qing-Feng; Xie, X C
2015-07-08
Exciton superfluid is a macroscopic quantum phenomenon in which large quantities of excitons undergo the Bose-Einstein condensation. Recently, exciton superfluid has been widely studied in various bilayer systems. However, experimental measurements only provide indirect evidence for the existence of exciton superfluid. In this article, by viewing the exciton in a bilayer system as an electric dipole, we derive the London-type and Ginzburg-Landau-type equations for the electric dipole superconductors. By using these equations, we discover the Meissner-type effect and the electric dipole current Josephson effect. These effects can provide direct evidence for the formation of the exciton superfluid state in bilayer systems and pave new ways to drive an electric dipole current.
The upper critical field in two-band layered superconductors
Liu Min-Xia; Gan Zi-Zhao
2007-01-01
The upper critical field of clean MgB2 is investigated using the two-band layered Ginzburg-Landau (GL) theory.The calculated results are fitted to the experimental data of clean MgB2 crystal very well in a broad temperature range.Based on the GL theory for clean superconductors,a phenomenOlogical theory for dirty superconductor is proposed.Selecting appropriate parameters,two-band layered GL theory is successfully applied to the crystal of Mg(B1-xCx)2 and the neutron irradiation samples of MgB2.
Thermoelectric power and transport entropy of dirty type-II superconductors
de Lange, O. L.; Gridin, V. V.
1992-09-01
The relation FT0c2S(B,T)dT~=Bħ/(2mc) presented recently for the thermoelectric power S of a dirty high-Tc superconductor [V. V. Gridin et al., Phys. Rev. B 40, 8814 (1989)] is considered. It is shown that measurements which have been reported for the thermomagnetic coefficients of nearly reversible conventional type-II superconductors provide additional support for this relation. The result obtained from time-dependent microscopic theory for vortex motion (time-dependent Ginzburg-Landau theory and linear-response theory) is also discussed.
Izmailov, Alexander; Myerson, Allan S.
1993-01-01
A new mathematical ansatz for a solution of the time-dependent Ginzburg-Landau non-linear partial differential equation is developed for non-critical systems such as non-critical binary solutions (solute + solvent) described by the non-conserved scalar order parameter. It is demonstrated that in such systems metastability initiates heterogeneous solute redistribution which results in formation of the non-equilibrium singly-periodic spatial solute structure. It is found how the time-dependent period of this structure evolves in time. In addition, the critical radius r(sub c) for solute embryo of the new solute rich phase together with the metastable state lifetime t(sub c) are determined analytically and analyzed.
Conformal invariance and renormalization group in quantum gravity near two dimensions
Aida, Toshiaki; Kitazawa, Yoshihisa; Kawai, Hikaru; Ninomiya, Masao
1994-09-01
We study quantum gravity in 2 + ɛ dimensions in such a way as to preserve the volume-preserving diffeomorphism invariance. In such a formulation, we prove the following trinity: the general covariance, the conformal invariance and the renormalization group flow to the Einstein theory at long distance. We emphasize that the consistent and macroscopic universes like our own can only exist for a matter central charge 0 effect and universes are found to bounce back from the big crunch. Our formulation may be viewed as a Ginzburg-Landau theory which can describe both the broken and the unbroken phase of quantum gravity and the phase transition between them.
Fluctuation conductivity in two-band superconductor SmFeAsO0.8F0.2
Askerzade I.N.
2015-09-01
Full Text Available In this study we have calculated the fluctuation conductivity near critical temperature of SmFeAsO0.8F0.2 superconductor using two-band Ginzburg-Landau theory. It was illustrated that in the absence of external magnetic field, the two-band model reduced to a single effective band theory with modified temperature dependences. The calculations revealed three-dimensional character of fluctuations of conductivity in the new Fe-based superconductor SmFeAsO0.8F0.2. It has been shown that such a model is in good agreement with experimental data for this compound.
Stationary states and dynamics of superconducting thin films
Ögren, Magnus; Sørensen, Mads Peter; Pedersen, Niels Falsig
of stationary states with the GL equation and with the time-dependent GL equation are given. Moreover we study real time evolution with the so called Schrödinger-GL equation [3]. For simplicity we here present numerical data for a twodimensional rectangular geometry, but we emphasize that our FEM formulation......The Ginzburg-Landau (GL) theory is a celebrated tool for theoretical modelling of superconductors [1]. We elaborate on different partial differential equations (PDEs) and boundary conditions for GL theory, formulated within the finite element method (FEM) [2]. Examples of PDEs for the calculation...
Fingerprints of Mott Superconductivity
王强华
2003-01-01
We improve a previous theory of doped Mott insulators with duality between pairing and magnetism by a further duality transform. As the result we obtained a quantum Ginzburg-Landau theory describing the Cooper pair condensate and the dual of spin condensate. We address the superconductivity by doping a Mott insulator,which we call the Mott superconductivity. Some fingerprints of such novelty in cuprates are the scaling between neutron resonance energy and superfluid density, and the induced quantized spin moment by vortices or Zn impurity (together with circulating charge super-current to be checked by experiments).
Stability Analysis of The Twisted Superconducting Semilocal Strings
Garaud, Julien
2007-01-01
We study the stability properties of the twisted vortex solutions in the semilocal Abelian Higgs model with a global $\\mathbf{SU}(2)$ invariance. This model can be viewed as the Weinberg-Salam theory in the limit where the non-Abelian gauge field decouples, or as a two component Ginzburg-Landau theory. The twisted vortices are characterized by a constant global current ${\\cal I}$, and for ${\\cal I}\\to 0$ they reduce to the semilocal strings, that is to the Abrikosov-Nielsen-Olesen vortices embedded into the semilocal model. Solutions with ${\\cal I}\
Study of Depolarization Field Influence on Ferroelectric Films Within Transverse Ising Model
TAO Yong-Mei; SHI Qin-Fen; JIANG Qing
2005-01-01
An improved transverse Ising model is proposed by taking the depolarization field effect into account.Within the framework of mean-field theory we investigate the behavior of the ferroelectric thin film. Our results show that the influence of the depolarization field is to flatten the spontaneous polarization profile and make the films more homogeneous, which is consistent with Ginzburg-Landau theory. This fact shows that this model can be taken as an effective model to deal with the ferroelectric film and can be further extended to refer to quantum effect. The competition between quantum effect and depolarization field induces some interesting phenomena on ferroelectric thin films.
Kalashnikov, Vladimir L
2010-01-01
The analytical theory of chirped dissipative soliton solutions of nonlinear complex Ginzburg-Landau equation is exposed. Obtained approximate solutions are easily traceable within an extremely broad range of the equation parameters and allow a clear physical interpretation as a representation of the strongly chirped pulses in mode-locked both solid-state and fiber oscillators. Scaling properties of such pulses demonstrate a feasibility of sub-mJ pulse generation in the continuous-wave mode-locking regime directly from an oscillator operating at the MHz repetition rate.
Magneto-transport and magnetic susceptibility of SmFeAsO1-xFx (x = 0.0 and 0.20)
Meena, R. S.; Pal, Anand; Kumar, Shiva; Rao, K V R; Awana, V.P.S.
2012-01-01
Bulk polycrystalline samples, SmFeAsO and the iso-structural superconducting SmFeAsO0.80F0.20 are explored through resistivity with temperature under magnetic field {\\rho}(T, H), AC and DC magnetization (M-T), and Specific heat (Cp) measurements. The Resistivity measurement shows superconductivity for x = 0.20 sample with Tc(onset) ~ 51.7K. The upper critical field, [Hc2(0)] is estimated ~3770kOe by Ginzburg-Landau (GL) theory. Broadening of superconducting transition in magneto transport is ...
Lattice-Symmetry-Driven Phase Competition in Vanadium Dioxide
Tselev, Alexander [ORNL; Luk' yanchuk, Prof. Igor A. [University of Picardie Jules Verne, Amiens, France; Ivanov, Ilia N [ORNL; Budai, John D [ORNL; Tischler, Jonathan Zachary [ORNL; Strelcov, Evgheni [Southern Illinois University; Kolmakov, Andrei [Southern Illinois University; Kalinin, Sergei V [ORNL
2011-01-01
We performed group-theoretical analysis of the symmetry relationships between lattice structures of R, M1, M2, and T phases of vanadium dioxide in the frameworks of the general Ginzburg-Landau phase transition theory. The analysis leads to a conclusion that the competition between the lower-symmetry phases M1, M2, and T in the metal-insulator transition is pure symmetry driven, since all the three phases correspond to different directions of the same multi-component structural order parameter. Therefore, the lower-symmetry phases can be stabilized in respect to each other by small perturbations such as doping or stress.
Lectures given at the 2nd Session of the Centro Internazionale Matematico Estivo (C.I.M.E.)
Struwe, Michael
1999-01-01
The international summer school on Calculus of Variations and Geometric Evolution Problems was held at Cetraro, Italy, 1996. The contributions to this volume reflect quite closely the lectures given at Cetraro which have provided an image of a fairly broad field in analysis where in recent years we have seen many important contributions. Among the topics treated in the courses were variational methods for Ginzburg-Landau equations, variational models for microstructure and phase transitions, a variational treatment of the Plateau problem for surfaces of prescribed mean curvature in Riemannian manifolds - both from the classical point of view and in the setting of geometric measure theory.
Vortex patterns in a superconducting-ferromagnetic rod
Romaguera, Antonio R. de C, E-mail: antonio.romaguera@df.ufrpe.b [Departamento de Fi' sica, Universidade Federal Rural de Pernambuco, 52171-900 Recife, Pernambuco (Brazil); Doria, Mauro M. [Departamento de Fi' sica dos Solidos, Universidade Federal do Rio de Janeiro, 21941-972 Rio de Janeiro (Brazil); Peeters, Francois M. [Departement Fysica, Universiteit Antwerpen, Groenenborgerlaan 171, B-2020 Antwerpen (Belgium)
2010-10-01
A superconducting rod with a magnetic moment on top develops vortices obtained here through 3D calculations of the Ginzburg-Landau theory. The inhomogeneity of the applied field brings new properties to the vortex patterns that vary according to the rod thickness. We find that for thin rods (disks) the vortex patterns are similar to those obtained in presence of a homogeneous magnetic field instead because they consist of giant vortex states. For thick rods novel patterns are obtained as vortices are curve lines in space that exit through the lateral surface.
Pattern control and suppression of spatiotemporal chaos using geometrical resonance
Gonzalez, J.A. E-mail: jorge@pion.ivic.ve; Bellorin, A.; Reyes, L.I.; Vasquez, C.; Guerrero, L.E
2004-11-01
We generalize the concept of geometrical resonance to perturbed sine-Gordon, Nonlinear Schroedinger, phi (cursive,open) Greek{sup 4}, and Complex Ginzburg-Landau equations. Using this theory we can control different dynamical patterns. For instance, we can stabilize breathers and oscillatory patterns of large amplitudes successfully avoiding chaos. On the other hand, this method can be used to suppress spatiotemporal chaos and turbulence in systems where these phenomena are already present. This method can be generalized to even more general spatiotemporal systems. A short report of some of our results has been published in [Europhys. Lett. 64 (2003) 743].
PARTITION PROPERTY OF DOMAIN DECOMPOSITION WITHOUT ELLIPTICITY
Mo Mu; Yun-qing Huang
2001-01-01
Partition property plays a central role in domain decomposition methods. Existing theory essentially assumes certain ellipticity. We prove the partition property for problems without ellipticity which are of practical importance. Example applications include implicit schemes applied to degenerate parabolic partial differential equations arising from superconductors, superfluids and liquid crystals. With this partition property, Schwarz algorithms can be applied to general non-elliptic problems with an h-independent optimal convergence rate. Application to the time-dependent Ginzburg-Landau model of superconductivity is illustrated and numerical results are presented.
Calero, J.M. [Univ. Industrial de Santander, Bucaramanga (Colombia). Escuela de Fisica; Granada, J.C. [Dept. de Fisica, Univ. del Valle, Cali (Colombia); Silva, E.Z. da [Inst. de Fisica, Univ. Estadual de Campinas (Brazil)
2000-07-01
A nonperturbative method for the evaluation of thermodynamic scaling functions in the critical region of three-dimensional anisotropic type-II superconductors is extended for the case of external magnetic fields with arbitrary angles with respect to the anisotropy axis. The calculations are carried out in the framework of the Ginzburg-Landau theory. Explicit relations are obtained for the angular dependence of the magnetization and specific heat. Our theoretical results are in good agreement with experiments performed in untwinned single crystals of YBa{sub 2}Cu{sub 3}O{sub 7-{delta}}. (orig.)
Bellafi, B.; Haddad, S.; Sfar, I.; Charfi-Kaddour, S.
2009-03-01
It has been reported that, in quasi-one dimensional organic conductors, superconductivity may coexist macroscopically with non-superconducting states giving rise to an inhomogeneous phase. We investigate, based on the time-dependent Ginzburg-Landau theory, the effect of disorder on the stability of the superconducting phase in such a mixed state. We also focus on the interplay between superconductivity and disorder in ropes of carbon nanotubes. We show that the superconducting transition temperature in quasi-one organic conductors is reduced by disorder but does not obey the Abrikosov-Gorkov law. However, and contrary to what is expected, disorder can further superconductivity in ropes of carbon nanotubes.
Magnetic response of holographic Lifshitz superconductors:Vortex and Droplet solutions
Lala, Arindam
2014-01-01
In this paper a holographic model of $s$-wave superconductor with anisotropic Lifshitz scaling has been considered. In the presence of an external magnetic field our holographic model exhibits both vortex and droplet solutions. Based on analytic methods we have shown that the anisotropy has no effects on the vortex and droplet solutions whereas it may affect the condensation. Our vortex solution closely resembles with the Ginzburg-Landau theory and a relation between the upper critical magnetic field and superconducting coherence length has been speculated from this comparison. Using Sturm-Liouville method the effects of anisotropy on the critical parameters in insulator/superconductor phase transitions has been analyzed.
Phase space reduction and vortex statistics: An anyon quantization ambiguity
Allen, T.J.; Bordner, A.J.; Crossley, D.B. (Department of Physics, University of Wisconsin, 1150 University Avenue, Madison, Wisconsin 53706 (United States))
1994-06-15
We examine the quantization of the motion of two charged vortices in a Ginzburg-Landau theory for the fractional quantum Hall effect recently proposed by the first two authors. The system has two second-class constraints which can be implemented either in the reduced phase space or Dirac-Gupta-Bleuler formalism. Using the intrinsic formulation of statistics, we show that these two ways of implementing the constraints are inequivalent unless the vortices are quantized with conventional statistics, either fermionic or bosonic.
Transition between different quantum states in a mesoscopic system: The superconducting ring
Horane, E.M. [Instituto Balseiro, Universidad Nacional de Cuyo and Comision Nacional de Energia Atomica, 8400 Bariloche (Argentina); Castro, J.I. [Departamento Fisico-Quimica, Facultad Filosofia Humanidades y Artes, Universidad Nacional de San Juan, San Juan (Argentina); Buscaglia, G.C.; Lopez, A. [Instituto Balseiro, and Centro Atomico Bariloche, Universidad Nacional de Cuyo and Comision Nacional de Energia Atomica, 8400 Bariloche (Argentina)
1996-04-01
We investigate the thermodynamic properties of a superconducting ring, both analytically and numerically, relying upon the Ginzburg-Landau theory. We find that modulated solutions for the order parameter play a role in describing the thermodynamic transitions between consecutive modes of uniform order parameter, associated with different quantum numbers. Exact expressions for these solutions are given in terms of elliptic functions. We identify the family of energy extrema which, being saddle points of the energy in the functional space of the distributions of the order parameter, represent the energy barrier to be overcome for transitions between different solutions. {copyright} {ital 1996 The American Physical Society.}
Pairing state with a time-reversal symmetry breaking in FeAs-based superconductors.
Lee, Wei-Cheng; Zhang, Shou-Cheng; Wu, Congjun
2009-05-29
We investigate the competition between the extended s+/--wave and dx2-y2-wave pairing order parameters in the iron-based superconductors. Because of the frustrating pairing interactions among the electron and the hole Fermi pockets, a time-reversal symmetry breaking s+id pairing state could be favored. We analyze this pairing state within the Ginzburg-Landau theory and explore the experimental consequences. In such a state, spatial inhomogeneity induces a supercurrent near a nonmagnetic impurity and the corners of a square sample. The resonance mode between the s+/-- and dx2-y2-wave order parameters can be detected through the B1g Raman spectroscopy.
Condensation Energy of a Spacetime Condensate
de Matos, Clovis Jacinto
2010-01-01
Starting from an analogy between the Planck-Einstein scale and the dual length scales in Ginzburg-Landau theory of superconductivity, and assuming that space-time is a condensate of neutral fermionic particles with Planck mass, we derive the baryonic mass of the universe. In that theoretical framework baryonic matter appears to be associated with the condensation energy gained by spacetime in the transition from its normal (symetric) to its (less symetric) superconducting-like phase. It is shown however that the critical transition temperature cannot be the Planck temperature. Thus leaving open the enigma of the microscopic description of spacetime at quantum level.
Imaging of vortex chains in Sr{sub 2}RuO{sub 4}
Dolocan, V.O.; Veauvy, C.; Liu, Y.; Servant, F.; Lejay, P.; Mailly, D.; Hasselbach, K
2004-05-01
Sr{sub 2}RuO{sub 4} is an unconventional superconductor with a superconducting transition temperature of {approx}1.5 K. The formation of vortex chains in Sr{sub 2}RuO{sub 4} is observed, they have been directly imaged by {mu}SQUID force microscopy at low temperature. Ginzburg-Landau theory for anisotropic superconductors is in qualitative agreement with the observed dependencies of the vortex chains on the variation of the tilting angle or the amplitude of the external magnetic field.
Some Recent Progress on Quark Pairings in Dense Quark and Nuclear Matter
庞锦毅; 王金成; 王群
2012-01-01
In this review article we give a brief overview on some recent progress in quark pairings in dense quark~nuclear matter mostly developed in the past five years. We focus on following aspects in particular： the BCS-BEC crossover in the CSC phase, the baryon formation and dissociation in dense quark/nuclear matter, the Ginzburg-Landau theory for three-flavor dense matter with UA （1） anomaly, and the collective and Nambu-Goldstone modes for the spin-one CSC.
Multicritical behavior in dissipative Ising models
Overbeck, Vincent R; Gorshkov, Alexey V; Weimer, Hendrik
2016-01-01
We analyze theoretically the many-body dynamics of a dissipative Ising model in a transverse field using a variational approach. We find that the steady state phase diagram is substantially modified compared to its equilibrium counterpart, including the appearance of a multicritical point belonging to a different universality class. Building on our variational analysis, we establish a field-theoretical treatment corresponding to a dissipative variant of a Ginzburg-Landau theory, which allows us to compute the upper critical dimension of the system. Finally, we present a possible experimental realization of the dissipative Ising model using ultracold Rydberg gases.
Absolutely stable solitons in two-component active systems
Malomed, B A; Malomed, Boris; Winful, Herbert
1995-01-01
As is known, a solitary pulse in the complex cubic Ginzburg-Landau (GL) equation is unstable. We demonstrate that a system of two linearly coupled GL equations with gain and dissipation in one subsystem and pure dissipation in another produces absolutely stable solitons and their bound states. The problem is solved in a fully analytical form by means of the perturbation theory. The soliton coexists with a stable trivial state; there is also an unstable soliton with a smaller amplitude, which is a separatrix between the two stable states. This model has a direct application in nonlinear fiber optics, describing an Erbium-doped laser based on a dual-core fiber.
Soto, F.; Berger, H.; Cabo, L.; Carballeira, C.; Mosqueira, J.; Pavuna, D.; Toimil, P.; Vidal, F.
2007-09-01
Electric and magnetic characterization of NbSe 2 single crystals is first presented in detail. Then, some preliminary measurements of the fluctuation-diamagnetism (FD) above the transition temperature TC are presented. The moderate uniaxial anisotropy of this compound allowed us to observe the fluctuation effects for magnetic fields H applied in the two main crystallographic orientations. The superconducting parameters resulting from the characterization suggest that it is possible to do a reliable analysis of the FD in terms of the Ginzburg-Landau (GL) theory.
Introduction to superconductivity and high-T sub c materials
Cyrot, M. (Grenoble (FR)); Pavuna, D. (Lausanne (CH))
1991-01-01
What sets this book apart from other introductions to superconductivity and high-T{sub c} materials is its pragmatic approach. In this book the authors describe all relevant superconducting phenomena and rely on the macroscopic Ginzburg-Landau theory to derive the most important results. Examples are chosen from selected conventional superconductors like NbTi and compared to those high-T{sub c} materials. The text should be of interest to non-specialists in superconductivity either as a textbook for those entering the field (one semester course) or as researchers in advanced technologies and even some managers of interdisciplinary research projects.
Soto, F. [LBTS, Departamento de Fisica da Materia Condensada, Universidade de Santiago de Compostela E-15782 (Spain); Berger, H. [Department of Physics, Ecole Politechnique Federale de Lausanne, CH-01015 Lausanne (Switzerland); Cabo, L.; Carballeira, C. [LBTS, Departamento de Fisica da Materia Condensada, Universidade de Santiago de Compostela E-15782 (Spain); Mosqueira, J. [LBTS, Departamento de Fisica da Materia Condensada, Universidade de Santiago de Compostela E-15782 (Spain)], E-mail: fmjesus@usc.es; Pavuna, D. [Department of Physics, Ecole Politechnique Federale de Lausanne, CH-01015 Lausanne (Switzerland); Toimil, P.; Vidal, F. [LBTS, Departamento de Fisica da Materia Condensada, Universidade de Santiago de Compostela E-15782 (Spain)
2007-09-01
Electric and magnetic characterization of NbSe{sub 2} single crystals is first presented in detail. Then, some preliminary measurements of the fluctuation-diamagnetism (FD) above the transition temperature T{sub C} are presented. The moderate uniaxial anisotropy of this compound allowed us to observe the fluctuation effects for magnetic fields H applied in the two main crystallographic orientations. The superconducting parameters resulting from the characterization suggest that it is possible to do a reliable analysis of the FD in terms of the Ginzburg-Landau (GL) theory.
Resistive states created in superconducting NbTiN filaments by an electrical current pulse
K. Harrabi
2015-03-01
Full Text Available We have observed as a function of the time the appearance of the voltage caused by a larger-than-critical (I > Ic step-pulse of current in narrow NbTiN strips at 4.2 K. Different current intensities produced either phase-slip centres characterized by a voltage saturating with the time, or ever expanding hot spots. These dissipative structures occur after a measurable delay time, whose dependence upon the ratio I/Ic can be analysed through a Ginzburg-Landau theory to yield a unique adjustable time constant.
Landau, I. L.; Ott, H. R.
2002-10-01
Using the Ginzburg-Landau theory in very general terms, we develop a simple scaling procedure which allows to establish the temperature dependence of the upper critical field Hc2 and the value of the superconducting critical temperature Tc of type-II superconductors from measurements of the reversible isothermal magnetization. An analysis of existing experimental data shows that the normalized dependencies of Hc2 on T/Tc are practically identical for all families of high-Tc superconductors at all temperatures for which the magnetization data are available.
Gauge dependence of the critical dynamics at the superconducting phase transition
M.Dudka
2007-01-01
Full Text Available The critical dynamics of superconductors in the charged regime is reconsidered within field-theory. For the dynamics, the Ginzburg-Landau model with complex order parameter coupled to the gauge field suggested earlier [Lannert et al. Phys. Rev. Lett. 92, 097004 (2004] is used. Assuming relaxational dynamics for both quantities, the renormalization group functions within one loop approximation are recalculated for different choices of the gauge. A gauge independent result for the divergence of the melectric conductivity is obtained only at the weak scaling fixed point unstable in one loop order where the timescales of the order parameter and the gauge field are different.
Nonequilibrium lattice-driven dynamics of stripes in nickelates using time-resolved x-ray scattering
Lee, W.S.; Kung, Y.F.; Moritz, B.; Coslovich, G.; Kaindl, R.A.; Chuang, Y.D.; Moore, R.G.; Lu, D.H.; Kirchmann, P.S.; Robinson, J.S.; Minitti, M.P.; Dakovski, G.; Schlotter, W.F.; Turner, J.J.; Gerber, S.; Sasagawa, T.; Hussain, Z.; Shen, Z.X.; Devereaux, T.P.
2017-03-13
We investigate the lattice coupling to the spin and charge orders in the striped nickelate, La 1.75 Sr 0.25 NiO 4 , using time-resolved resonant x-ray scattering. Lattice-driven dynamics of both spin and charge orders are observed when the pump photon energy is tuned to that of an E u bond- stretching phonon. We present a likely scenario for the behavior of the spin and charge order parameters and its implications using a Ginzburg-Landau theory.
Sun Pu-Nan; Cui Lian; Lü Tian-Quan
2009-01-01
Within the framework of modified Ginzburg-Landau-Devonshire phenomenological theory,a ferroelectric bilayer film with a transition layer within each constituent film and an interfacial coupling between two materials has been studied.Properties including the Curie temperature and the spontaneous polarization of a bilayer film composed of two equally thick ferroelectric constituent films are discussed.The results show that the combined effect of the transition layer and the interfacial coupling plays an important role in explaining the interesting behaviour of ferroelectric multilayer structures consisting of two ferroelectric materials.
Izmailov, Alexander F.; Myerson, Allan S.
1993-01-01
A new mathematical ansatz is developed for solution of the time-dependent Ginzburg-Landau nonlinear partial differential equation describing metastable state relaxation in binary (solute+solvent) non-critical solutions with non-conserved scalar order parameter in presence of a gravitational field. It has been demonstrated analytically that in such systems metastability initiates heterogeneous solute redistribution which results in the formation of a non-equilibrium singly-periodic spatial solute structure in the new solute-rich phase. The critical radius of nucleation and the induction time in these systems are gravity-dependent. It has also been proved that metastable state relaxation in vertical columns of supersaturated non-critical binary solutions leads to formation of the solute concentration gradient. Analytical expression for this concentration gradient is found and analysed. It is concluded that gravity can initiate phase separation (nucleation or spinodal decomposition).
Andrade Landeta, J.; Lascano, I.
2017-07-01
A theorical model has been developed based on the theory of Ginzburg-Landau-Devonshire to study and predict the effects the decreasing of size particle in a nanosphere of PbTiO3 subjected to the action of depolarization fields and mechanical stress. It was considered that the nanosphere is surrounded by a layer of space charges on its surface, and containing 180° domains generated by minimizing free energy of depolarization. Energy density of depolarization, wall domain and electro-elastic energy have been incorporated into the free energy of the theory Ginzburg-Landau-Devonshire. Free energy minimization was performed to determine the spontaneous polarization and transition temperature system. These results show that the transition temperature for nanosphere is substantially smaller than the corresponding bulk material. Also, it has been obtained that the stability of the ferroelectric phase of nanosphere is favored for configurations with a large number of 180° domains, with the decreasing of thickness space charge layer, and the application of tensile stress and decreases with compressive stress. (Author)
On the interplay of superconductivity and magnetism
Powell, B J
2002-01-01
We explore the exchange field dependence of the Hubbard model with a attractive, effective, pairwise, nearest neighbour interaction via the Hartree-Fock-Gorkov approximation. We derive a Ginzburg-Landau theory of spin triplet superconductivity in an exchange field. For microscopic parameters which lead to ABM phase superconductivity in zero field, the Ginzburg-Landau theory allows both an axial (A, A sub 1 or A sub 2) solution with the vector order parameter, d(k), perpendicular to the field, H, and an A phase solution with d(k) parallel to H. We study the spin-generalised Bogoliubov-de Gennes (BdG) equations for this model with parameters suitable for strontium ruthenate (Sr sub 2 RuO sub 4). The A sub 2 phase is found to be stable in a magnetic field. However, in the real material, spin-orbit coupling could pin the order parameter to the crystallographic c-axis which would favour the A phase for fields parallel to the c-axis. We show that the low temperature thermodynamic behaviour in a magnetic field could...
Detailed magnetization study of superconducting properties of YBa2Cu3O7-x ceramic spheres
Landau, I. L.; Willems, J. B.; Hulliger, J.
2008-03-01
We present a magnetization study of low density YBa2Cu3O7-x ceramics carried out in magnetic fields H such that 0.5 Oe85 K, using low field magnetization measurements, we were able to evaluate the temperature dependence of λ, which turned out to be very close to predictions from conventional Ginzburg-Landau theory. Although the present samples consisted of randomly oriented grains, specifics of magnetization measurements allowed for evaluation of λab(T). Good agreement between our estimation of the grain size and the real sample structure provides evidence for the validity of this analysis of magnetization data. Measurements of the equilibrium magnetization in high magnetic fields were used for evaluation of Hc2(T). At temperatures close to Tc, the Hc2(T) dependence turned out to be linear, in agreement with Ginzburg-Landau theory. The value of the temperature at which Hc2 vanishes coincides with the superconducting critical temperature evaluated from low field measurements, which is important evidence of the validity of both approaches to the analysis of magnetization data.
Schuler, James J.; Felippa, Carlos A.
1994-01-01
The present work is part of a research program for the numerical simulation of electromagnetic (EM) fields within conventional Ginzburg-Landau (GL) superconductors. The final goal of this research is to formulate, develop and validate finite element (FE) models that can accurately capture electromagnetic thermal and material phase changes in a superconductor. The formulations presented here are for a time-independent Ginzburg-Landau superconductor and are derived from a potential-based variational principle. We develop an appropriate variational formulation of time-independent supercontivity for the general three-dimensional case and specialize it to the one-dimensional case. Also developed are expressions for the material-dependent parameters alpha and beta of GL theory and their dependence upon the temperature T. The one-dimensional formulation is then discretized for finite element purposes and the first variation of these equations is obtained. The resultant Euler equations contain nonlinear terms in the primary variables. To solve these equations, an incremental-iterative solution method is used. Expressions for the internal force vector, external force vector, loading vector and tangent stiffness matrix are therefore developed for use with the solution procedure.
Non-equilibrium crystalline superconductors in Zr-Si binary alloys rapidly quenched from melts
Inoue, A.; Takahashi, Y.; Toyota, N.; Fukase, T.; Masumoto, T. (Tohoku Univ., Sendai (Japan). Research Inst. for Iron, Steel and Other Metals)
1982-08-01
The new non-equilibrium superconductor with a bcc structure has been found in rapidly quenched Zr-Si alloys. The silicon content in the bcc alloys was limited to the narrow range between 8 and 11 at%. The bcc alloys showed a superconducting transition whose temperature increased from 3.20 to 3.84 K with decreasing silicon content. The upper critical magnetic field and the critical current density for Zr/sub 92/Si/sub 8/ alloy were of the order of 3.58 x 10/sup 6/ Am/sup -1/ at 2.0 K and 3.3 x 10/sup 6/ Am/sup -2/ at 2.42 K in the absence of an applied field. The upper critical field gradient at the transition temperature and the electrical resistivity at 4.2 K were about -1.82 x 10/sup 6/ Am/sup -1/ K/sup -1/ and about 150 ..mu cap omega.. cm. The Ginzburg-Landau parameter and coherence length were estimated to be about 65 and 6.3 nm, respectively, from these experimental values by using the Ginzburg-Landau-Abrikosov-Gorkov theory and hence it is concluded that the present bcc alloys are extremely 'soft' type-II superconductors with a high degree of dirtiness.
Sivakov, A. G.; Pokhila, A. S.; Glukhov, A. M.; Kuplevakhsky, S. V.; Omelyanchouk, A. N.
2014-05-01
We report the results of experimental and theoretical studies of critical current oscillations in thin doubly-connected Sn films in an external perpendicular magnetic field. The experiments were performed on samples that consisted of two wide electrodes joined together by two narrow channels. The length of the channels l satisfied the condition l ≫ ξ (ξ is the Ginzburg-Landau coherence length). At temperatures close to the critical temperature Tc, the dependence of the critical current Ic on average external magnetic flux Φ¯e has the form of a piecewise linear function, periodic with respect to the flux quantum Φ0. The amplitude of the Ic oscillation at a given temperature is proportional to the factor ξ/l. Moreover, the dependence Ic=Ic(Φ ¯e) is found to be multivalued, hence indicating the presence of metastable states. Based on the Ginzburg-Landau approximation, a theory was constructed that explains the above features of the oscillation phenomenon taking a perfectly symmetric system as an example. Further, the experiments displayed the effects related to the critical currents imbalance between the superconducting channels, i.e., shift of the maxima of the dependence Ic=Ic(Φ ¯e) accompanied by an asymmetry with respect to the transport current direction.
Vortex properties of mesoscopic superconducting samples
Cabral, Leonardo R.E. [Laboratorio de Supercondutividade e Materiais Avancados, Departamento de Fisica, Universidade Federal de Pernambuco, Recife 50670-901 (Brazil); Barba-Ortega, J. [Grupo de Fi' sica de Nuevos Materiales, Departamento de Fisica, Universidad Nacional de Colombia, Bogota (Colombia); Souza Silva, C.C. de [Laboratorio de Supercondutividade e Materiais Avancados, Departamento de Fisica, Universidade Federal de Pernambuco, Recife 50670-901 (Brazil); Albino Aguiar, J., E-mail: albino@df.ufpe.b [Laboratorio de Supercondutividade e Materiais Avancados, Departamento de Fisica, Universidade Federal de Pernambuco, Recife 50670-901 (Brazil)
2010-10-01
In this work we investigated theoretically the vortex properties of mesoscopic samples of different geometries, submitted to an external magnetic field. We use both London and Ginzburg-Landau theories and also solve the non-linear Time Dependent Ginzburg-Landau equations to obtain vortex configurations, equilibrium states and the spatial distribution of the superconducting electron density in a mesoscopic superconducting triangle and long prisms with square cross-section. For a mesoscopic triangle with the magnetic field applied perpendicularly to sample plane the vortex configurations were obtained by using Langevin dynamics simulations. In most of the configurations the vortices sit close to the corners, presenting twofold or three-fold symmetry. A study of different meta-stable configurations with same number of vortices is also presented. Next, by taking into account de Gennes boundary conditions via the extrapolation length, b, we study the properties of a mesoscopic superconducting square surrounded by different metallic materials and in the presence of an external magnetic field applied perpendicularly to the square surface. It is determined the b-limit for the occurrence of a single vortex in a mesoscopic square of area d{sup 2}, for 4{xi}(0){<=}d{<=}10{xi}(0).
Quantum field kinetics of QCD quark-gluon transport theory for light-cone dominated processes
Kinder-Geiger, Klaus
1996-01-01
A quantum kinetic formalism is developed to study the dynamical interplay of quantum and statistical-kinetic properties of non-equilibrium multi-parton systems produced in high-energy QCD processes. The approach provides the means to follow the quantum dynamics in both space-time and energy-momentum, starting from an arbitrary initial configuration of high-momentum quarks and gluons. Using a generalized functional integral representation and adopting the `closed-time-path' Green function techniques, a self-consistent set of equations of motions is obtained: a Ginzburg-Landau equation for a possible color background field, and Dyson-Schwinger equations for the 2-point functions of the gluon and quark fields. By exploiting the `two-scale nature' of light-cone dominated QCD processes, i.e. the separation between the quantum scale that specifies the range of short-distance quantum fluctuations, and the kinetic scale that characterizes the range of statistical binary inter- actions, the quantum-field equations of ...
Ikuhiro Yamaguchi
Full Text Available Time delay is known to induce sustained oscillations in many biological systems such as electroencephalogram (EEG activities and gene regulations. Furthermore, interactions among delay-induced oscillations can generate complex collective rhythms, which play important functional roles. However, due to their intrinsic infinite dimensionality, theoretical analysis of interacting delay-induced oscillations has been limited. Here, we show that the two primary methods for finite-dimensional limit cycles, namely, the center manifold reduction in the vicinity of the Hopf bifurcation and the phase reduction for weak interactions, can successfully be applied to interacting infinite-dimensional delay-induced oscillations. We systematically derive the complex Ginzburg-Landau equation and the phase equation without delay for general interaction networks. Based on the reduced low-dimensional equations, we demonstrate that diffusive (linearly attractive coupling between a pair of delay-induced oscillations can exhibit nontrivial amplitude death and multimodal phase locking. Our analysis provides unique insights into experimentally observed EEG activities such as sudden transitions among different phase-locked states and occurrence of epileptic seizures.
Novel superconductivity: from bulk to nano systems
Das, M. P.; Wilson, B. J.
2015-03-01
We begin with an introduction of superconductivity by giving a brief history of the phenomenon. The phenomenological Ginzburg-Landau theory and the microscopic theory of Bardeen, Cooper and Schrieffer are outlined. In view of recently available multi-band superconductors, relevant theories of both types are discussed. Unlike the traditional GL theory an extended GL theory is developed relevant to temperatures below the critical temperature. Superconductivity in a nanosystem is the highlight of the remaining part of the paper. Theories and experiments are discussed to give an interested reader an updated account and overview of what is new in this active area of research. Keynote talk at the 7th International Workshop on Advanced Materials Science and Nanotechnology IWAMSN2014, 2-6 November, 2014, Ha Long, Vietnam
Weakly nonlinear dynamics in reaction-diffusion systems with Levy flights
Nec, Y; Nepomnyashchy, A A [Department of Mathematics, Technion-Israel Institute of Technology, Haifa 32000 (Israel); Golovin, A A [Department of Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, IL 60208 (United States)], E-mail: flyby@techunix.technion.ac.il
2008-12-15
Reaction-diffusion equations with a fractional Laplacian are reduced near a long wave Hopf bifurcation. The obtained amplitude equation is shown to be the complex Ginzburg-Landau equation with a fractional Laplacian. Some of the properties of the normal complex Ginzburg-Landau equation are generalized for the fractional analogue. In particular, an analogue of the Kuramoto-Sivashinsky equation is derived.
Habeney, Lucas
2016-09-23
The purpose of this work was to give the reader insight into the topic of conventional superconductors. It started out with defining the superconductive state itself as a state of ideal conductivity and ideal diamagnetism. An important phenomenon to keep in mind in this regard is the Meissner-Ochsenfeld effect. It then went on to attempt to understand those properties on a macroscopic level. This was achieved in the framework of the two major macroscopic theories, the London theory and the Ginzburg-Landau theory. While the London theory focused on the electrodynamic qualities of the superconductive state, the Ginzburg-Landau theory dealt with events close to the superconducting phase transition in a thermodynamic scope. The highlight of this section was the investigation of the Abrikosov lattice, the geometric disposition of the flux tubes in the intermediate Shubnikov phase. We closed with the BCS theory as the premier microscopic theory of superconductivity. Main subjects of this section were the concept of Cooper pairs and the calculation of various energy gap equations. We also looked at real properties of superconductors such as the specific heat to test our rather abstract calculations and came to outstanding agreements. The principles presented in this document should serve as a foundation to work on more advanced problems in superconductivity. Especially the large field of unconventional superconductivity is of huge interest in current research, as most of the high T{sub c} superconductors fall in that category. As unconventional superconductors can not be explained with BCS theory, the search for a uniform theory to describe them is still on-going. Unconventional superconductors include but are not limited to cuprates (T{sub c}
余王辉
2001-01-01
本文证明了:当Ginzburg-Landau参数足够大时,一维Ginzburg-Landau超导方程组的对称解是唯一的.该问题的难点在于所考虑的解具有“奇点”:也即,当Ginzburg-Landau参数趋于无穷大时,解的导数在这些点处趋于无穷.证明的关键是要得到解在这些奇点近旁的精细估计.
Variational methods in molecular modeling
2017-01-01
This book presents tutorial overviews for many applications of variational methods to molecular modeling. Topics discussed include the Gibbs-Bogoliubov-Feynman variational principle, square-gradient models, classical density functional theories, self-consistent-field theories, phase-field methods, Ginzburg-Landau and Helfrich-type phenomenological models, dynamical density functional theory, and variational Monte Carlo methods. Illustrative examples are given to facilitate understanding of the basic concepts and quantitative prediction of the properties and rich behavior of diverse many-body systems ranging from inhomogeneous fluids, electrolytes and ionic liquids in micropores, colloidal dispersions, liquid crystals, polymer blends, lipid membranes, microemulsions, magnetic materials and high-temperature superconductors. All chapters are written by leading experts in the field and illustrated with tutorial examples for their practical applications to specific subjects. With emphasis placed on physical unders...
Zeng, Hua-Bi; Zong, Hong-Shi
2009-01-01
A classical SU(2) Einstein-Yang-Mills theory in 3+1 dimensional anti-de Sitter spacetime is believed to be dual to a p-wave superconductor in 2+1 dimensional flat spacetime. In order to calculate the superconductiong coherence length $\\xi$ of the holographic superconductor near the superconducting phase transition point, we study the perturbation of the gravity theory analytically. The superconductiong coherence length $\\xi$ is found to be proportional to $(1-T/T_c)^{-1/2}$ near the critical temperature $T_c$. We also obtain the magnetic penetration depth $\\lambda\\propto(T_c-T)^{1/2}$ by adding a small external homogeneous magnetic field. The results agree with the Ginzburg-Landau theory.
Phase-field modeling of isothermal quasi-incompressible multicomponent liquids
Tóth, Gyula I.
2016-09-01
In this paper general dynamic equations describing the time evolution of isothermal quasi-incompressible multicomponent liquids are derived in the framework of the classical Ginzburg-Landau theory of first order phase transformations. Based on the fundamental equations of continuum mechanics, a general convection-diffusion dynamics is set up first for compressible liquids. The constitutive relations for the diffusion fluxes and the capillary stress are determined in the framework of gradient theories. Next the general definition of incompressibility is given, which is taken into account in the derivation by using the Lagrange multiplier method. To validate the theory, the dynamic equations are solved numerically for the quaternary quasi-incompressible Cahn-Hilliard system. It is demonstrated that variable density (i) has no effect on equilibrium (in case of a suitably constructed free energy functional) and (ii) can influence nonequilibrium pattern formation significantly.
Phase-field modeling of isothermal quasi-incompressible multicomponent liquids
Toth, Gyula I
2016-01-01
In this paper general dynamic equations describing the time evolution of isothermal quasi-incompressible multicomponent liquids are derived in the framework of the classical Ginzburg-Landau theory of first order phase transformations. Based on the fundamental continuum mechanical equations, a general convection-diffusion dynamics is set up first for compressible liquids. The constitutive relations for the diffusion fluxes and the capillary stress are determined in the framework of gradient theories. A mathematically precise definition of incompressibility is then given, which is taken into account by using the Lagrange multiplier method. To validate the theory, the general dynamic equations are solved numerically for the quaternary quasi-incompressible Cahn-Hilliard system. It is demonstrated that variable density (i) has no effect on equilibrium only in case of a suitably constructed free energy functional, while (ii) may influence non-equilibrium pattern formation significantly.
Berezinskii-Kosterlitz-Thouless transition in homogeneously disordered superconducting films
König, E. J.; Levchenko, A.; Protopopov, I. V.; Gornyi, I. V.; Burmistrov, I. S.; Mirlin, A. D.
2015-12-01
We develop a theory for the vortex-unbinding transition in homogeneously disordered superconducting films. This theory incorporates the effects of quantum, mesoscopic, and thermal fluctuations stemming from length scales ranging from the superconducting coherence length down to the Fermi wavelength. In particular, we extend the renormalization group treatment of the diffusive nonlinear sigma model to the superconducting side of the transition. Furthermore, we explore the mesoscopic fluctuations of parameters in the Ginzburg-Landau functional. Using the developed theory, we determine the dependence of essential observables (including the vortex-unbinding temperature, the superconducting density, as well as the temperature-dependent resistivity and thermal conductivity) on microscopic characteristics such as the disorder-induced scattering rate and bare interaction couplings.
Vortices in superconducting bulk, films and SQUIDs
Ernst Helmut Brandt
2006-01-01
The properties of the ideal periodic vortex lattice in bulk superconductors and in films of any thickness can be calculated from Ginzburg-Landau theory by an iteration method using Fourier series. The London theory yields general analytic expressions for the magnetic field and energy of arbitrary arrangements of straight or curved vortex lines. The elasticity of the vortex lattice is highly nonlocal. The magnetic response of superconductors of realistic shapes like thin and thick strips and disks or thin rectangular plates or films, containing pinned vortices, can be computed within continuum theory by solving an integral equation. A useful example is a thin square with a central hole and a radial slit, used as superconducting quantum interference device (SQUID).
Wæver, Ole
2009-01-01
Kenneth N. Waltz's 1979 book, Theory of International Politics, is the most influential in the history of the discipline. It worked its effects to a large extent through raising the bar for what counted as theoretical work, in effect reshaping not only realism but rivals like liberalism and refle......Kenneth N. Waltz's 1979 book, Theory of International Politics, is the most influential in the history of the discipline. It worked its effects to a large extent through raising the bar for what counted as theoretical work, in effect reshaping not only realism but rivals like liberalism...... and reflectivism. Yet, ironically, there has been little attention to Waltz's very explicit and original arguments about the nature of theory. This article explores and explicates Waltz's theory of theory. Central attention is paid to his definition of theory as ‘a picture, mentally formed' and to the radical anti......-empiricism and anti-positivism of his position. Followers and critics alike have treated Waltzian neorealism as if it was at bottom a formal proposition about cause-effect relations. The extreme case of Waltz being so victorious in the discipline, and yet being consistently mis-interpreted on the question of theory...
Theoretical study of magnetoelectric effects in noncentrosymmetric and cuprate superconductors
Kashyap, Manoj K.
A century after the discovery of superconductivity at the lab of Kamerlingh Onnes in 1911, it is noticeable that the phenomenon is quite ubiquitous in nature. In addition to a long list of superconducting alloys and compounds, almost half the elements in the periodic table superconduct. By the late seventies, superconductivity was thought to be well understood. This turned out to be a myth, with the discovery of unconventional superconductors that defied Bardeen-Cooper-Schrieffer (BCS) theory. Cuprates have been the most prominent example among them ever since their discovery in 1986 by Bednorz and Muller. Another example of non-compliance with BCS theory lie among noncentrosymmetric superconductors. In this dissertation, magnetoelectric (ME) effects in these two classes of superconductors have been studied from different perspectives, utilizing Ginzburg-Landau (GL) theory. Even though GL theory was proposed before the BCS theory, it was not given much importance due to its phenomenological nature until Gor'kov proved that it is a limiting form of the microscopic BCS theory. However today, in the absence of any complete microscopic theory to explain superconductivity in unconventional superconductors, Ginzburg-Landau theory is an important tool to move ahead and qualitatively understand the behavior of varied superconducting systems. Noncentrosymmetric superconductors have generated much theoretical interest since 2004 despite been known for long. The absence of inversion symmetry in non- centrosymmetric superconductors allows for extra terms called Lifshitz invariants in the Ginzburg-Landau functional. This leads to magnetoelectric effects that do not exist in centrosymmetric superconductors. One manifestation of this is in the vortex structure in materials with a cubic point group O. In particular, a current is predicted to flow parallel to the applied magnetic field in such a vortex in addition to the usual vortex supercurrents. In this work, we present both
Strong-Coupling and the Stripe Phase of ^3He
Wiman, Joshua J.; Sauls, J. A.
2016-09-01
Thin films of superfluid 3He were predicted, based on weak-coupling BCS theory, to have a stable phase which spontaneously breaks translational symmetry in the plane of the film. This crystalline superfluid, or "stripe" phase, develops as a one-dimensional periodic array of domain walls separating degenerate B phase domains. We report calculations of the phases and phase diagram for superfluid 3He in thin films using a strong-coupling Ginzburg-Landau theory that accurately reproduces the bulk 3He superfluid phase diagram. We find that the stability of the Stripe phase is diminished relative to the A phase, but the Stripe phase is stable in a large range of temperatures, pressures, confinement, and surface conditions.
Contraction of Information on Brain Wave Fluctuations by Information Geometrical Approach
Konno, Hidetoshi
2005-08-01
We will first propose a method of EEG signal identification with the use of the stochastic complex Ginzburg-Landau (CGL) equation having complex coefficients with the aid of the method of information geometrical approach to determine the system parameters. After the contracting information on the natures of fluctuations of amplitude and phase in the EEG signals on human scalp, we combine the information with other information such as complex measures like Higuchi's fractal dimension and multi-scale entropies. A new theory of unification of the information is also proposed. To exhibit the potentiality of our new method, we show the result of application of the theory and method to practical EEG data from elderly sound and demented people.
Nonequilibrium dynamical mean-field study of the nonthermal fixed point in the Hubbard model
Tsuji, Naoto; Eckstein, Martin; Werner, Philipp
2014-03-01
A fundamental question of whether and how an isolated quantum many-body system thermalizes has been posed and attracted broad interest since its ideal realization using cold atomic gases. In particular, it has been indicated by various theoretical studies that the system does not immediately thermalize but often shows ``prethermalization'' as a quasi-stationary state, where local observables quickly arrive at the thermal values while the full momentum distribution stays nonthermal for long time. Here we study the thermalization process for the fermionic Hubbard model in the presence of the antiferromagnetic long-range order. Time evolution is obtained by the nonequilibrium dynamical mean-field theory. Due to classical fluctuations, prethermalization is prevented, and the transient dynamics is governed by a nonthermal fixed point, which we discuss belongs to a universality class distinct from the conventional Ginzburg-Landau theory.
Quantum fluctuations in the time-dependent BCS-BEC crossover.
Breid, B M; Anglin, J R
2008-08-28
We describe the time-dependent formation of a molecular Bose-Einstein condensate from a BCS state of fermionic atoms as a result of slow sweeping through a Feshbach resonance. We apply a path integral approach for the molecules, and use two-body adiabatic approximations to solve the atomic evolution in the presence of the classical molecular fields, obtaining an effective action for the molecules. In the narrow resonance limit, the problem becomes semiclassical, and we discuss the growth of the molecular condensate in the saddle point approximation. Considering this time-dependent process as an analogue of the cosmological Zurek scenario, we compare the way condensate growth is driven in this rigorous theory with its phenomenological description via time-dependent Ginzburg-Landau theory.
Feynman Path Integrals Over Entangled States
Green, A G; Keeling, J; Simon, S H
2016-01-01
The saddle points of a conventional Feynman path integral are not entangled, since they comprise a sequence of classical field configurations. We combine insights from field theory and tensor networks by constructing a Feynman path integral over a sequence of matrix product states. The paths that dominate this path integral include some degree of entanglement. This new feature allows several insights and applications: i. A Ginzburg-Landau description of deconfined phase transitions. ii. The emergence of new classical collective variables in states that are not adiabatically continuous with product states. iii. Features that are captured in product-state field theories by proliferation of instantons are encoded in perturbative fluctuations about entangled saddles. We develop a general formalism for such path integrals and a couple of simple examples to illustrate their utility.
Spin-Orbit Coupling and Multiple phases in Spin-Triplet Superconductor Sr2RuO4
Yanase, Youichi; Takamatsu, Shuhei; Udagawa, Masafumi
2014-06-01
We study the spin-orbit coupling in spin-triplet Cooper pairs and clarify multiple superconducting (SC) phases in Sr2RuO4. Based on the analysis of the three-orbital Hubbard model with atomic LS coupling, we show some selection rules of the spin-orbit coupling in Cooper pairs. The spin-orbit coupling is small when the two-dimensional γ-band is the main cause of the superconductivity, although the LS coupling is much larger than the SC gap. Considering this case, we investigate multiple SC transitions in the magnetic fields for both H || [001] and H || [100] using the Ginzburg-Landau theory and the quasi-classical theory. Rich phase diagrams are obtained because the spin degree of freedom in Cooper pairs is not quenched by the spin-orbit coupling. Experimental indications for the multiple phases in Sr2RuO4 are discussed.
Prescod-Weinstein, Chanda; Bertschinger, Edmund
2014-03-01
Motivated by the desire to fully understand Bose-Einstein condensates in curved spacetimes, we present a generalization of the Faddeev-Jackiw technique for constraint reduction that simplifies calculating the Poisson brackets for gauge field theories in curved backgrounds. The Faddeev-Jackiw technique is a symplectic approach to phase space coordinate reduction on singular Lagrangians which offers an alternative to the Dirac technique. This approach was generalized by Barcelos-Nieto and Wotzasek to make its application easier. We find that the technique is a useful tool that avoids some of the subtle complications of the Dirac approach to constraints. A major difference between our work and previous formulations is that we do not explicitly construct the symplectic matrix, as that is not necessary. We apply this formulation to the Ginzburg-Landau action and calculate its Poisson brackets in a curved spacetime. We sketch out steps to apply the technique to a Bose field in the gauge theory General Relativity.
Conformal invariance and renormalization group in quantum gravity near two dimensions
Aida, T; Kawai, H; Ninomiya, M
1994-01-01
We study quantum gravity in 2+\\epsilon dimensions in such a way to preserve the volume preserving diffeomorphism invariance. In such a formulation, we prove the following trinity: the general covariance, the conformal invariance and the renormalization group flow to Einstein theory at long distance. We emphasize that the consistent and macroscopic universes like our own can only exist for matter central charge 0
Hamiltonian and action principle formalisms for spin-1/2 magnetohydrodynamics
Lingam, M., E-mail: manasvi@physics.utexas.edu [Department of Physics and Institute for Fusion Studies, The University of Texas at Austin, Austin, Texas 78712 (United States)
2015-02-15
A Hamiltonian and Action Principle formulation of spin-1/2 magnetohydrodynamics is presented via a first-principles derivation of the underlying Lagrangian, and the associated Hamiltonian. The derivation invokes the notion of “frozen-in” constraints, symmetry breaking, and similarities with Ginzburg-Landau theory to arrive at the relevant terms in the Hamiltonian. The model thus obtained includes the effects of spin and other quantum corrections and is shown to be in full agreement with existent models in the literature. It is also indicated how two-fluid effects, gyroviscosity, and anisotropic pressure can be included in the model, in addition to incorporating higher-order (nonlinear) quantum spin corrections. An interesting analogy with the theory of liquid crystals is also highlighted.
Dynamical systems approach to one-dimensional spatiotemporal chaos: A cyclist's view
Lan, Yueheng
We propose a dynamical systems approach to the study of weak turbulence (spatiotemporal chaos) based on the periodic orbit theory, emphasizing the role of recurrent patterns and coherent structures. After a brief review of the periodic orbit theory and its application to low-dimensional dynamics, we discuss its possible extension to study dynamics of spatially extended systems. The discussion is three-fold. First, we introduce a novel variational scheme for finding periodic orbits in high-dimensional systems. Second, we prove rigorously the existence of periodic structures (modulated amplitude waves) near the first instability of the complex Ginzburg-Landau equation, and check their role in pattern formation. Third, we present the extensive numerical exploration of the Kuramoto-Sivashinsky system in the chaotic regime: structure of the equilibrium solutions, our search for the shortest periodic orbits, description of the chaotic invariant set in terms of intrinsic coordinates and return maps on the Poincare section.
Gauzzi, Andrea; Pavuna, Davor
1995-06-01
We report on in-plane paraconductivity measurements in thin YBa2Cu3O6.9 films. Our analysis of the data shows that the temperature dependence of paraconductivity is affected by lattice disorder and deviates at all temperatures from the universal power laws predicted by both scaling and mean-field theories. This gives evidence for the absence of critical fluctuations and for the failure of the Aslamazov-Larkin universal relation between critical exponent and dimensionality of the spectrum of Gaussian fluctuations. We account quantitatively for the data within the experimental error by introducing a short-wavelength cutoff into this spectrum. This implies that three-dimensional short-wavelength Gaussian fluctuations dominate in YBa2Cu3O6.9 and suggests a rapid attenuation of these fluctuations with decreasing wavelength in short-coherence-length systems as compared to the case of the conventional Ginzburg-Landau theory.
Nuclear level density of even-even nuclei with temperature-dependent pairing energy
Dehghani, V.; Alavi, S.A. [University of Sistan and Baluchestan, Physics Department, Faculty of Sciences, Zahedan (Iran, Islamic Republic of)
2016-10-15
The influence of using a temperature-dependent pairing term on the back-shifted Fermi gas (BSFG) model of nuclear level density of some even-even nuclei has been investigated. We have chosen an approach to determine the adjustable parameters from theoretical calculations, directly. The exact Ginzburg-Landau (EGL) theory was used to determine the temperature-dependent pairing energy as back-shifted parameter of the BSFG model. The level density parameter of the BSFG model has been determined through the Thomas-Fermi approximation. The level densities of {sup 96}Mo, {sup 106,112}Cd, {sup 106,108}Pd, {sup 164}Dy, {sup 232}Th, {sup 238}U and heat capacities of {sup 96}Mo and {sup 164}Dy nuclei were calculated. Good agreement between theory and experiment was observed. (orig.)
The Renormalization-Group Method Applied to Asymptotic Analysis of Vector Fields
Kunihiro, T
1996-01-01
The renormalization group method of Goldenfeld, Oono and their collaborators is applied to asymptotic analysis of vector fields. The method is formulated on the basis of the theory of envelopes, as was done for scalar fields. This formulation actually completes the discussion of the previous work for scalar equations. It is shown in a generic way that the method applied to equations with a bifurcation leads to the Landau-Stuart and the (time-dependent) Ginzburg-Landau equations. It is confirmed that this method is actually a powerful theory for the reduction of the dynamics as the reductive perturbation method is. Some examples for ordinary diferential equations, such as the forced Duffing, the Lotka-Volterra and the Lorenz equations, are worked out in this method: The time evolution of the solution of the Lotka-Volterra equation is explicitly given, while the center manifolds of the Lorenz equation are constructed in a simple way in the RG method.
Quasiperiodic superconducting V/Zr multilayers: critical magnetic fields and crossover
Fogel, N. Ya.; Cherkasova, V. G.; Mikhailov, M. Yu.; Bomze, Yu. V.; Yuzephovich, O. I.; Dmitrenko, I. M.; Stetsenko, A. N.
1998-08-01
Critical magnetic fields parallel and perpendicular to the planes of quasiperiodic superconducting Fibonacci multilayers (ML) consisting of vanadium and zirconium are measured. The temperature dependence of the parallel critical field Hc∥ displays two crossovers. The Hc∥(T) dependence is of square-root type in the vicinity of the transition temperature Tc and linear at low temperatures. Between these temperature intervals, the dependence follows a power law: Hc∥˜(1-T/Tc)α, α=0,78±0,02. The complex nature of this dependence can be explained in the framework of the Ginzburg-Landau theory for a quasiperiodic ML, as well as by the scaling theory for fractal multilayers which takes into account the different structure length scales in the case of ML with a complex sequence of layers.
Universal critical behavior of noisy coupled oscillators: a renormalization group study.
Risler, Thomas; Prost, Jacques; Jülicher, Frank
2005-07-01
We show that the synchronization transition of a large number of noisy coupled oscillators is an example for a dynamic critical point far from thermodynamic equilibrium. The universal behaviors of such critical oscillators, arranged on a lattice in a d -dimensional space and coupled by nearest-neighbors interactions, can be studied using field-theoretical methods. The field theory associated with the critical point of a homogeneous oscillatory instability (or Hopf bifurcation of coupled oscillators) is the complex Ginzburg-Landau equation with additive noise. We perform a perturbative renormalization group (RG) study in a (4-epsilon)-dimensional space. We develop an RG scheme that eliminates the phase and frequency of the oscillations using a scale-dependent oscillating reference frame. Within Callan-Symanzik's RG scheme to two-loop order in perturbation theory, we find that the RG fixed point is formally related to the one of the model A dynamics of the real Ginzburg-Landau theory with an O2 symmetry of the order parameter. Therefore, the dominant critical exponents for coupled oscillators are the same as for this equilibrium field theory. This formal connection with an equilibrium critical point imposes a relation between the correlation and response functions of coupled oscillators in the critical regime. Since the system operates far from thermodynamic equilibrium, a strong violation of the fluctuation-dissipation relation occurs and is characterized by a universal divergence of an effective temperature. The formal relation between critical oscillators and equilibrium critical points suggests that long-range phase order exists in critical oscillators above two dimensions.
Nekrasov, Nikita
2004-01-01
We present the evidence for the existence of the topological string analogue of M-theory, which we call Z-theory. The corners of Z-theory moduli space correspond to the Donaldson-Thomas theory, Kodaira-Spencer theory, Gromov-Witten theory, and Donaldson-Witten theory. We discuss the relations of Z-theory with Hitchin's gravities in six and seven dimensions, and make our own proposal, involving spinor generalization of Chern-Simons theory of three-forms. Based on the talk at Strings'04 in Paris.
R. Dhote
2016-01-01
Full Text Available The behavior of shape memory alloy (SMA nanostructures is influenced by strain rate and temperature evolution during dynamic loading. The coupling between temperature, strain, and strain rate is essential to capture inherent thermomechanical behavior in SMAs. In this paper, we propose a new 3D phase-field model that accounts for two-way coupling between mechanical and thermal physics. We use the strain-based Ginzburg-Landau potential for cubic-to-tetragonal phase transformations. The variational formulation of the developed model is implemented in the isogeometric analysis framework to overcome numerical challenges. We have observed a complete disappearance of the out-of-plane martensitic variant in a very high aspect ratio SMA domain as well as the presence of three variants in equal portions in a low aspect ratio SMA domain. The dependence of different boundary conditions on the microstructure morphology has been examined energetically. The tensile tests on rectangular prism nanowires, using the displacement based loading, demonstrate the shape memory effect and pseudoelastic behavior. We have also observed that higher strain rates, as well as the lower aspect ratio domains, resulting in high yield stress and phase transformations occur at higher stress during dynamic axial loading.
Surface Scattering Effect and the Stripe Order in Films of the Superfluid 3He B Phase
Aoyama, Kazushi
2016-09-01
Surface scattering effects in thin films of the superfluid 3He B phase have been theoretically investigated, with an emphasis on the stability of the stripe order with spontaneous broken translational symmetry in the film plane and quasiparticle excitations in this spatially inhomogeneous phase. Based on the Ginzburg-Landau theory in the weak coupling limit, we have shown that the stripe order, which was originally discussed for a film with two specular surfaces, can be stable in a film with one specular and one diffusive surfaces which should correspond to superfluid 3He on a substrate. It is also found by numerically solving the Eilenberger equation that due to the stripe structure, a midgap state distinct from the surface Andreev bound state emerges and its signature is reflected in the local density of states.
Shape memory alloy nanostructures with coupled dynamic thermo-mechanical effects
Dhote, R. P.; Gomez, H.; Melnik, R. N. V.; Zu, J.
2015-07-01
Employing the Ginzburg-Landau phase-field theory, a new coupled dynamic thermo-mechanical 3D model has been proposed for modeling the cubic-to-tetragonal martensitic transformations in shape memory alloy (SMA) nanostructures. The stress-induced phase transformations and thermo-mechanical behavior of nanostructured SMAs have been investigated. The mechanical and thermal hysteresis phenomena, local non-uniform phase transformations and corresponding non-uniform temperatures and deformations' distributions are captured successfully using the developed model. The predicted microstructure evolution qualitatively matches with the experimental observations. The developed coupled dynamic model has provided a better understanding of underlying martensitic transformation mechanisms in SMAs, as well as their effect on the thermo-mechanical behavior of nanostructures.
The Dynamic Mutation Characteristics of Thermonuclear Reaction in Tokamak
Jing Li
2014-01-01
Full Text Available The stability and bifurcations of multiple limit cycles for the physical model of thermonuclear reaction in Tokamak are investigated in this paper. The one-dimensional Ginzburg-Landau type perturbed diffusion equations for the density of the plasma and the radial electric field near the plasma edge in Tokamak are established. First, the equations are transformed to the average equations with the method of multiple scales and the average equations turn to be a Z2-symmetric perturbed polynomial Hamiltonian system of degree 5. Then, with the bifurcations theory and method of detection function, the qualitative behavior of the unperturbed system and the number of the limit cycles of the perturbed system for certain groups of parameter are analyzed. At last, the stability of the limit cycles is studied and the physical meaning of Tokamak equations under these parameter groups is given.
Information Dynamics at a Phase Transition
Sowinski, Damian
2016-01-01
We propose a new way of investigating phase transitions in the context of information theory. We use an information-entropic measure of spatial complexity known as configurational entropy (CE) to quantify both the storage and exchange of information in a lattice simulation of a Ginzburg-Landau model with a scalar order parameter coupled to a heat bath. The CE is built from the Fourier spectrum of fluctuations around the mean-field and reaches a minimum at criticality. In particular, we investigate the behavior of CE near and at criticality, exploring the relation between information and the emergence of ordered domains. We show that as the temperature is increased from below, the CE displays three essential scaling regimes at different spatial scales: scale free, turbulent, and critical. Together, they offer an information-entropic characterization of critical behavior where the storage and processing of information is maximized at criticality.
Thermodynamics of Gauge-Invariant U(1) Vortices from Lattice Monte Carlo Simulations
Kajantie, Keijo; Laine, Mikko; Peisa, J; Rajantie, A
1998-01-01
We study non-perturbatively and from first principles the thermodynamics of vortices in 3d U(1) gauge+Higgs theory, or the Ginzburg-Landau model, which has frequently been used as a model for cosmological topological defect formation. We discretize the system and introduce a gauge-invariant definition of a vortex passing through a loop on the lattice. We then study with Monte Carlo simulations the total vortex density, extract the physically meaningful part thereof, and demonstrate that it has a well-defined continuum limit. The total vortex density behaves as a pseudo order parameter, having a discontinuity in the regime of first order transitions and behaving continuously in the regime of second order transitions. Finally, we discuss further gauge-invariant observables to be measured.
Critical currents and superconductivity ferromagnetism coexistence in high-Tc oxides
Khene, Samir
2016-01-01
The book comprises six chapters which deal with the critical currents and the ferromagnetism-superconductivity coexistence in high-Tc oxides. It begins by gathering key data for superconducting state and the fundamental properties of the conventional superconductors, followed by a recap of the basic theories of superconductivity. It then discusses the differences introduced by the structural anisotropy on the Ginzburg-Landau approach and the Lawrence-Doniach model before addressing the dynamics of vortices and the ferromagnetism-superconductivity coexistence in high-Tc oxides, and provides an outline of the pinning phenomena of vortices in these materials, in particular the pinning of vortices by the spins. It elucidates the methods to improve the properties of superconducting materials for industrial applications. This optimization aims at obtaining critical temperatures and densities of critical currents at the maximum level possible. Whereas the primary objective is the basic mechanisms pushing the superco...
Dynamics with Low-Level Fractionality
Tarasov, V E; Tarasov, Vasily E.; Zaslavsky, George M.
2005-01-01
The notion of fractional dynamics is related to equations of motion with one or a few terms with derivatives of a fractional order. This type of equation appears in the description of chaotic dynamics, wave propagation in fractal media, and field theory. For the fractional linear oscillator the physical meaning of the derivative of order $\\alpha<2$ is dissipation. In systems with many spacially coupled elements (oscillators) the fractional derivative, along the space coordinate, corresponds to a long range interaction. We discuss a method of constructing a solution using an expansion in $\\epsilon=n-\\alpha$ with small $\\epsilon$ and positive integer $n$. The method is applied to the fractional linear and nonlinear oscillators and to fractional Ginzburg-Landau or parabolic equations.
Anisotropic criteria for the type of superconductivity
Kogan, V. G.; Prozorov, R.
2014-08-01
The classical criterion for classification of superconductors as type I or type II based on the isotropic Ginzburg-Landau theory is generalized to arbitrary temperatures for materials with anisotropic Fermi surfaces and order parameters. We argue that the relevant quantity for this classification is the ratio of the upper and thermodynamic critical fields Hc2/Hc, rather than the traditional ratio of the penetration depth and the coherence length λ /ξ. Even in the isotropic case, Hc2/Hc coincides with √2 λ /ξ only at the critical temperature Tc and they differ as T decreases, the long-known fact. Anisotropies of Fermi surfaces and order parameters may amplify this difference and render false the criterion based on the value of κ =λ/ξ.
The Lichnerowicz-Weitzenboeck formula and superconductivity
Vargas-Paredes, Alfredo A.; Doria, Mauro M. [Departamento de Fisica dos Solidos, Universidade Federal do Rio de Janeiro, 21941-972 Rio de Janeiro (Brazil); Neto, Jose Abdala Helayeel [Centro Brasileiro de Pesquisas Fisicas, 22290-160 Rio de Janeiro RJ (Brazil)
2013-01-15
We derive the Lichnerowicz-Weitzenboeck formula for the two-component order parameter superconductor, which provides a twofold view of the kinetic energy of the superconductor. For the one component order parameter superconductor we review the connection between the Lichnerowicz-Weitzenboeck formula and the Ginzburg-Landau theory. For the two-component case we claim that this formula opens a venue to describe inhomogeneous superconducting states intertwined by spin correlations and charged dislocation. In this case the Lichnerowicz-Weitzenboeck formula displays local rotational and electromagnetic gauge symmetry (SU(2) Circled-Times U(1)) and relies on local commuting momentum and spin operators. The order parameter lives in a space with curvature and torsion described by Elie Cartan geometrical formalism. The Lichnerowickz-Weitzenboeck formula leads to first order differential equations that are a three-dimensional version of the Seiberg-Witten equations.
Liu, Fangxun; Cheng, Rongjun; Ge, Hongxia; Yu, Chenyan
2016-12-01
In this study, a new car-following model is proposed based on taking the effect of the leading vehicle's velocity difference between the current speed and the historical speed into account. The model's linear stability condition is obtained via the linear stability theory. The time-dependent Ginzburg-Landau (TDGL) equation and the modified Korteweg-de Vries (mKdV) equation are deduced through the nonlinear analysis. The kink-antikink soliton can interpret the traffic jams near the critical point. In addition, the connection between the TDGL and the mKdV equations is also given. Numerical simulation shows that the new model can improve the stability of traffic flow, which is consistent with the theoretical analysis correspondingly.
The car following model considering traffic jerk
Ge, Hong-Xia; Zheng, Peng-jun; Wang, Wei; Cheng, Rong-Jun
2015-09-01
Based on optimal velocity car following model, a new model considering traffic jerk is proposed to describe the jamming transition in traffic flow on a highway. Traffic jerk means the sudden braking and acceleration of vehicles, which has a significant impact on traffic movement. The nature of the model is researched by using linear and nonlinear analysis method. A thermodynamic theory is formulated to describe the phase transition and critical phenomenon in traffic flow. The time-dependent Ginzburg-Landau (TDGL) equation and the modified Korteweg-de Vries (mKdV) equation are derived to describe the traffic flow near the critical point and the traffic jam. In addition, the connection between the TDGL and the mKdV equations are also given.
Deterministic phase slips in mesoscopic superconducting rings
Petković, I.; Lollo, A.; Glazman, L. I.; Harris, J. G. E.
2016-11-01
The properties of one-dimensional superconductors are strongly influenced by topological fluctuations of the order parameter, known as phase slips, which cause the decay of persistent current in superconducting rings and the appearance of resistance in superconducting wires. Despite extensive work, quantitative studies of phase slips have been limited by uncertainty regarding the order parameter's free-energy landscape. Here we show detailed agreement between measurements of the persistent current in isolated flux-biased rings and Ginzburg-Landau theory over a wide range of temperature, magnetic field and ring size; this agreement provides a quantitative picture of the free-energy landscape. We also demonstrate that phase slips occur deterministically as the barrier separating two competing order parameter configurations vanishes. These results will enable studies of quantum and thermal phase slips in a well-characterized system and will provide access to outstanding questions regarding the nature of one-dimensional superconductivity.
Thermal fluctuations in the high-temperature superconductor CaLaBaCu{sub 3}O{sub 7-{delta}}
Landinez Tellez, D.A. [Universidad Nacional de Colombia, Bogota (Colombia). Dept. de Fisica; Roa-Rojas, J. [Escuela Colombiana de Ingenieria, Bogota (Colombia); Albino Aguiar, J. [Dept. de Fisica, Univ. Federal de Pernambuco, Recife, PE (Brazil); Calero, J.M. [Escuela de Fisica, Univ. Industrial de Santander, Bucaramanga (Colombia)
2000-07-01
Magnetization measurements on a polycrystal of CaLaBaCu{sub 3}O{sub 7-{delta}} in high magnetic fields (20 to 50 kOe) are reported. The sample has a zero-field transition temperature T{sub c0} = 77 K and a transition width of 2.0 K. The results show large fluctuation effects, which can be explained by Ginzburg-Landau fluctuation theory for a two-dimensional system. The magnetization displays good scaling behavior as a function of [T - T{sub c}(H)]/(TH){sup 1/2}. The experimental data were fitted by using a theoretical model based in the lowest Landau levels approximation, showing good agreement. We also analyze fluctuation effects in conductivity measurements at zero magnetic field. (orig.)
Stojchevska, L.; Borovšak, M.; Foury-Leylekian, P.; Pouget, J.-P.; Mertelj, T.; Mihailovic, D.
2017-07-01
All-optical femtosecond relaxation dynamics in a single crystal of monophosphate tungsten bronze (PO2)4(WO3)2m with alternate stacking m =6 of WO3 layers was studied through the three consequent charge-density-wave (CDW) transitions. Several transient coherent collective modes associated with the different CDW transitions were observed and analyzed in the framework of the time-dependent Ginzburg-Landau theory. Remarkably, the interference of the modes leads to an apparent rectification effect in the transient reflectivity response. A saturation of the coherent-mode amplitudes with increasing pump fluence well below the CDWs destruction threshold fluence indicates a decoupling of the electronic and lattice parts of the order parameter on the femtosecond timescale.
Guo, Hanqi; Phillips, Carolyn L; Peterka, Tom; Karpeyev, Dmitry; Glatz, Andreas
2016-01-01
We propose a method for the vortex extraction and tracking of superconducting magnetic flux vortices for both structured and unstructured mesh data. In the Ginzburg-Landau theory, magnetic flux vortices are well-defined features in a complex-valued order parameter field, and their dynamics determine electromagnetic properties in type-II superconductors. Our method represents each vortex line (a 1D curve embedded in 3D space) as a connected graph extracted from the discretized field in both space and time. For a time-varying discrete dataset, our vortex extraction and tracking method is as accurate as the data discretization. We then apply 3D visualization and 2D event diagrams to the extraction and tracking results to help scientists understand vortex dynamics and macroscale superconductor behavior in greater detail than previously possible.
A phase-field study of the scaling law in free-standing ferroelectric thin films.
Yin, Binglun; Mao, Huina; Qu, Shaoxing
2015-12-18
The scaling law for ferroelectric stripe domains is investigated in free-standing BaTiO3 and PbTiO3 thin films via phase-field simulations. The results agree with the Kittel law, where the square of the domain width is found to be proportional to the thin film thickness. After being rescaled by the corresponding domain wall thickness, the generalized scaling law is also demonstrated, with the dimensionless scaling constant M estimated to be ∼3.3 in two ferroelectric materials. Moreover, we predict the effect of the exchange constant which is incorporated in Ginzburg-Landau theory on the equilibrium domain width and the critical thickness of the ferroelectric thin films.
Effect of a magnetic field on fourth sound in /sup 3/He
Daly, K.
1988-05-01
The influence of a magnetic field on the propagation of fourth sound in superfluid /sup 3/He is studied. The field and temperature dependences of the average superfluid density /anti rho//sub s///rho/ and fourth sound Q are measured. The field dependence of /anti rho//sub s///rho/ is very different in a porous medium than predicted by Ginzburg-Landau theory applied to bulk liquid. In particular, a magnetic suppression of /anti rho//sub s///rho/ is observed in the temperature and pressure ranges corresponding to the A phase in bulk liquid. There is strong evidence of a magnetic suppression of T/sub c/ itself. The measured /anti rho//sub s///rho/ has a slight history dependence in a magnetic field, but none in zero field. The fourth-sound Q values are compared to the theoretical work of Smith, Jensen, and Wolfle. Quantitative confirmation of their work is problematic.
Anisotropic criteria for the type of superconductivity
Kogan, Vladimir G [Ames Laboratory; Prozorov, Ruslan [Ames Laboratory
2014-08-01
The classical criterion for classification of superconductors as type I or type II based on the isotropic Ginzburg-Landau theory is generalized to arbitrary temperatures for materials with anisotropic Fermi surfaces and order parameters. We argue that the relevant quantity for this classification is the ratio of the upper and thermodynamic critical fields Hc2/Hc, rather than the traditional ratio of the penetration depth and the coherence length λ/ξ. Even in the isotropic case, Hc2/Hc coincides with 2√λ/ξ only at the critical temperature Tc and they differ as T decreases, the long-known fact. Anisotropies of Fermi surfaces and order parameters may amplify this difference and render false the criterion based on the value of κ=λ/ξ.
Self-organized correlations lead to explosive synchronization.
Chen, Yang; Cao, Zhoujian; Wang, Shihong; Hu, Gang
2015-02-01
Very recently, a first-order phase transition, named explosive synchronization (ES), has attracted great attention due to its remarkable novelty in theory and significant impact in applications. However, so far, all observations of ES have been associated with various correlation constraints on system parameters, which restrict its generality and applications. Here we consider heterogeneous networks around Hopf bifurcation point described by chemical reaction-diffusion systems and also by their reduced order parameter versions, the complex Ginzburg-Landau equations, and demonstrate that explosive synchronization can appear as an emergent feature of oscillatory networks, and the restrictions on specific parameter correlations used so far for ES can be lifted entirely. Theoretical analyses and numerical simulations show with a perfect agreement that explosive synchronization can appear in networks with nodes having identical natural frequencies, and necessary correlation conditions for ES can be realized in a self-organized manner by network evolution.
A phase-field study of the scaling law in free-standing ferroelectric thin films
Yin, Binglun; Mao, Huina; Qu, Shaoxing
2015-12-01
The scaling law for ferroelectric stripe domains is investigated in free-standing BaTiO3 and PbTiO3 thin films via phase-field simulations. The results agree with the Kittel law, where the square of the domain width is found to be proportional to the thin film thickness. After being rescaled by the corresponding domain wall thickness, the generalized scaling law is also demonstrated, with the dimensionless scaling constant M estimated to be ˜3.3 in two ferroelectric materials. Moreover, we predict the effect of the exchange constant which is incorporated in Ginzburg-Landau theory on the equilibrium domain width and the critical thickness of the ferroelectric thin films.
Optical and electrical enhancement of the propagation time in superconducting transmission lines
Cho, S H
2000-01-01
optical pulse energy and current controlled delays in the propagation time of electrical picosecond pulses in YBa sub 2 Cu sub 3 O sub 7 sub - sub x (YBCO) superconducting transmission lines have been investigated by using picosecond optoelectronic techniques. Electrical pulses, generated using silicon-on-sapphire photoconductive switches driven by a mode-locked Nd:YAG pumped dye laser, are propagated on superconducting transmission lines. The lines are patterned in the geometry of a microstrip and illuminated by the frequency-doubled output of an Nd:YAG laser. The measured propagation time shows a squared dependence on the optical pulse energy. For the applied current dependence, the delay through the line is tuned by 16 psec by varying the bias from zero to 190 mA. The results are in good agreement with the Ginzburg-Landau theory for the case of a uniform current density through a thin film.
Hyperbolic Metamaterials with Bragg Polaritons
Sedov, Evgeny S.; Iorsh, I. V.; Arakelian, S. M.; Alodjants, A. P.; Kavokin, Alexey
2015-06-01
We propose a novel mechanism for designing quantum hyperbolic metamaterials with the use of semiconductor Bragg mirrors containing periodically arranged quantum wells. The hyperbolic dispersion of exciton-polariton modes is realized near the top of the first allowed photonic miniband in such a structure which leads to the formation of exciton-polariton X waves. Exciton-light coupling provides a resonant nonlinearity which leads to nontrivial topologic solutions. We predict the formation of low amplitude spatially localized oscillatory structures: oscillons described by kink shaped solutions of the effective Ginzburg-Landau-Higgs equation. The oscillons have direct analogies in gravitational theory. We discuss implementation of exciton-polariton Higgs fields for the Schrödinger cat state generation.
Stochastic analysis of the time evolution of Laminar-Turbulent bands of plane Couette flow
Rolland, Joran
2015-01-01
This article is concerned with the time evolution of the oblique laminar-turbulent bands of transitional plane Couette flow under the influence of turbulent noise. Our study is focused on the amplitude of modulation of turbulence. In order to guide the numerical study of the flow, we first perform an analytical and numerical analysis of a Stochastic Ginzburg-Landau equation for a complex order parameter. The modulus of this order parameter models the amplitude of modulation of turbulence. Firstly, we compute the autocorrelation function of said modulus once the band is established. Secondly, we perform a calculation of average and fluctuations around the exponential growth of the order parameter. This type of analysis is similar to the Stochastic Structural Stability Theory. We then perform numerical simulations of the Navier-Stokes equations in order to confront these predictions with the actual behaviour of the bands. Computation of the autocorrelation function of the modulation of turbulence shows quantita...
Molecular tilt on monolayer-protected nanoparticles
Giomi, L.
2012-02-01
The structure of the tilted phase of monolayer-protected nanoparticles is investigated by means of a simple Ginzburg-Landau model. The theory contains two dimensionless parameters representing the preferential tilt angle and the ratio ε between the energy cost due to spatial variations in the tilt of the coating molecules and that of the van der Waals interactions which favors the preferential tilt. We analyze the model for both spherical and octahedral particles. On spherical particles, we find a transition from a tilted phase, at small ε, to a phase where the molecules spontaneously align along the surface normal and tilt disappears. Octahedral particles have an additional phase at small ε characterized by the presence of six topological defects. These defective configurations provide preferred sites for the chemical functionalization of monolayer-protected nanoparticles via place-exchange reactions and their consequent linking to form molecules and bulk materials. Copyright © EPLA, 2012.
Weak Nonlinear Double-Diffusive Magnetoconvection in a Newtonian Liquid under Temperature Modulation
B. S. Bhadauria
2014-01-01
Full Text Available The present paper deals with a weak nonlinear theory of double-diffusive magnetoconvection in an electrically conducting Newtonian liquid, confined between two horizontal surfaces, under a constant vertical magnetic field, and subjected to imposed time-periodic thermal boundaries. The temperature of both walls is varied time periodic in this case. The disturbances are expanded in terms of power series of amplitude of convection, which is assumed to be small. Using nonautonomous Ginzburg-Landau equation, the Nusselt and Sherwood numbers obtained analytically and studied heat and mass transport in the system. Effect of various parameters on the heat and mass transport is discussed extensively. It is found that the effect of magnetic field is to stabilize the system. Further, it is also notified that the heat and mass transport can be controlled by suitably adjusting the external parameters of the system.
Information Dynamics at a Phase Transition
Sowinski, Damian; Gleiser, Marcelo
2017-03-01
We propose a new way of investigating phase transitions in the context of information theory. We use an information-entropic measure of spatial complexity known as configurational entropy (CE) to quantify both the storage and exchange of information in a lattice simulation of a Ginzburg-Landau model with a scalar order parameter coupled to a heat bath. The CE is built from the Fourier spectrum of fluctuations around the mean-field and reaches a minimum at criticality. In particular, we investigate the behavior of CE near and at criticality, exploring the relation between information and the emergence of ordered domains. We show that as the temperature is increased from below, the CE displays three essential scaling regimes at different spatial scales: scale free, turbulent, and critical. Together, they offer an information-entropic characterization of critical behavior where the storage and fidelity of information processing is maximized at criticality.
On n-quantum vortices in superconductors
Marchenko, V I
2002-01-01
The conditions of the n-quantum vortices observation in the superconductors are discussed. It is established in the course of calculating the coefficient by the |psi| sup 6 (psi - the order parameter) in the Ginzburg-Landau theory for the BCS standard model that the sign of this coefficient is negative. This favours the possibility of observing the n-quantum vortices in the superconductors, wherein the vortex lattice with gravitation is formed. The existence of gravitation is manifested in the magnetization finite jump in the H sub 0 = H sub c sub sup 1 field. When by the temperature change the superconductor behavior changes in such a way, that its magnetization in the H sub 0 = H sub c field reduces to the zero, than the observation of the n-quantum vortices near this transition is possible
介观超导环中的电荷分布%Charge distributions in mesoscopic superconducting rings
涂必红; 查国桥; 周世平
2007-01-01
The charge distribution in thin mesoscopic superconducting ring is studied by the phenomenological GinzburgLandau theory. In the giant vortex states we find that the mesoscopic rings may present three kinds of charge distribution while the disk only owns the first two kinds. The charge near the inner radius may change its sign from negative to positive with increasing applied field. In the multivortex state we find that there exist saddle-point states and stable multivortex states.The distribution of charge and the superconducting electron density in the (0:2) saddle states and the (0:4), and (1:5) stable multivortex states has also been studied. The contour plot of the charge distribution and the Cooper pair density distribution are given.
Landau, I L; Willems, J B; Hulliger, J [Department of Chemistry and Biochemistry, University of Berne, Freiestrasse 3, CH-3012 Berne (Switzerland)], E-mail: landau@iac.unibe.ch
2008-03-05
We present a magnetization study of low density YBa{sub 2}Cu{sub 3}O{sub 7-x} ceramics carried out in magnetic fields H such that 0.5 Oe
Odagaki, Takashi
2017-08-01
Extending the concept of the Ginzburg-Landau theory of phase transition to non-equilibrium systems, I present a free energy landscape (FEL) formalism of non-equilibrium statistical mechanics and show that the FEL formalism provides a framework for unified description of thermodynamic and dynamic properties of non-equilibrium systems. I first show that a conditional free energy Φ (T,V,N,{ Ri} ) can be defined as a function of configuration {Ri} of a given average position of atoms so that the probability of finding the configuration {Ri} is in proportion to \\exp [ - Φ (T,V,N,{ Ri} )/kBT]. Thermodynamic quantities in quasi-equilibrium states are given by their average over the configuration, and the temperature dependence of the FEL manifests itself in the temperature derivatives of thermodynamic quantities. As an example, I discuss the entropy and the specific heat, focusing on the contributions due to configuration and the temperature dependence of the FEL, and show that an additional contribution due to the temperature dependence of the FEL exists in the specific heat. I generalize the FEL formalism so that time dependent phenomena can be analyzed in a frame work similar to the time-dependent Ginzburg-Landau theory. I introduce a time-dependent probability function of configuration and describe its time dependence by a Fokker-Planck equation which guarantees that the probability function satisfies the initial condition and the proper long-time limit. The time dependence of a physical quantity is given by its average over the time-dependent distribution function. In order to show the robustness of the FEL formalism in explaining thermodynamic and dynamic effects in a unified frame work, I discuss several phenomena found in super-cooled liquids on the basis of the FEL formalism which includes glass transition singularities, slow relaxations, cooling rate dependence of the specific heat, the ac specific heat, temperature dependence of the crystallization time and
Marino Beiras, Marcos
2001-01-01
We give an overview of the relations between matrix models and string theory, focusing on topological string theory and the Dijkgraaf--Vafa correspondence. We discuss applications of this correspondence and its generalizations to supersymmetric gauge theory, enumerative geometry and mirror symmetry. We also present a brief overview of matrix quantum mechanical models in superstring theory.
Game Theory is a collection of short interviews based on 5 questions presented to some of the most influential and prominent scholars in game theory. We hear their views on game theory, its aim, scope, use, the future direction of game theory and how their work fits in these respects....
Levitas, Valery I.; Javanbakht, Mahdi
2015-09-01
Thermodynamically consistent, three-dimensional (3D) phase field approach (PFA) for coupled multivariant martensitic transformations (PTs), including cyclic PTs, variant-variant transformations (i.e., twinning), and dislocation evolution is developed at large strains. One of our key points is in the justification of the multiplicative decomposition of the deformation gradient into elastic, transformational, and plastic parts. The plastic part includes four mechanisms: dislocation motion in martensite along slip systems of martensite and slip systems of austenite inherited during PT and dislocation motion in austenite along slip systems of austenite and slip systems of martensite inherited during reverse PT. The plastic part of the velocity gradient for all these mechanisms is defined in the crystal lattice of the austenite utilizing just slip systems of austenite and inherited slip systems of martensite, and just two corresponding types of order parameters. The explicit expressions for the Helmholtz free energy and the transformation and plastic deformation gradients are presented to satisfy the formulated conditions related to homogeneous thermodynamic equilibrium states of crystal lattice and their instabilities. In particular, they result in a constant (i.e., stress- and temperature-independent) transformation deformation gradient and Burgers vectors. Thermodynamic treatment resulted in the determination of the driving forces for change of the order parameters for PTs and dislocations. It also determined the boundary conditions for the order parameters that include a variation of the surface energy during PT and exit of dislocations. Ginzburg-Landau equations for dislocations include variation of properties during PTs, which in turn produces additional contributions from dislocations to the Ginzburg-Landau equations for PTs. A complete system of coupled PFA and mechanics equations is presented. A similar theory can be developed for PFA to dislocations and other
Studies on the pyroelectric properties of ferroelectric bilayer film%铁电薄膜热释电性质的研究
张芹; 董亚男; 陈红
2013-01-01
Using Ginzburg-Landau-Devonshire theory, a ferroelectric bilayer film consisting of two different ferroelectric constituent films with the transition layer within each constituent film is considered. Introduced a parameter,which described the differences of physical properties between two constituent films, to investigate the temperature dependence of the pyroelectric coefficient of the bilayer film. It is shown that one or two peaks can be obtained in the pyroelectric curve by the adjustment of parameter Q. The modification of ferroelectric interfacial coupling cofficient,parameter a and surficial transition layer parameter leads to the peaks of the pyroelectric curve shifting to the higher or lower temperature region.%利用Ginzburg-Landau-Devonshire (GLD)热力学唯象理论,对由2种不同铁电材料构成的含有表面过渡层的铁电双层膜体系进行了探讨.通过引入一个描述2种铁电材料物理性能差异大小的物理参量α,并考虑2种铁电材料物理性能的差异,研究了铁电双层膜的热释电性质.结果表明:通过控制参量α的大小,热释电曲线上会呈现1个或2个峰；改变铁电界面耦合系数、参量α以及表面过渡层参量的大小,热释电曲线的峰位向高温区或低温区移动.
Wetting, prewetting and surface transitions in type-I superconductors
Indekeu, J. O.; van Leeuwen, J. M. J.
1995-02-01
Within the Ginzburg-Landau theory, which is quantitatively correct for classical superconductors, it is shown that a type-I superconductor can display an interface delocalization or “wetting” transition, in which a macroscopically thick superconducting layer intrudes from the surface into the bulk normal phase. The condition for this transition to occur is that the superconducting order parameter | ψ| 2 is enhanced at the surface. This corresponds to a negative surface extrapolation length b. The wetting transition takes place at bulk two-phase coexistence of normal and superconducting phases, at a temperature TD below the critical temperature Tc, and at magnetic field HD = Hc( TD). The field is applied parallel to the surface. Surprisingly, the order of the wetting transition is controlled by a bulk material constant, the Ginzburg-Landau parameter κ. This is very unusual, since in other systems (fluids, Ising magnets,…) the order of the wetting transition depends on surface parameters that are difficult to determine or control. For superconductors, first-order wetting is predicted for 0 ≤ κ wetting for 0.374 wetting, the prewetting extension is also found. Unlike in standard wetting problems, the prewetting line does not terminate at a critical point but changes from first to second order at a tricritical point. Twinning-plane superconductivity (TPS) is reinterpreted as a prewetting phenomenon. The possibility of critical wetting in superconductors is especially interesting because this phenomenon has largely eluded experimental verification in any system until now. Furthermore, superconductors provide a realization of wetting in systems with short-range (exponentially decaying) interactions. This is very different from the usual long-range (algebraically decaying) interactions, such as van der Waals forces, and has important consequences for the wetting characteristics.
Johnstone, PT
2014-01-01
Focusing on topos theory's integration of geometric and logical ideas into the foundations of mathematics and theoretical computer science, this volume explores internal category theory, topologies and sheaves, geometric morphisms, other subjects. 1977 edition.
Williams, Jeffrey
1994-01-01
Considers the recent flood of anthologies of literary criticism and theory as exemplifications of the confluence of pedagogical concerns, economics of publishing, and other historical factors. Looks specifically at how these anthologies present theory. Cites problems with their formatting theory and proposes alternative ways of organizing theory…
Linder, Stefan; Foss, Nicolai Juul
Agency theory studies the problems and solutions linked to delegation of tasks from principals to agents in the context of conflicting interests between the parties. Beginning from clear assumptions about rationality, contracting and informational conditions, the theory addresses problems of ex...... agency theory to enjoy considerable scientific impact on social science; however, it has also attracted considerable criticism....
Loring, FH
2014-01-01
Summarising the most novel facts and theories which were coming into prominence at the time, particularly those which had not yet been incorporated into standard textbooks, this important work was first published in 1921. The subjects treated cover a wide range of research that was being conducted into the atom, and include Quantum Theory, the Bohr Theory, the Sommerfield extension of Bohr's work, the Octet Theory and Isotopes, as well as Ionisation Potentials and Solar Phenomena. Because much of the material of Atomic Theories lies on the boundary between experimentally verified fact and spec
Linder, Stefan; Foss, Nicolai Juul
2015-01-01
Agency theory studies the problems and solutions linked to delegation of tasks from principals to agents in the context of conflicting interests between the parties. Beginning from clear assumptions about rationality, contracting, and informational conditions, the theory addresses problems of ex ...... agency theory to enjoy considerable scientific impact on social science; however, it has also attracted considerable criticism.......Agency theory studies the problems and solutions linked to delegation of tasks from principals to agents in the context of conflicting interests between the parties. Beginning from clear assumptions about rationality, contracting, and informational conditions, the theory addresses problems of ex...
Linder, Stefan; Foss, Nicolai Juul
Agency theory studies the problems and solutions linked to delegation of tasks from principals to agents in the context of conflicting interests between the parties. Beginning from clear assumptions about rationality, contracting and informational conditions, the theory addresses problems of ex a...... agency theory to enjoy considerable scientific impact on social science; however, it has also attracted considerable criticism.......Agency theory studies the problems and solutions linked to delegation of tasks from principals to agents in the context of conflicting interests between the parties. Beginning from clear assumptions about rationality, contracting and informational conditions, the theory addresses problems of ex...
Rowen, Louis H
1991-01-01
This is an abridged edition of the author's previous two-volume work, Ring Theory, which concentrates on essential material for a general ring theory course while ommitting much of the material intended for ring theory specialists. It has been praised by reviewers:**""As a textbook for graduate students, Ring Theory joins the best....The experts will find several attractive and pleasant features in Ring Theory. The most noteworthy is the inclusion, usually in supplements and appendices, of many useful constructions which are hard to locate outside of the original sources....The audience of non
Harris, Tina
2015-04-29
Grounded theory is a popular research approach in health care and the social sciences. This article provides a description of grounded theory methodology and its key components, using examples from published studies to demonstrate practical application. It aims to demystify grounded theory for novice nurse researchers, by explaining what it is, when to use it, why they would want to use it and how to use it. It should enable nurse researchers to decide if grounded theory is an appropriate approach for their research, and to determine the quality of any grounded theory research they read.
SPECTRAL METHODS FOR THE GL-BBM EQUATIONS
郭柏灵; 蒋慕蓉
2002-01-01
In this paper, the semi-discrete and fully discrete Fourier spectral schemes for theGinzburg-Landau coupled with BBM equations with periodic initial value problem are proposed,and the convergence and stabilities for the schemes are proved.
Attractors for the Ginzburg—Landau—BBM Equations in an Unbounded Domain
BolingGUO; MurongJIANG
1998-01-01
In this paper,the long time behavior of the global solutions of the Ginzburg-Landau equation coupled with BBM equation in an unbounded domain is considered,The existence of the maximal attractor is obtained.
Frequency-Uniform Decomposition, Function Spaces , and Applications to Nonlinear Evolution Equations
Shaolei Ru
2013-01-01
Full Text Available By combining frequency-uniform decomposition with (, we introduce a new class of function spaces (denoted by . Moreover, we study the Cauchy problem for the generalized NLS equations and Ginzburg-Landau equations in .
Chang, CC
2012-01-01
Model theory deals with a branch of mathematical logic showing connections between a formal language and its interpretations or models. This is the first and most successful textbook in logical model theory. Extensively updated and corrected in 1990 to accommodate developments in model theoretic methods - including classification theory and nonstandard analysis - the third edition added entirely new sections, exercises, and references. Each chapter introduces an individual method and discusses specific applications. Basic methods of constructing models include constants, elementary chains, Sko
Aubin, Jean-Pierre; Saint-Pierre, Patrick
2011-01-01
Viability theory designs and develops mathematical and algorithmic methods for investigating the adaptation to viability constraints of evolutions governed by complex systems under uncertainty that are found in many domains involving living beings, from biological evolution to economics, from environmental sciences to financial markets, from control theory and robotics to cognitive sciences. It involves interdisciplinary investigations spanning fields that have traditionally developed in isolation. The purpose of this book is to present an initiation to applications of viability theory, explai
Roman, Steven
2006-01-01
Intended for graduate courses or for independent study, this book presents the basic theory of fields. The first part begins with a discussion of polynomials over a ring, the division algorithm, irreducibility, field extensions, and embeddings. The second part is devoted to Galois theory. The third part of the book treats the theory of binomials. The book concludes with a chapter on families of binomials - the Kummer theory. This new edition has been completely rewritten in order to improve the pedagogy and to make the text more accessible to graduate students. The exercises have also been im
Hashiguchi, Koichi
2009-01-01
This book details the mathematics and continuum mechanics necessary as a foundation of elastoplasticity theory. It explains physical backgrounds with illustrations and provides descriptions of detailed derivation processes..
Cox, David A
2012-01-01
Praise for the First Edition ". . .will certainly fascinate anyone interested in abstract algebra: a remarkable book!"—Monatshefte fur Mathematik Galois theory is one of the most established topics in mathematics, with historical roots that led to the development of many central concepts in modern algebra, including groups and fields. Covering classic applications of the theory, such as solvability by radicals, geometric constructions, and finite fields, Galois Theory, Second Edition delves into novel topics like Abel’s theory of Abelian equations, casus irreducibili, and the Galo
Dufwenberg, Martin
2011-03-01
Game theory is a toolkit for examining situations where decision makers influence each other. I discuss the nature of game-theoretic analysis, the history of game theory, why game theory is useful for understanding human psychology, and why game theory has played a key role in the recent explosion of interest in the field of behavioral economics. WIREs Cogni Sci 2011 2 167-173 DOI: 10.1002/wcs.119 For further resources related to this article, please visit the WIREs website.
Gamma-stability and vortex motion in type II superconductors
Kurzke, Matthias; Spirn, Daniel
2009-07-15
We consider a time-dependent Ginzburg-Landau equation for superconductors with a strictly complex relaxation parameter, and derive motion laws for the vortices in the case of a finite number of vortices in a bounded magnetic field. The motion laws correspond to the flux-flow Hall effect. As our main tool, we develop a quantitative {gamma}-stability result relating the Ginzburg-Landau energy to the renormalized energy. (orig.)
Nonlinear Rayleigh--Taylor instability of the cylindrical fluid flow with mass and heat transfer
ALY R SEADAWY; K EL-RASHIDY
2016-08-01
The nonlinear Rayleigh--Taylor stability of the cylindrical interface between the vapour and liquid phases of a fluid is studied. The phases enclosed between two cylindrical surfaces coaxial with mass and heat transfer is derived from nonlinear Ginzburg--Landau equation. The F-expansion method is used to get exactsolutions for a nonlinear Ginzburg--Landau equation. The region of solutions is displayed graphically.
Manning, Phillip
2011-01-01
The study of quantum theory allowed twentieth-century scientists to examine the world in a new way, one that was filled with uncertainties and probabilities. Further study also led to the development of lasers, the atomic bomb, and the computer. This exciting new book clearly explains quantum theory and its everyday uses in our world.
Ion N.Chiuta
2009-05-01
Full Text Available The paper determines relations for shieldingeffectiveness relative to several variables, includingmetal type, metal properties, thickness, distance,frequency, etc. It starts by presenting some relationshipsregarding magnetic, electric and electromagnetic fieldsas a pertinent background to understanding and applyingfield theory. Since literature about electromagneticcompatibility is replete with discussions about Maxwellequations and field theory only a few aspects arepresented.
Liu, Baoding
2015-01-01
When no samples are available to estimate a probability distribution, we have to invite some domain experts to evaluate the belief degree that each event will happen. Perhaps some people think that the belief degree should be modeled by subjective probability or fuzzy set theory. However, it is usually inappropriate because both of them may lead to counterintuitive results in this case. In order to rationally deal with belief degrees, uncertainty theory was founded in 2007 and subsequently studied by many researchers. Nowadays, uncertainty theory has become a branch of axiomatic mathematics for modeling belief degrees. This is an introductory textbook on uncertainty theory, uncertain programming, uncertain statistics, uncertain risk analysis, uncertain reliability analysis, uncertain set, uncertain logic, uncertain inference, uncertain process, uncertain calculus, and uncertain differential equation. This textbook also shows applications of uncertainty theory to scheduling, logistics, networks, data mining, c...
Bjerg, Ole; Presskorn-Thygesen, Thomas
2017-01-01
The paper is a contribution to current debates about conspiracy theories within philosophy and cultural studies. Wittgenstein’s understanding of language is invoked to analyse the epistemological effects of designating particular questions and explanations as a ‘conspiracy theory......’. It is demonstrated how such a designation relegates these questions and explanations beyond the realm of meaningful discourse. In addition, Agamben’s concept of sovereignty is applied to explore the political effects of using the concept of conspiracy theory. The exceptional epistemological status assigned...... to alleged conspiracy theories within our prevalent paradigms of knowledge and truth is compared to the exceptional legal status assigned to individuals accused of terrorism under the War on Terror. The paper concludes by discussing the relation between conspiracy theory and ‘the paranoid style...
Lukeš, Jaroslav; Netuka, Ivan; Veselý, Jiří
1988-01-01
Within the tradition of meetings devoted to potential theory, a conference on potential theory took place in Prague on 19-24, July 1987. The Conference was organized by the Faculty of Mathematics and Physics, Charles University, with the collaboration of the Institute of Mathematics, Czechoslovak Academy of Sciences, the Department of Mathematics, Czech University of Technology, the Union of Czechoslovak Mathematicians and Physicists, the Czechoslovak Scientific and Technical Society, and supported by IMU. During the Conference, 69 scientific communications from different branches of potential theory were presented; the majority of them are in cluded in the present volume. (Papers based on survey lectures delivered at the Conference, its program as well as a collection of problems from potential theory will appear in a special volume of the Lecture Notes Series published by Springer-Verlag). Topics of these communications truly reflect the vast scope of contemporary potential theory. Some contributions deal...
Hjørland, Birger
2009-01-01
Concept theory is an extremely broad, interdisciplinary and complex field of research related to many deep fields with very long historical traditions without much consensus. However, information science and knowledge organization cannot avoid relating to theories of concepts. Knowledge...... organizing systems (e.g. classification systems, thesauri and ontologies) should be understood as systems basically organizing concepts and their semantic relations. The same is the case with information retrieval systems. Different theories of concepts have different implications for how to construe......, evaluate and use such systems. Based on "a post-Kuhnian view" of paradigms this paper put forward arguments that the best understanding and classification of theories of concepts is to view and classify them in accordance with epistemological theories (empiricism, rationalism, historicism and pragmatism...
Bjerg, Ole; Presskorn-Thygesen, Thomas
2017-01-01
The paper is a contribution to current debates about conspiracy theories within philosophy and cultural studies. Wittgenstein’s understanding of language is invoked to analyse the epistemological effects of designating particular questions and explanations as a ‘conspiracy theory......’. It is demonstrated how such a designation relegates these questions and explanations beyond the realm of meaningful discourse. In addition, Agamben’s concept of sovereignty is applied to explore the political effects of using the concept of conspiracy theory. The exceptional epistemological status assigned...... to alleged conspiracy theories within our prevalent paradigms of knowledge and truth is compared to the exceptional legal status assigned to individuals accused of terrorism under the War on Terror. The paper concludes by discussing the relation between conspiracy theory and ‘the paranoid style...
Bernardo, Jose M
2000-01-01
This highly acclaimed text, now available in paperback, provides a thorough account of key concepts and theoretical results, with particular emphasis on viewing statistical inference as a special case of decision theory. Information-theoretic concepts play a central role in the development of the theory, which provides, in particular, a detailed discussion of the problem of specification of so-called prior ignorance . The work is written from the authors s committed Bayesian perspective, but an overview of non-Bayesian theories is also provided, and each chapter contains a wide-ranging critica
Kathleen Holtz Deal
2007-05-01
Full Text Available Psychodynamic theory, a theory of personality originated by Sigmund Freud, has a long and complex history within social work and continues to be utilized by social workers. This article traces the theory’s development and explains key concepts with an emphasis on its current relational focus within object relations theory and self-psychology. Empirical support for theoretical concepts and the effectiveness of psychodynamic therapies is reviewed and critiqued. Future directions are discussed, including addressing cultural considerations, increasing research, and emphasizing a relational paradigm
Andrews, George E
1994-01-01
Although mathematics majors are usually conversant with number theory by the time they have completed a course in abstract algebra, other undergraduates, especially those in education and the liberal arts, often need a more basic introduction to the topic.In this book the author solves the problem of maintaining the interest of students at both levels by offering a combinatorial approach to elementary number theory. In studying number theory from such a perspective, mathematics majors are spared repetition and provided with new insights, while other students benefit from the consequent simpl
Smith, Shelley
This paper came about within the context of a 13-month research project, Focus Area 1 - Method and Theory, at the Center for Public Space Research at the Royal Academy of the Arts School of Architecture in Copenhagen, Denmark. This project has been funded by RealDania. The goals of the research...... project, Focus Area 1 - Method and Theory, which forms the framework for this working paper, are: * To provide a basis from which to discuss the concept of public space in a contemporary architectural and urban context - specifically relating to theory and method * To broaden the discussion of the concept...
Lubliner, Jacob
2008-01-01
The aim of Plasticity Theory is to provide a comprehensive introduction to the contemporary state of knowledge in basic plasticity theory and to its applications. It treats several areas not commonly found between the covers of a single book: the physics of plasticity, constitutive theory, dynamic plasticity, large-deformation plasticity, and numerical methods, in addition to a representative survey of problems treated by classical methods, such as elastic-plastic problems, plane plastic flow, and limit analysis; the problem discussed come from areas of interest to mechanical, structural, and
Nel, Louis
2016-01-01
This book presents a detailed, self-contained theory of continuous mappings. It is mainly addressed to students who have already studied these mappings in the setting of metric spaces, as well as multidimensional differential calculus. The needed background facts about sets, metric spaces and linear algebra are developed in detail, so as to provide a seamless transition between students' previous studies and new material. In view of its many novel features, this book will be of interest also to mature readers who have studied continuous mappings from the subject's classical texts and wish to become acquainted with a new approach. The theory of continuous mappings serves as infrastructure for more specialized mathematical theories like differential equations, integral equations, operator theory, dynamical systems, global analysis, topological groups, topological rings and many more. In light of the centrality of the topic, a book of this kind fits a variety of applications, especially those that contribute to ...
Hodges, Wilfrid
1993-01-01
An up-to-date and integrated introduction to model theory, designed to be used for graduate courses (for students who are familiar with first-order logic), and as a reference for more experienced logicians and mathematicians.
Koschmann, Timothy; Roschelle, Jeremy; Nardi, Bonnie A.
1998-01-01
Includes three articles that discuss activity theory, based on "Context and Consciousness." Topics include human-computer interaction; computer interfaces; hierarchical structuring; mediation; contradictions and development; failure analysis; and designing educational technology. (LRW)
Gould, Ronald
2012-01-01
This introduction to graph theory focuses on well-established topics, covering primary techniques and including both algorithmic and theoretical problems. The algorithms are presented with a minimum of advanced data structures and programming details. This thoroughly corrected 1988 edition provides insights to computer scientists as well as advanced undergraduates and graduate students of topology, algebra, and matrix theory. Fundamental concepts and notation and elementary properties and operations are the first subjects, followed by examinations of paths and searching, trees, and networks. S
1988-06-30
MATRICES . The monograph Nonnegative Matrices [6] is an advanced book on all aspect of the theory of nonnegative matrices and...and on inverse eigenvalue problems for nonnegative matrices . The work explores some of the most recent developments in the theory of nonnegative...k -1, t0 . Define the associated polynomial of type <z>: t t-t 2 t-t 3 t-tk_ 1,X - x - x . . .X- where t = tk . The
Possibility Theory versus Probability Theory in Fuzzy Measure Theory
Parul Agarwal
2015-05-01
Full Text Available The purpose of this paper is to compare probability theory with possibility theory, and to use this comparison in comparing probability theory with fuzzy set theory. The best way of comparing probabilistic and possibilistic conceptualizations of uncertainty is to examine the two theories from a broader perspective. Such a perspective is offered by evidence theory, within which probability theory and possibility theory are recognized as special branches. While the various characteristic of possibility theory within the broader framework of evidence theory are expounded in this paper, we need to introduce their probabilistic counterparts to facilitate our discussion.
Carroll, Joseph; Clasen, Mathias; Jonsson, Emelie
2017-01-01
Biocultural theory is an integrative research program designed to investigate the causal interactions between biological adaptations and cultural constructions. From the biocultural perspective, cultural processes are rooted in the biological necessities of the human life cycle: specifically human...... and ideological beliefs, and artistic practices such as music, dance, painting, and storytelling. Establishing biocultural theory as a program that self-consciously encompasses the different particular forms of human evolutionary research could help scholars and scientists envision their own specialized areas...... of research as contributions to a coherent, collective research program. This article argues that a mature biocultural paradigm needs to be informed by at least 7 major research clusters: (a) gene-culture coevolution; (b) human life history theory; (c) evolutionary social psychology; (d) anthropological...
Donnellan, Thomas; Maxwell, E A; Plumpton, C
1968-01-01
Lattice Theory presents an elementary account of a significant branch of contemporary mathematics concerning lattice theory. This book discusses the unusual features, which include the presentation and exploitation of partitions of a finite set. Organized into six chapters, this book begins with an overview of the concept of several topics, including sets in general, the relations and operations, the relation of equivalence, and the relation of congruence. This text then defines the relation of partial order and then partially ordered sets, including chains. Other chapters examine the properti
S Varadhan, S R
2001-01-01
This volume presents topics in probability theory covered during a first-year graduate course given at the Courant Institute of Mathematical Sciences. The necessary background material in measure theory is developed, including the standard topics, such as extension theorem, construction of measures, integration, product spaces, Radon-Nikodym theorem, and conditional expectation. In the first part of the book, characteristic functions are introduced, followed by the study of weak convergence of probability distributions. Then both the weak and strong limit theorems for sums of independent rando
Stewart, Ian
2003-01-01
Ian Stewart's Galois Theory has been in print for 30 years. Resoundingly popular, it still serves its purpose exceedingly well. Yet mathematics education has changed considerably since 1973, when theory took precedence over examples, and the time has come to bring this presentation in line with more modern approaches.To this end, the story now begins with polynomials over the complex numbers, and the central quest is to understand when such polynomials have solutions that can be expressed by radicals. Reorganization of the material places the concrete before the abstract, thus motivating the g
Effective theories of universal theories
Wells, James D
2015-01-01
It is well-known but sometimes overlooked that constraints on the oblique parameters (most notably $S$ and $T$ parameters) are only applicable to a special class of new physics scenarios known as universal theories. In the effective field theory (EFT) framework, the oblique parameters should not be associated with Wilson coefficients in a particular operator basis, unless restrictions have been imposed on the EFT so that it describes universal theories. We work out these restrictions, and present a detailed EFT analysis of universal theories. We find that at the dimension-6 level, universal theories are completely characterized by 16 parameters. They are conveniently chosen to be: 5 oblique parameters that agree with the commonly-adopted ones, 4 anomalous triple-gauge couplings, 3 rescaling factors for the $h^3$, $hff$, $hVV$ vertices, 3 parameters for $hVV$ vertices absent in the Standard Model, and 1 four-fermion coupling of order $y_f^2$. All these parameters are defined in an unambiguous and basis-indepen...
Lenz, Alexander
2016-01-01
We set the scene for theoretical issues in charm physics that were discussed at CHARM 2016 in Bologna. In particular we emphasize the importance of improving our understanding of standard model contributions to numerous charm observables and we discuss also possible tests of our theory tools, like the Heavy Quark Expansion via the lifetime ratios of $D$-mesons
Friedrich, Harald [Technische Univ. Muenchen, Garching (Germany). Physik-Department
2013-08-01
Written by the author of the widely acclaimed textbook. Theoretical Atomic Physics Includes sections on quantum reflection, tunable Feshbach resonances and Efimov states. Useful for advanced students and researchers. This book presents a concise and modern coverage of scattering theory. It is motivated by the fact that experimental advances have shifted and broadened the scope of applications where concepts from scattering theory are used, e.g. to the field of ultracold atoms and molecules, which has been experiencing enormous growth in recent years, largely triggered by the successful realization of Bose-Einstein condensates of dilute atomic gases in 1995. In the present treatment, special attention is given to the role played by the long-range behaviour of the projectile-target interaction, and a theory is developed, which is well suited to describe near-threshold bound and continuum states in realistic binary systems such as diatomic molecules or molecular ions. The level of abstraction is kept as low as at all possible, and deeper questions related to mathematical foundations of scattering theory are passed by. The book should be understandable for anyone with a basic knowledge of nonrelativistic quantum mechanics. It is intended for advanced students and researchers, and it is hoped that it will be useful for theorists and experimentalists alike.
Plummer, MD
1986-01-01
This study of matching theory deals with bipartite matching, network flows, and presents fundamental results for the non-bipartite case. It goes on to study elementary bipartite graphs and elementary graphs in general. Further discussed are 2-matchings, general matching problems as linear programs, the Edmonds Matching Algorithm (and other algorithmic approaches), f-factors and vertex packing.
R. Veenhoven (Ruut)
2014-01-01
markdownabstract__Abstract__ Assumptions Livability theory involves the following six key assumptions: 1. Like all animals, humans have innate needs, such as for food, safety, and companionship. 2. Gratification of needs manifests in hedonic experience. 3. Hedonic experience determines how much we
Monthoux, Pierre Guillet de; Statler, Matt
2014-01-01
The recent Carnegie report (Colby, et al., 2011) characterizes the goal of business education as the development of practical wisdom. In this chapter, the authors reframe Scharmer’s Theory U as an attempt to develop practical wisdom by applying certain European philosophical concepts. Specificall...
Guillet de Monthoux, Pierre; Statler, Matt
2017-01-01
The recent Carnegie report (Colby, et al., 2011) characterizes the goal of business education as the development of practical wisdom. In this chapter, the authors reframe Scharmer's Theory U as an attempt to develop practical wisdom by applying certain European philosophical concepts. Specificall...
de Vreese, C.H.; Lecheler, S.; Mazzoleni, G.; Barnhurst, K.G.; Ikeda, K.; Maia, R.C.M.; Wessler, H.
2016-01-01
Political issues can be viewed from different perspectives and they can be defined differently in the news media by emphasizing some aspects and leaving others aside. This is at the core of news framing theory. Framing originates within sociology and psychology and has become one of the most used th
Hall, Marshall
2011-01-01
Includes proof of van der Waerden's 1926 conjecture on permanents, Wilson's theorem on asymptotic existence, and other developments in combinatorics since 1967. Also covers coding theory and its important connection with designs, problems of enumeration, and partition. Presents fundamentals in addition to latest advances, with illustrative problems at the end of each chapter. Enlarged appendixes include a longer list of block designs.
Bertelsen, Olav Wedege; Bødker, Susanne
2003-01-01
the young HCI research tradition. But HCI was already facing problems: lack of consideration for other aspects of human behavior, for interaction with other people, for culture. Cognitive science-based theories lacked means to address several issues that came out of the empirical projects....
Monthoux, Pierre Guillet de; Statler, Matt
2014-01-01
The recent Carnegie report (Colby, et al., 2011) characterizes the goal of business education as the development of practical wisdom. In this chapter, the authors reframe Scharmer’s Theory U as an attempt to develop practical wisdom by applying certain European philosophical concepts. Specifically...
Stein, Irene F.; Stelter, Reinhard
2011-01-01
Communication theory covers a wide variety of theories related to the communication process (Littlejohn, 1999). Communication is not simply an exchange of information, in which we have a sender and a receiver. This very technical concept of communication is clearly outdated; a human being...... is not a data processing device. In this chapter, communication is understood as a process of shared meaning-making (Bruner, 1990). Human beings interpret their environment, other people, and themselves on the basis of their dynamic interaction with the surrounding world. Meaning is essential because people...... ascribe specific meanings to their experiences, their actions in life or work, and their interactions. Meaning is reshaped, adapted, and transformed in every communication encounter. Furthermore, meaning is cocreated in dialogues or in communities of practice, such as in teams at a workplace or in school...
Helms, Lester L
2014-01-01
Potential Theory presents a clear path from calculus to classical potential theory and beyond, with the aim of moving the reader into the area of mathematical research as quickly as possible. The subject matter is developed from first principles using only calculus. Commencing with the inverse square law for gravitational and electromagnetic forces and the divergence theorem, the author develops methods for constructing solutions of Laplace's equation on a region with prescribed values on the boundary of the region. The latter half of the book addresses more advanced material aimed at those with the background of a senior undergraduate or beginning graduate course in real analysis. Starting with solutions of the Dirichlet problem subject to mixed boundary conditions on the simplest of regions, methods of morphing such solutions onto solutions of Poisson's equation on more general regions are developed using diffeomorphisms and the Perron-Wiener-Brelot method, culminating in application to Brownian motion. In ...
Hashiguchi, Koichi
2014-01-01
This book was written to serve as the standard textbook of elastoplasticity for students, engineers and researchers in the field of applied mechanics. The present second edition is improved thoroughly from the first edition by selecting the standard theories from various formulations and models, which are required to study the essentials of elastoplasticity steadily and effectively and will remain universally in the history of elastoplasticity. It opens with an explanation of vector-tensor analysis and continuum mechanics as a foundation to study elastoplasticity theory, extending over various strain and stress tensors and their rates. Subsequently, constitutive equations of elastoplastic and viscoplastic deformations for monotonic, cyclic and non-proportional loading behavior in a general rate and their applications to metals and soils are described in detail, and constitutive equations of friction behavior between solids and its application to the prediction of stick-slip phenomena are delineated. In additi...
2015-01-01
A one-sentence definition of operator theory could be: The study of (linear) continuous operations between topological vector spaces, these being in general (but not exclusively) Fréchet, Banach, or Hilbert spaces (or their duals). Operator theory is thus a very wide field, with numerous facets, both applied and theoretical. There are deep connections with complex analysis, functional analysis, mathematical physics, and electrical engineering, to name a few. Fascinating new applications and directions regularly appear, such as operator spaces, free probability, and applications to Clifford analysis. In our choice of the sections, we tried to reflect this diversity. This is a dynamic ongoing project, and more sections are planned, to complete the picture. We hope you enjoy the reading, and profit from this endeavor.
Diestel, Reinhard
2017-01-01
This standard textbook of modern graph theory, now in its fifth edition, combines the authority of a classic with the engaging freshness of style that is the hallmark of active mathematics. It covers the core material of the subject with concise yet reliably complete proofs, while offering glimpses of more advanced methods in each field by one or two deeper results, again with proofs given in full detail. The book can be used as a reliable text for an introductory course, as a graduate text, and for self-study. From the reviews: “This outstanding book cannot be substituted with any other book on the present textbook market. It has every chance of becoming the standard textbook for graph theory.”Acta Scientiarum Mathematiciarum “Deep, clear, wonderful. This is a serious book about the heart of graph theory. It has depth and integrity. ”Persi Diaconis & Ron Graham, SIAM Review “The book has received a very enthusiastic reception, which it amply deserves. A masterly elucidation of modern graph theo...
Friedrich, Harald
2016-01-01
This corrected and updated second edition of "Scattering Theory" presents a concise and modern coverage of the subject. In the present treatment, special attention is given to the role played by the long-range behaviour of the projectile-target interaction, and a theory is developed, which is well suited to describe near-threshold bound and continuum states in realistic binary systems such as diatomic molecules or molecular ions. It is motivated by the fact that experimental advances have shifted and broadened the scope of applications where concepts from scattering theory are used, e.g. to the field of ultracold atoms and molecules, which has been experiencing enormous growth in recent years, largely triggered by the successful realization of Bose-Einstein condensates of dilute atomic gases in 1995. The book contains sections on special topics such as near-threshold quantization, quantum reflection, Feshbach resonances and the quantum description of scattering in two dimensions. The level of abstraction is k...
Blyth, T S; Sneddon, I N; Stark, M
1972-01-01
Residuation Theory aims to contribute to literature in the field of ordered algebraic structures, especially on the subject of residual mappings. The book is divided into three chapters. Chapter 1 focuses on ordered sets; directed sets; semilattices; lattices; and complete lattices. Chapter 2 tackles Baer rings; Baer semigroups; Foulis semigroups; residual mappings; the notion of involution; and Boolean algebras. Chapter 3 covers residuated groupoids and semigroups; group homomorphic and isotone homomorphic Boolean images of ordered semigroups; Dubreil-Jacotin and Brouwer semigroups; and loli
Diestel, Reinhard
2012-01-01
HauptbeschreibungThis standard textbook of modern graph theory, now in its fourth edition, combinesthe authority of a classic with the engaging freshness of style that is the hallmarkof active mathematics. It covers the core material of the subject with concise yetreliably complete proofs, while offering glimpses of more advanced methodsin each field by one or two deeper results, again with proofs given in full detail.The book can be used as a reliable text for an introductory course, as a graduatetext, and for self-study. Rezension"Deep, clear, wonderful. This is a serious book about the
2009-01-01
This book deals with the basic subjects of design theory. It begins with balanced incomplete block designs, various constructions of which are described in ample detail. In particular, finite projective and affine planes, difference sets and Hadamard matrices, as tools to construct balanced incomplete block designs, are included. Orthogonal latin squares are also treated in detail. Zhu's simpler proof of the falsity of Euler's conjecture is included. The construction of some classes of balanced incomplete block designs, such as Steiner triple systems and Kirkman triple systems, are also given.
Goldie, Charles M
1991-01-01
This book is an introduction, for mathematics students, to the theories of information and codes. They are usually treated separately but, as both address the problem of communication through noisy channels (albeit from different directions), the authors have been able to exploit the connection to give a reasonably self-contained treatment, relating the probabilistic and algebraic viewpoints. The style is discursive and, as befits the subject, plenty of examples and exercises are provided. Some examples and exercises are provided. Some examples of computer codes are given to provide concrete illustrations of abstract ideas.
Merris, Russell
2001-01-01
A lively invitation to the flavor, elegance, and power of graph theoryThis mathematically rigorous introduction is tempered and enlivened by numerous illustrations, revealing examples, seductive applications, and historical references. An award-winning teacher, Russ Merris has crafted a book designed to attract and engage through its spirited exposition, a rich assortment of well-chosen exercises, and a selection of topics that emphasizes the kinds of things that can be manipulated, counted, and pictured. Intended neither to be a comprehensive overview nor an encyclopedic reference, th
Diestel, Reinhard
2000-01-01
This book is a concise, yet carefully written, introduction to modern graph theory, covering all its major recent developments. It can be used both as a reliable textbook for an introductory course and as a graduate text: on each topic it covers all the basic material in full detail, and adds one or two deeper results (again with detailed proofs) to illustrate the more advanced methods of that field. This second edition extends the first in two ways. It offers a thoroughly revised and updated chapter on graph minors, which now includes full new proofs of two of the central Robertson-Seymour theorems (as well as a detailed sketch of the entire proof of their celebrated Graph Minor Theorem). Second, there is now a section of hints for all the exercises, to enhance their value for both individual study and classroom use.
刘敏霞; 何林; 张耿; 叶海; 黄晓园; 徐永钊
2016-01-01
LaNiC2 is one of ternary RNiC2 compounds, where R is a rare earth or Y. Its space group is Amm2. the symmetry along the c-axis of the crystal structure lacks inversion symmetry along the c-axis. In 2009, Hillier et al. performed the muon spin relaxation experiment (µSR) which implied that time-reversal symmetry is broken in LaNiC2. As a weak correlation noncentrosymmetric superconductor, LaNiC2 has attracted wide research interest in recent years. Though a lot of theoretical and experimental studies have been carried out, the order parameter of this compound remains highly controversial. The measurements of specific heat and nuclear quadrupole relaxation suggest that LaNiC2 is“normally BCS-like”, which is further supported by theoretical calculations. But recently another study showed that the London penetration depth depends on T 2 below 0.4 Tc indicative of nodes in the energy gap. Evidence of possible nodal superconductivity can also be inferred from the early measurements of specific heat given by Lee et al. However, the experimental results obtained by Chen et al. supported the existence of two-gap superconductivity in LaNiC2. Based on the above case, the two-band Ginzburg-Landau theory is used to study the temperature dependence of the upper critical field for the superconductor LaNiC2 in this paper. Choosing the Ginzburg-Landau theory for calculating the upper critical field is just because Ginzburg-Landau theoretical model is simple, easy to understand, low-calculation, and the clear physical meanings of the parameters. The theoretical results in this paper accord with the experimental data very well in the whole temperature range. The curve of Hc2 (T ) has an obvious positive curvature near the critical temperature, which is typical feature of multi-gap superconductor. Therefore, our results show strong evidence that two-gap scenario is better to account for the superconductivity of LaNiC2, consistent with the results of Chen Jian et al. The
General Theories of Regulation
Hertog, J.A. den
1999-01-01
This chapter makes a distinction between three types of theories of regulation: public interest theories, the Chicago theory of regulation and the public choice theories. The Chicago theory is mainly directed at the explanation of economic regulation; public interest theories and public choice theor
Metallic magnets without inversion symmetry and antiferromagnetic quantum critical points
Fischer, I.A.
2006-07-01
This thesis focusses on two classes of systems that exhibit non-Fermi liquid behaviour in experiments: we investigated aspects of chiral ferromagnets and of antiferromagnetic metals close to a quantum critical point. In chiral ferromagnets, the absence of inversion symmetry makes spin-orbit coupling possible, which leads to a helical modulation of the ferromagnetically ordered state. We studied the motion of electrons in the magnetically ordered state of a metal without inversion symmetry by calculating their generic band-structure. We found that spin-orbit coupling, although weak, has a profound effect on the shape of the Fermi surface: On a large portion of the Fermi surface the electron motion parallel to the helix practically stops. Signatures of this effect can be expected to show up in measurements of the anomalous Hall effect. Recent neutron scattering experiments uncovered the existence of a peculiar kind of partial order in a region of the phase diagram adjacent to the ordered state of the chiral ferromagnet MnSi. Starting from the premise that this partially ordered state is a thermodynamically distinct phase, we investigated an extended Ginzburg-Landau theory for chiral ferromagnets. In a certain parameter regime of the Ginzburg-Landau theory we identified crystalline phases that are reminiscent of the so-called blue phases in liquid crystals. Many antiferromagnetic heavy-fermion systems can be tuned into a regime where they exhibit non-Fermi liquid exponents in the temperature dependence of thermodynamic quantities such as the specific heat capacity; this behaviour could be due to a quantum critical point. If the quantum critical behaviour is field-induced, the external field does not only suppress antiferromagnetism but also induces spin precession and thereby influences the dynamics of the order parameter. We investigated the quantum critical behavior of clean antiferromagnetic metals subject to a static, spatially uniform external magnetic field. We
THEORIES OF CORPORATE GOVERNANCE
Sorin Nicolae BORLEA
2013-03-01
Full Text Available This study attempts to provide a theoretical framework for the corporate governance debate. The review of various corporate governance theories enhances the major objective of corporate governance which is maximizing the value for shareholders by ensuring good social and environment performances. The theories of corporate governance are rooted in agency theory with the theory of moral hazard’s implications, further developing within stewardship theory and stakeholder theory and evolving at resource dependence theory, transaction cost theory and political theory. Later, to these theories was added ethics theory, information asymmetry theory or the theory of efficient markets. These theories are defined based on the causes and effects of variables such as: the configuration of the board of directors, audit committee, independence of managers, the role of top management and their social relations beyond the legal regulatory framework. Effective corporate governance requires applying a combination
Gauge theory and little gauge theory
Koizumi, Kozo
2016-01-01
The gauge theory is the most important type of the field theory, in which the interactions of the elementary particles are described by the exchange of the gauge bosons.In this article, the gauge theory is reexamined as geometry of the vector space, and a new concept of "little gauge theory" is introduced. A key peculiarity of the little gauge theory is that the theory is able to give a restriction for form of the connection field. Based on the little gauge theory, Cartan geometry, a charged boson and the Dirac fermion field theory are investigated. In particular, the Dirac fermion field theory leads to an extension of Sogami's covariant derivative. And it is interpreted that Higgs bosons are included in new fields introduced in this article.
Riyopoulos, Spilios
1996-03-01
A guiding center fluid theory is applied to model steady-state, single mode, high-power magnetron operation. A hub of uniform, prescribed density, feeds the current spokes. The spoke charge follows from the continuity equation and the incompressibility of the guiding center flow. Included are the spoke self-fields (DC and AC), obtained by an expansion around the unperturbed (zero-spoke charge) flow in powers of ν/V1, ν, and V1 being the effective charge density and AC amplitude. The spoke current is obtained as a nonlinear function of the detuning from the synchronous (Buneman-Hartree, BH) voltage Vs; the spoke charge is included in the self-consistent definition of Vs. It is shown that there is a DC voltage region of width ‖V-Vs‖˜V1, where the spoke width is constant and the spoke current is simply proportional to the AC voltage. The magnetron characteristic curves are ``flat'' in that range, and are approximated by a linear expansion around Vs. The derived formulas differ from earlier results [J. F. Hull, in Cross Field Microwave Devices, edited by E. Okress (Academic, New York, 1961), pp. 496-527] in (a) there is no current cutoff at synchronism; the tube operates well below as well above the BH voltage; (b) the characteristics are single valued within the synchronous voltage range; (c) the hub top is not treated as virtual cathode; and (d) the hub density is not equal to the Brillouin density; comparisons with tube measurements show the best agreement for hub density near half the Brillouin density. It is also shown that at low space charge and low power the gain curve is symmetric relative to the voltage (frequency) detuning. While symmetry is broken at high-power/high space charge magnetron operation, the BH voltage remains between the current cutoff voltages.
Levitas, Valery I.; Warren, James A.
2016-06-01
A thermodynamically consistent, large-strain, multi-phase field approach (with consequent interface stresses) is generalized for the case with anisotropic interface (gradient) energy (e.g. an energy density that depends both on the magnitude and direction of the gradients in the phase fields). Such a generalization, if done in the "usual" manner, yields a theory that can be shown to be manifestly unphysical. These theories consider the gradient energy as anisotropic in the deformed configuration, and, due to this supposition, several fundamental contradictions arise. First, the Cauchy stress tensor is non-symmetric and, consequently, violates the moment of momentum principle, in essence the Herring (thermodynamic) torque is imparting an unphysical angular momentum to the system. In addition, this non-symmetric stress implies a violation of the principle of material objectivity. These problems in the formulation can be resolved by insisting that the gradient energy is an isotropic function of the gradient of the order parameters in the deformed configuration, but depends on the direction of the gradient of the order parameters (is anisotropic) in the undeformed configuration. We find that for a propagating nonequilibrium interface, the structural part of the interfacial Cauchy stress is symmetric and reduces to a biaxial tension with the magnitude equal to the temperature- and orientation-dependent interface energy. Ginzburg-Landau equations for the evolution of the order parameters and temperature evolution equation, as well as the boundary conditions for the order parameters are derived. Small strain simplifications are presented. Remarkably, this anisotropy yields a first order correction in the Ginzburg-Landau equation for small strains, which has been neglected in prior works. The next strain-related term is third order. For concreteness, specific orientation dependencies of the gradient energy coefficients are examined, using published molecular dynamics
Müller, Gert; Sacks, Gerald
1990-01-01
These proceedings contain research and survey papers from many subfields of recursion theory, with emphasis on degree theory, in particular the development of frameworks for current techniques in this field. Other topics covered include computational complexity theory, generalized recursion theory, proof theoretic questions in recursion theory, and recursive mathematics.
1982-02-01
of collections of associations, Need theory consists of interrelated concepts, social learning theory consists of rule application in the social...Ryan’s Learning Subdivisions Hierarchically Arranged -27- Landy: ONR Annual Report Expectancy Theory Effectance Theory Social Learning Theory Self-Esteem
Floquet engineering of Haldane Chern insulators and chiral bosonic phase transitions
Plekhanov, Kirill; Roux, Guillaume; Le Hur, Karyn
2017-01-01
The realization of synthetic gauge fields has attracted a lot of attention recently in relation to periodically driven systems and the Floquet theory. In ultracold atom systems in optical lattices and photonic networks, this allows one to simulate exotic phases of matter such as quantum Hall phases, anomalous quantum Hall phases, and analogs of topological insulators. In this paper, we apply the Floquet theory to engineer anisotropic Haldane models on the honeycomb lattice and two-leg ladder systems. We show that these anisotropic Haldane models still possess a topologically nontrivial band structure associated with chiral edge modes. Focusing on (interacting) boson systems in s -wave bands of the lattice, we show how to engineer through the Floquet theory, a quantum phase transition (QPT) between a uniform superfluid and a Bose-Einstein condensate analog of Fulde-Ferrell-Larkin-Ovchinnikov states, where bosons condense at nonzero wave vectors. We perform a Ginzburg-Landau analysis of the QPT on the graphene lattice, and compute observables such as chiral currents and the momentum distribution. The results are supported by exact diagonalization calculations and compared with those of the isotropic situation. The validity of high-frequency expansion in the Floquet theory is also tested using time-dependent simulations for various parameters of the model. Last, we show that the anisotropic choice for the effective vector potential allows a bosonization approach in equivalent ladder (strip) geometries.
Composite Photon Theory Versus Elementary Photon Theory
Perkins, Walton A
2015-01-01
The purpose of this paper is to show that the composite photon theory measures up well against the Standard Model's elementary photon theory. This is done by comparing the two theories area by area. Although the predictions of quantum electrodynamics are in excellent agreement with experiment (as in the anomalous magnetic moment of the electron), there are some problems, such as the difficulty in describing the electromagnetic field with the four-component vector potential because the photon has only two polarization states. In most areas the two theories give similar results, so it is impossible to rule out the composite photon theory. Pryce's arguments in 1938 against a composite photon theory are shown to be invalid or irrelevant. Recently, it has been realized that in the composite theory the antiphoton does not interact with matter because it is formed of a neutrino and an antineutrino with the wrong helicity. This leads to experimental tests that can determine which theory is correct.
Decidability of formal theories and hyperincursivity theory
Grappone, Arturo G.
2000-05-01
This paper shows the limits of the Proof Standard Theory (briefly, PST) and gives some ideas of how to build a proof anticipatory theory (briefly, PAT) that has no such limits. Also, this paper considers that Gödel's proof of the undecidability of Principia Mathematica formal theory is not valid for axiomatic theories that use a PAT to build their proofs because the (hyper)incursive functions are self-representable.
Mangani, P
2011-01-01
This title includes: Lectures - G.E. Sacks - Model theory and applications, and H.J. Keisler - Constructions in model theory; and, Seminars - M. Servi - SH formulas and generalized exponential, and J.A. Makowski - Topological model theory.
Decoding the architectural theory
Gu Mengchao
2008-01-01
Starting from the illustration of the definition and concept of the architectural theory, the author established his unique understanding about the framework of the architectural theory and the innovation of the architectural theory underlined by Chinese characteristics.
Murray, Paul R.; Paul R., Murray
2001-01-01
This paper deals with two difficult questions: (1) What is literary theory? and (2) What does literary theory do? Literary theory is contrasted to literary criticism, and theory is found to be a more all-embracing, inclusive field than criticism, which is tied more closely to literature itself. Literary theory is shown to be a multitude of differing ways of looking at literature, with each theory yielding differing results.
Review of Hydroelasticity Theories
Chen, Xu-jun; Wu, You-sheng; Cui, Wei-cheng
2006-01-01
Existing hydroelastic theories are reviewed. The theories are classified into different types: two-dimensional linear theory, two-dimensional nonlinear theory, three-dimensional linear theory and three-dimensional nonlinear theory. Applications to analysis of very large floating structures (VLFS)......) are reviewed and discussed in details. Special emphasis is placed on papers from China and Japan (in native languages) as these papers are not generally publicly known in the rest of the world....
Grounded theory, feminist theory, critical theory: toward theoretical triangulation.
Kushner, Kaysi Eastlick; Morrow, Raymond
2003-01-01
Nursing and social science scholars have examined the compatibility between feminist and grounded theory traditions in scientific knowledge generation, concluding that they are complementary, yet not without certain tensions. This line of inquiry is extended to propose a critical feminist grounded theory methodology. The construction of symbolic interactionist, feminist, and critical feminist variants of grounded theory methodology is examined in terms of the presuppositions of each tradition and their interplay as a process of theoretical triangulation.
陈辉; 成泰民; 陈思群
2011-01-01
A theoretical model of ferroelectric thin film composite by three ferroelectric materials with different phase-transition temperatures has been built, in which the three components composite perpendicular to the polarization. Using ginzburg-landau-devonshire(GLD) theory, a local distribution function has been introduced to describe the properties of the transition layers, and the pyroelectric properties of the composite ferroelectric thin films have been mainly investigated. Polarization distributions, transition temperatures and pyroelectric coefficients were calculated with different composite methods. It was shown that the composite methods had importance influence on polarization and pyroelectric properties; two pyroelectric peaks appeared with the change of the film temperature. The composite ferroelectric thin film under new model presented many new properties, especially provide a reference on the improvement of pyroelectric devices. This composite film may be a new choice of multi-layer films in applications.%建立3种具有不同相变温度的铁电材料垂直于极化方向复合而成的铁电薄膜的理论模型,在ginzburg-landau-devonshire (GLD)唯象理论的框架下展开研究,同时引入局域分布函数来描述不同材料间过渡层的性质,主要研究了复合铁电薄膜的热释电性质.通过改变3种不同铁电材料的复合方式,计算了铁电多层膜内部的极化强度分布、相变温度及热释电系数.研究表明,具有不同相变温度的铁电材料间的复合方式对铁电薄膜的极化和热释电性质有着重要的影响,3种不同材料复合而成的铁电薄膜随着温度的变化出现了2个热释电峰.新模型下的复合铁电薄膜表现很多新的特性,尤其对于铁电热释电器件性能的改良提出了一种参考,该种复合薄膜也许能够成为通常使用的多层膜的一种选择.
Postnikov, MM; Stark, M; Ulam, S
1962-01-01
Foundations of Galois Theory is an introduction to group theory, field theory, and the basic concepts of abstract algebra. The text is divided into two parts. Part I presents the elements of Galois Theory, in which chapters are devoted to the presentation of the elements of field theory, facts from the theory of groups, and the applications of Galois Theory. Part II focuses on the development of general Galois Theory and its use in the solution of equations by radicals. Equations that are solvable by radicals; the construction of equations solvable by radicals; and the unsolvability by radica
Boley, Bruno A
1997-01-01
Highly regarded text presents detailed discussion of fundamental aspects of theory, background, problems with detailed solutions. Basics of thermoelasticity, heat transfer theory, thermal stress analysis, more. 1985 edition.
Gravitational Field Shielding by Scalar Field and Type II Superconductors
Zhang B. J.
2013-01-01
Full Text Available The gravitational field shielding by scalar field and type II superconductors are theoret- ically investigated. In accord with the well-developed five-dimensional fully covariant Kaluza-Klein theory with a scalar field, which unifies the Einsteinian general relativity and Maxwellian electromagnetic theory, the scalar field cannot only polarize the space as shown previously, but also flatten the space as indicated recently. The polariza- tion of space decreases the electromagnetic field by increasing the equivalent vacuum permittivity constant, while the flattening of space decreases the gravitational field by decreasing the equivalent gravitational constant. In other words, the scalar field can be also employed to shield the gravitational field. A strong scalar field significantly shield the gravitational field by largely decreasing the equivalent gravitational constant. According to the theory of gravitational field shielding by scalar field, the weight loss experimentally detected for a sample near a rotating ceramic disk at very low tempera- ture can be explained as the shielding of the Earth gravitational field by the Ginzburg- Landau scalar field, which is produced by the type II superconductors. The significant shielding of gravitational field by scalar field produced by superconductors may lead to a new spaceflight technology in future.
Jardine, John F
2015-01-01
This monograph on the homotopy theory of topologized diagrams of spaces and spectra gives an expert account of a subject at the foundation of motivic homotopy theory and the theory of topological modular forms in stable homotopy theory. Beginning with an introduction to the homotopy theory of simplicial sets and topos theory, the book covers core topics such as the unstable homotopy theory of simplicial presheaves and sheaves, localized theories, cocycles, descent theory, non-abelian cohomology, stacks, and local stable homotopy theory. A detailed treatment of the formalism of the subject is interwoven with explanations of the motivation, development, and nuances of ideas and results. The coherence of the abstract theory is elucidated through the use of widely applicable tools, such as Barr's theorem on Boolean localization, model structures on the category of simplicial presheaves on a site, and cocycle categories. A wealth of concrete examples convey the vitality and importance of the subject in topology, n...
't Hooft, Gerardus; Witten, Edward
2005-01-01
In his later years, Einstein sought a unified theory that would extend general relativity and provide an alternative to quantum theory. There is now talk of a "theory of everything"; fifty years after his death, how close are we to such a theory? (3 pages)
Hendricks, Vincent F.
Game Theory is a collection of short interviews based on 5 questions presented to some of the most influential and prominent scholars in game theory. We hear their views on game theory, its aim, scope, use, the future direction of game theory and how their work fits in these respects....
de Bruin, B.P.
2005-01-01
Game theory is the mathematical study of strategy and conflict. It has wide applications in economics, political science, sociology, and, to some extent, in philosophy. Where rational choice theory or decision theory is concerned with individual agents facing games against nature, game theory deals
Contemporary theories of democracy
Mladenović Ivan
2008-01-01
Full Text Available The aim of this paper is two-fold: first, to analyze several contemporary theories of democracy, and secondly, to propose a theoretical framework for further investigations based on analyzed theories. The following four theories will be analyzed: pluralism, social choice theory, deliberative democracy and participatory democracy.
Banks, Tom
2008-09-01
1. Introduction; 2. Quantum theory of free scalar fields; 3. Interacting field theory; 4. Particles of spin one, and gauge invariance; 5. Spin 1/2 particles and Fermi statistics; 6. Massive quantum electrodynamics; 7. Symmetries, Ward identities and Nambu Goldstone bosons; 8. Non-abelian gauge theory; 9. Renormalization and effective field theory; 10. Instantons and solitons; 11. Concluding remarks; Appendices; References; Index.
Hendricks, Vincent F.
Game Theory is a collection of short interviews based on 5 questions presented to some of the most influential and prominent scholars in game theory. We hear their views on game theory, its aim, scope, use, the future direction of game theory and how their work fits in these respects....
Moschovakis, YN
1987-01-01
Now available in paperback, this monograph is a self-contained exposition of the main results and methods of descriptive set theory. It develops all the necessary background material from logic and recursion theory, and treats both classical descriptive set theory and the effective theory developed by logicians.
Balanced Topological Field Theories
Dijkgraaf, R.; Moore, G.
We describe a class of topological field theories called ``balanced topological field theories''. These theories are associated to moduli problems with vanishing virtual dimension and calculate the Euler character of various moduli spaces. We show that these theories are closely related to the geometry and equivariant cohomology of ``iterated superspaces'' that carry two differentials. We find the most general action for these theories, which turns out to define Morse theory on field space. We illustrate the constructions with numerous examples. Finally, we relate these theories to topological sigma-models twisted using an isometry of the target space.
Balanced Topological Field Theories
Dijkgraaf, R
1997-01-01
We describe a class of topological field theories called ``balanced topological field theories.'' These theories are associated to moduli problems with vanishing virtual dimension and calculate the Euler character of various moduli spaces. We show that these theories are closely related to the geometry and equivariant cohomology of ``iterated superspaces'' that carry two differentials. We find the most general action for these theories, which turns out to define Morse theory on field space. We illustrate the constructions with numerous examples. Finally, we relate these theories to topological sigma-models twisted using an isometry of the target space.
Zimmerman Jones, Andrew
2010-01-01
Making Everything Easier!. String Theory for Dummies. Learn:. The basic concepts of this controversial theory;. How string theory builds on physics concepts;. The different viewpoints in the field;. String theory's physical implications. Andrew Zimmerman Jones. Physics Guide, About.com. with Daniel Robbins, PhD in Physics. Your plain-English guide to this complex scientific theory. String theory is one of the most complicated sciences being explored today. Not to worry though! This informative guide clearly explains the basics of this hot topic, discusses the theory's hypotheses and prediction
梁景宏
2010-01-01
In this essay, I wish to invite young scholars to learn, use, and contribute to accounting theory. In this invitation, I argue theory has lineage, is important and can be fun. Its lineage comes from the post-WWII scientific revolution in management education and research. Theory is important because it is the successful interaction between theory and empirical work that ultimately advances an academic discipline. Theory can be fun because when done well, learning, using and contributing to theory can be an enjoyable activity for all scholars, either as consumers or as producers of theory.
无
2003-01-01
The basic ideas of game theory were originated from the problems of maximum and minimum given by J.Yon Neumann in 1928. Later, wars accelerated the study of game theory, there are many developments that contributed to the advancement of game theory, many problems of optimum appeared in economic development process. Scientists applied mathematic methods to studying game theory to make the theory more profound and perfect. The axiomatic structure of game theory was nearly complete in 1944. The path of the development of game theory started from finite to infinite, from two players to many players, from expressing gains with quantity to showing the ending of game theory with abstract result, and from certainty problems to random problems. Thus development of game theory is closely related to the economic development. In recent years, the research on the non-differentiability of Shapley value posed by Belgian Mertens is one of the advanced studies in game theory.
Quantum Theory is an Information Theory
D'Ariano, Giacomo M.; Perinotti, Paolo
2016-03-01
In this paper we review the general framework of operational probabilistic theories (OPT), along with the six axioms from which quantum theory can be derived. We argue that the OPT framework along with a relaxed version of five of the axioms, define a general information theory. We close the paper with considerations about the role of the observer in an OPT, and the interpretation of the von Neumann postulate and the Schrödinger-cat paradox.
Teaching Theory X and Theory Y in Organizational Communication
Noland, Carey
2014-01-01
The purpose of the activity described here is to integrate McGregor's Theory X and Theory Y into a group application: design a syllabus that embodies either Theory X or Theory Y tenets. Students should be able to differentiate between Theory X and Theory Y, create a syllabus based on Theory X or Theory Y tenets, evaluate the different syllabi…
Conlon, Joseph
2016-01-01
Is string theory a fraud or one of the great scientific advances? Why do so many physicists work on string theory if it cannot be tested? This book provides insight into why such a theory, with little direct experimental support, plays such a prominent role in theoretical physics. The book gives a modern and accurate account of string theory and science, explaining what string theory is, why it is regarded as so promising, and why it is hard to test.
2015-01-01
Purpose To provide a small overview of genre theory and its associated concepts and to show how genre theory has had its antecedents in certain parts of the social sciences and not in the humanities. Findings The chapter argues that the explanatory force of genre theory may be explained with its...... emphasis on everyday genres, de facto genres. Originality/value By providing an overview of genre theory, the chapter demonstrates the wealth and richness of forms of explanations in genre theory....
Foundations of Information Theory
Burgin, Mark
2008-01-01
Information is the basic concept of information theory. However, there is no definition of this concept that can encompass all uses of the term information in information theories and beyond. Many question a possibility of such a definition. However, foundations of information theory developed in the context of the general theory of information made it possible to build such a relevant and at the same time, encompassing definition. Foundations of information theory are built in a form of onto...
Andersen, Jack
2015-01-01
Purpose To provide a small overview of genre theory and its associated concepts and to show how genre theory has had its antecedents in certain parts of the social sciences and not in the humanities. Findings The chapter argues that the explanatory force of genre theory may be explained with its...... emphasis on everyday genres, de facto genres. Originality/value By providing an overview of genre theory, the chapter demonstrates the wealth and richness of forms of explanations in genre theory....
Computability theory an introduction to recursion theory
Enderton, Herbert B
2010-01-01
Computability Theory: An Introduction to Recursion Theory, provides a concise, comprehensive, and authoritative introduction to contemporary computability theory, techniques, and results. The basic concepts and techniques of computability theory are placed in their historical, philosophical and logical context. This presentation is characterized by an unusual breadth of coverage and the inclusion of advanced topics not to be found elsewhere in the literature at this level. The text includes both the standard material for a first course in computability and more advanced looks at degree str
Gauge theory loop operators and Liouville theory
Drukker, Nadav [Humboldt Univ. Berlin (Germany). Inst. fuer Physik; Gomis, Jaume; Okuda, Takuda [Perimeter Inst. for Theoretical Physics, Waterloo, ON (Canada); Teschner, Joerg [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2009-10-15
We propose a correspondence between loop operators in a family of four dimensional N=2 gauge theories on S{sup 4} - including Wilson, 't Hooft and dyonic operators - and Liouville theory loop operators on a Riemann surface. This extends the beautiful relation between the partition function of these N=2 gauge theories and Liouville correlators found by Alday, Gaiotto and Tachikawa. We show that the computation of these Liouville correlators with the insertion of a Liouville loop operator reproduces Pestun's formula capturing the expectation value of a Wilson loop operator in the corresponding gauge theory. We prove that our definition of Liouville loop operators is invariant under modular transformations, which given our correspondence, implies the conjectured action of S-duality on the gauge theory loop operators. Our computations in Liouville theory make an explicit prediction for the exact expectation value of 't Hooft and dyonic loop operators in these N=2 gauge theories. The Liouville loop operators are also found to admit a simple geometric interpretation within quantum Teichmueller theory as the quantum operators representing the length of geodesics. We study the algebra of Liouville loop operators and show that it gives evidence for our proposal as well as providing definite predictions for the operator product expansion of loop operators in gauge theory. (orig.)
Towards a theory of spacetime theories
Schiemann, Gregor; Scholz, Erhard
2017-01-01
This contributed volume is the result of a July 2010 workshop at the University of Wuppertal Interdisciplinary Centre for Science and Technology Studies which brought together world-wide experts from physics, philosophy and history, in order to address a set of questions first posed in the 1950s: How do we compare spacetime theories? How do we judge, objectively, which is the “best” theory? Is there even a unique answer to this question? The goal of the workshop, and of this book, is to contribute to the development of a meta-theory of spacetime theories. Such a meta-theory would reveal insights about specific spacetime theories by distilling their essential similarities and differences, deliver a framework for a class of theories that could be helpful as a blueprint to build other meta-theories, and provide a higher level viewpoint for judging which theory most accurately describes nature. But rather than drawing a map in broad strokes, the focus is on particularly rich regions in the “space of spaceti...
The distribution of 3D superconductivity near the second critical field
Kachmar, Ayman; Nasrallah, Marwa
2016-09-01
We study the minimizers of the Ginzburg-Landau energy functional with a uniform magnetic field in a three dimensional bounded domain. The functional depends on two positive parameters, the Ginzburg-Landau parameter and the intensity of the applied magnetic field, and acts on complex-valued functions and vector fields. We establish a formula for the distribution of the L 2-norm of the minimizing complex-valued function (order parameter). The formula is valid in the regime where the Ginzburg-Landau parameter is large and the applied magnetic field is close to and strictly below the second critical field—the threshold value corresponding to the transition from the superconducting to the normal phase in the bulk of the sample. Earlier results are valid in 2D domains and for the L 4-norm in 3D domains.
Vortex and characteristics of prestrained type-II deformable superconductors under magnetic fields
Ma, Zeling; Wang, Xingzhe; Zhou, Youhe
2016-04-01
Based on the time-dependent Ginzburg-Landau (TDGL) theory and the linear deformation theory, we present a numerical investigation of magnetic vortex characteristics of a type-II deformable superconductor with prestrain. The effect of prestrain on the wave function, vortex dynamics and energy density of a superconducting film is analyzed by solving the nonlinear TDGL equations in the presence of magnetic field. The results show that the prestrain has a remarkable influence on the magnetic vortex distribution and the vortex dynamics, as well as value of wave function of the superconductor. The different prestrains, i.e., pre-given compression and tension strains, result in dissimilar characteristics on a half-plane of deformable superconductor in an applied magnetic field, and the vortex distribution and entrance in a two dimensional superconducting film. The studies demonstrated that the compression prestrain may speed up the vortexes entering into the region of the superconducting film and increases the vortex number in comparison with those of free-prestrain case, while the tension prestrain shows the reversal features. The energy density and spectrum in the superconductor are further demonstrated numerically and discussed. The present investigation is an attempt to give insight into the superconductivity and electromagnetic characteristics taking into account the elastic deformation in superconductors.
Sato, K; Yuan, X-F; Kawakatsu, T
2010-02-01
Numerous numerical and experimental evidence suggest that shear banding behavior looks like first-order phase transitions. In this paper, we demonstrate that this correspondence is actually established in the so-called non-local diffusive Johnson-Segalman model (the DJS model), a typical mechanical constitutive model that has been widely used for describing shear banding phenomena. In the neighborhood of the critical point, we apply the reduction procedure based on the center manifold theory to the governing equations of the DJS model. As a result, we obtain a time evolution equation of the flow field that is equivalent to the time-dependent Ginzburg-Landau (TDGL) equations for modeling thermodynamic first-order phase transitions. This result, for the first time, provides a mathematical proof that there is an analogy between the mechanical instability and thermodynamic phase transition at least in the vicinity of the critical point of the shear banding of DJS model. Within this framework, we can clearly distinguish the metastable branch in the stress-strain rate curve around the shear banding region from the globally stable branch. A simple extension of this analysis to a class of more general constitutive models is also discussed. Numerical simulations for the original DJS model and the reduced TDGL equation is performed to confirm the range of validity of our reduction theory.
Salem-Sugui, S., Jr.; Alvarenga, A. D.; Luo, H.-Q.; Zhang, R.; Gong, D.-L.
2017-01-01
We analysed the flux-flow region of isofield magnetoresistivity data obtained on three crystals of {{BaFe}}2-x Ni x As2 with T c ˜ 20 K for three different geometries relative to the angle formed between the applied magnetic field and the c-axis of the crystals. The field dependent activation energy, U 0, was obtained from the thermal assisted flux-flow (TAFF) and modified vortex-glass models, which were compared with the values of U 0 obtained from flux-creep available in the literature. We observed that the U 0 obtained from the TAFF model show deviations among the different crystals, while the correspondent glass lines obtained from the vortex-glass model are virtually coincident. It is shown that the data is well explained by the modified vortex-glass model, allowing extract of values of T g, the glass transition temperature, and {T}* , a temperature which scales with the mean field critical temperature {T}{{c}}(H). The resulting glass lines obey the anisotropic Ginzburg-Landau theory and are well fitted by a theory developed in the literature by considering the effect of disorder.
Charukhchyan, M. V.; Sedov, E. S.; Arakelian, S. M.; Alodjants, A. P.
2014-06-01
We consider the problem of formation of small-amplitude spatially localized oscillatory structures for atomic Bose-Einstein condensates confined in two- and three-dimensional optical lattices, respectively. Our approach is based on applying the regions with different signs of atomic effective masses where an atomic system exhibits effective hyperbolic dispersion within the first Brillouin zone. By using the kp method we have demonstrated mapping of the initial Gross-Pitaevskii equation on nonlinear Klein-Gordon and/or Ginzburg-Landau-Higgs equations, which is inherent in matter fields within ϕ4-field theories. Formation of breatherlike oscillating localized states—atomic oscillons—as well as kink-shaped states have been predicted in this case. Apart from classical field theories atomic field oscillons occurring in finite lattice structures possess a critical number of particles for their formation. The obtained results pave the way to simulating some analogues of fundamental cosmological processes occurring during our Universe's evolution and to modeling nonlinear hyperbolic metamaterials with condensed matter (atomic) systems.
Dependence of the ferroelectric domain shape on the electric field of the microscope tip
Starkov, Alexander S. [Institute of Refrigeration and Biotechnology, National Research University of Information Technologies, Mechanics and Optics, Kronverksky pr. 49, 197101 St. Petersburg (Russian Federation); Starkov, Ivan A., E-mail: starkov@feec.vutbr.cz [SIX Research Centre, Brno University of Technology, Technická 12, 616 00 Brno (Czech Republic)
2015-08-21
A theory of an equilibrium shape of the domain formed in an electric field of a scanning force microscope (SFM) tip is proposed. We do not assume a priori that the domain has a fixed form. The shape of the domain is defined by the minimum of the free energy of the ferroelectric. This energy includes the energy of the depolarization field, the energy of the domain wall, and the energy of the interaction between the domain and the electric field of the SFM tip. The contributions of the apex and conical part of the tip are examined. Moreover, in the proposed approach, any narrow tip can be considered. The surface energy is determined on the basis of the Ginzburg-Landau-Devonshire theory and takes into account the curvature of the domain wall. The variation of the free energy with respect to the domain shape leads to an integro-differential equation, which must be solved numerically. Model results are illustrated for lithium tantalate ceramics.
双能隙介观超导体的涡旋结构模拟*%Numerical simulation of vortex structure in mesoscopic two-gap superconductor∗
史良马; 张世军; 朱仁义
2013-01-01
本文运用了含时Ginzburg-Landau理论研究了双能带结构的介观超导体在外磁场作用下涡旋随时间的演化。给出了实际温度在s波和d波的临界温度之间s波、d波以及磁场的分布，从理论上模拟得到涡旋进入和退出样品的磁场“过热”与“过冷”现象，以及介观超导样品边界对涡旋结构分布的影响。%In this paper, the evolution of vortex configuration for mesoscopic two-gap superconductor is investigated by the time-dependent Ginzburg-Landau theory in the presence of an externally applied field. The vortex configurations of s-wave and d-wave, and the distribution of magnetic field are given when the temperature is between critical temperatures of s-wave and d-wave. In theory, the over-cold and the over-hot field, and the boundary effect on vortex are simulated when the magnetic flux penetrates the superconductor.
Nonequilibrium Dynamics Of Emergent Field Configurations
Howell, R C
2003-01-01
The processes by which nonlinear physical systems approach thermal equilibrium is of great importance in many areas of science. Central to this is the mechanism by which energy is transferred between the many degrees of freedom comprising these systems. With this in mind, in this research the nonequilibrium dynamics of nonperturbative fluctuations within Ginzburg-Landau models are investigated. In particular, two questions are addressed. In both cases the system is initially prepared in one of two minima of a double-well potential. First, within the context of a (2 + 1) dimensional field theory, we investigate whether emergent spatio-temporal coherent structures play a dynamcal role in the equilibration of the field. We find that the answer is sensitive to the initial temperature of the system. At low initial temperatures, the dynamics are well approximated with a time-dependent mean-field theory. For higher temperatures, the strong nonlinear coupling between the modes in the field does give rise to the synch...
Gauzzi, A.; Pavuna, D. [Department of Physics-IMO, Swiss Federal Institute of Technology at Lausanne (EPFL), CH-1015 Lausanne (Switzerland)
1995-06-01
We report on in-plane paraconductivity measurements in thin YBa{sub 2}Cu{sub 3}O{sub 6.9} films. Our analysis of the data shows that the temperature dependence of paraconductivity is affected by lattice disorder and deviates at all temperatures from the universal power laws predicted by both scaling and mean-field theories. This gives evidence for the absence of critical fluctuations and for the failure of the Aslamazov-Larkin universal relation between critical exponent and dimensionality of the spectrum of Gaussian fluctuations. We account quantitatively for the data within the experimental error by introducing a short-wavelength cutoff into this spectrum. This implies that three-dimensional short-wavelength Gaussian fluctuations dominate in YBa{sub 2}Cu{sub 3}O{sub 6.9} and suggests a rapid attenuation of these fluctuations with decreasing wavelength in short-coherence-length systems as compared to the case of the conventional Ginzburg-Landau theory.
The magnetoresistance of YBCO/BZO composite superconductors
Malik, Bilal A.; Asokan, K.; Ganesan, V.; Singh, Durgesh; Malik, Manzoor A.
2016-12-01
We study the effect of addition of BaZrO3 (BZO) on normal and superconducting state of YBa2Cu3O7-δ (YBCO). We find that in general both room temperature and residual resistivity increase with the addition of BZO except at low concentration of BZO. The temperature dependence of resistivity in presence of magnetic field also shows less resistivity broadening in composites containing low concentration of BZO below transition temperature (TC). The zero temperature upper critical field (Hc2(0)), estimated by using Werthamer, Helfand and Hohenberg theory and Ginzburg Landau theory, shows an increase by the finite addition of BZO in YBCO. Further, the activation energy (U0) determined from Arrhenius plots and vortex glass transition temperature (Tg) also increase with the limited addition of BZO. Such an enhancement in Hc2(0), Uo and Tg has been attributed to the increase in grain connectivity of YBCO . We conclude that the limited addition of BZO in YBCO significantly improves its superconducting performance in magnetic environment.
Hao, Zhihao; Javanparast, Behnam; Enjalran, Matthew; Gingras, Michel
2014-03-01
We study the problem of partially ordered phases with periodically arranged disordered sites on the pyrochlore lattice. The periodicity of the phases is characterized by one or more wave vectors k = {1/21/21/2 } . Starting from a general microscopic Hamiltonian including anisotropic nearest-neighbor exchange, long-range dipolar interactions and second- and third-nearest neighbor exchange, we identify using standard mean-field theory (s-MFT) an extended range of interaction parameters that support partially ordered phases. We demonstrate that thermal fluctuations beyond s-MFT are responsible for the selection of one particular partially ordered phase, e.g. the ``4- k'' phase over the ``1- k'' phase. We suggest that the transition into the 4- k phase is continuous with its critical properties controlled by the cubic fixed point of a Ginzburg-Landau theory with a 4-component vector order-parameter. By combining an extension of the Thouless-Anderson-Palmer method originally used to study fluctuations in spin glasses with parallel-tempering Monte-Carlo simulations, we establish the phase diagram for different types of partially ordered phases. Our result reveals the origin of 4- k phase observed bellow 1K in Gd2Ti2O7. Funded by NSERC of Canada. M. G. acknowledge funding from Canadian Research Chair program (Tier 1).
Javanparast, Behnam; Hao, Zhihao; Enjalran, Matthew; Gingras, Michel J. P.
2015-04-01
We study the problem of partially ordered phases with periodically arranged disordered (paramagnetic) sites on the pyrochlore lattice, a network of corner-sharing tetrahedra. The periodicity of these phases is characterized by one or more wave vectors k ={1/2 1/2 1/2 } . Starting from a general microscopic Hamiltonian including anisotropic nearest-neighbor exchange, long-range dipolar interactions, and second- and third-nearest neighbor exchange, we use standard mean-field theory (SMFT) to identify an extended range of interaction parameters that support partially ordered phases. We demonstrate that thermal fluctuations ignored in SMFT are responsible for the selection of one particular partially ordered phase, e.g., the "4 -k " phase over the "1 -k " phase. We suggest that the transition into the 4 -k phase is continuous with its critical properties controlled by the cubic fixed point of a Ginzburg-Landau theory with a four-component vector order parameter. By combining an extension of the Thouless-Anderson-Palmer method originally used to study fluctuations in spin glasses with parallel-tempering Monte Carlo simulations, we establish the phase diagram for different types of partially ordered phases. Our results elucidate the long-standing puzzle concerning the origin of the 4 -k partially ordered phase observed in the Gd2Ti2O7 dipolar pyrochlore antiferromagnet below its paramagnetic phase transition temperature.
Advanced classical field theory
Giachetta, Giovanni; Sardanashvily, Gennadi
2009-01-01
Contemporary quantum field theory is mainly developed as quantization of classical fields. Therefore, classical field theory and its BRST extension is the necessary step towards quantum field theory. This book aims to provide a complete mathematical foundation of Lagrangian classical field theory and its BRST extension for the purpose of quantization. Based on the standard geometric formulation of theory of nonlinear differential operators, Lagrangian field theory is treated in a very general setting. Reducible degenerate Lagrangian theories of even and odd fields on an arbitrary smooth manifold are considered. The second Noether theorems generalized to these theories and formulated in the homology terms provide the strict mathematical formulation of BRST extended classical field theory
Fabris, J C
2015-01-01
General Relativity is the modern theory of gravitation. It has replaced the newtonian theory in the description of the gravitational phenomena. In spite of the remarkable success of the General Relativity Theory, the newtonian gravitational theory is still largely employed, since General Relativity, in most of the cases, just makes very small corrections to the newtonian predictions. Moreover, the newtonian theory is much simpler, technically and conceptually, when compared to the relativistic theory. In this text, we discuss the possibility of extending the traditional newtonian theory in order to incorporate typical relativistic effects, but keeping the simplicity of the newtonian framework. We denominate these extensions neo-newtonian theories. These theories are discussed mainly in the contexts of cosmology and compact astrophysical objects.
Separation-individuation theory and attachment theory.
Blum, Harold P
2004-01-01
Separation-individuation and attachment theories are compared and assessed in the context of psychoanalytic developmental theory and their application to clinical work. As introduced by Margaret Mahler and John Bowlby, respectively, both theories were initially regarded as diverging from traditional views. Separation-individuation theory, though it has had to be corrected in important respects, and attachment theory, despite certain limitations, have nonetheless enriched psychoanalytic thought. Without attachment an infant would die, and with severely insecure attachment is at greater risk for serious disorders. Development depends on continued attachment to a responsive and responsible caregiver. Continued attachment to the primary object was regarded by Mahler as as intrinsic to the process of separation-individuation. Attachment theory does not account for the essential development of separateness, and separation-individuation is important for the promotion of autonomy, independence, and identity. Salient historical and theoretical issues are addressed, including the renewed interest in attachment theory and the related decline of interest in separation-individuation theory.
Rotor theories by Professor Joukowsky: Momentum theories
van Kuik, G. A. M.; Sørensen, Jens Nørkær; Okulov, V. L.
2015-01-01
This paper is the first of two papers on the history of rotor aerodynamics with special emphasis on the role of Joukowsky. The present one focuses on the development of the momentum theory while the second one surveys the development of vortex theory for rotors. Joukowsky has played a major role ...
Generalizability theory and item response theory
Glas, Cornelis A.W.; Eggen, T.J.H.M.; Veldkamp, B.P.
2012-01-01
Item response theory is usually applied to items with a selected-response format, such as multiple choice items, whereas generalizability theory is usually applied to constructed-response tasks assessed by raters. However, in many situations, raters may use rating scales consisting of items with a
Generalizability theory and item response theory
Glas, C.A.W.; Eggen, T.J.H.M.; Veldkamp, B.P.
2012-01-01
Item response theory is usually applied to items with a selected-response format, such as multiple choice items, whereas generalizability theory is usually applied to constructed-response tasks assessed by raters. However, in many situations, raters may use rating scales consisting of items with a s
Generalizability Theory and Classical Test Theory
Brennan, Robert L.
2011-01-01
Broadly conceived, reliability involves quantifying the consistencies and inconsistencies in observed scores. Generalizability theory, or G theory, is particularly well suited to addressing such matters in that it enables an investigator to quantify and distinguish the sources of inconsistencies in observed scores that arise, or could arise, over…
Vivian B. Martin, Ph.D.
2005-03-01
Full Text Available Bookshelf will provide critical reviews and perspectives on books on theory and methodology of interest to grounded theory. This issue includes a review of Heaton’s Reworking Qualitative Data, of special interest for some of its references to grounded theory as a secondary analysis tool; and Goulding’s Grounded Theory: A practical guide for management, business, and market researchers, a book that attempts to explicate the method and presents a grounded theory study that falls a little short of the mark of a fully elaborated theory.Reworking Qualitative Data, Janet Heaton (Sage, 2004. Paperback, 176 pages, $29.95. Hardcover also available.
Lurie, Jacob
2009-01-01
Higher category theory is generally regarded as technical and forbidding, but part of it is considerably more tractable: the theory of infinity-categories, higher categories in which all higher morphisms are assumed to be invertible. In Higher Topos Theory, Jacob Lurie presents the foundations of this theory, using the language of weak Kan complexes introduced by Boardman and Vogt, and shows how existing theorems in algebraic topology can be reformulated and generalized in the theory's new language. The result is a powerful theory with applications in many areas of mathematics. The book's firs
Marciano, W.J.
1984-12-01
The present state of the art in elementary particle theory is reviewed. Topics include quantum electrodynamics, weak interactions, electroweak unification, quantum chromodynamics, and grand unified theories. 113 references. (WHK)
Molder, te H.F.M.
2009-01-01
Available in both print and electronic formats, the Encyclopedia of Communication Theory provides students and researchers with a comprehensive two-volume overview of contemporary communication theory. Reference librarians report that students frequently approach them seeking a source that will
Economic theories of dictatorship
2010-01-01
This article reviews recent advances in economic theories of dictatorships and their lessons for the political stability and economic performance of dictatorships. It reflects on the general usefulness of economic theories of dictatorship, with an application to foreign relations.
Clemmensen, Torkil; Kaptelinin, Victor; Nardi, Bonnie
2016-01-01
This paper reports a study of the use of activity theory in human–computer interaction (HCI) research. We analyse activity theory in HCI since its first appearance about 25 years ago. Through an analysis and meta-synthesis of 109 selected HCI activity theory papers, we created a taxonomy of 5...... different ways of using activity theory: (1) analysing unique features, principles, and problematic aspects of the theory; (2) identifying domain-specific requirements for new theoretical tools; (3) developing new conceptual accounts of issues in the field of HCI; (4) guiding and supporting empirical...... analyses of HCI phenomena; and (5) providing new design illustrations, claims, and guidelines. We conclude that HCI researchers are not only users of imported theory, but also theory-makers who adapt and develop theory for different purposes....
Liu Baoding [Tsinghua Univ., Beijing (China). Uncertainty Theory Lab.
2007-07-01
Uncertainty theory is a branch of mathematics based on normality, monotonicity, self-duality, and countable subadditivity axioms. The goal of uncertainty theory is to study the behavior of uncertain phenomena such as fuzziness and randomness. The main topics include probability theory, credibility theory, and chance theory. For this new edition the entire text has been totally rewritten. More importantly, the chapters on chance theory and uncertainty theory are completely new. This book provides a self-contained, comprehensive and up-to-date presentation of uncertainty theory. The purpose is to equip the readers with an axiomatic approach to deal with uncertainty. Mathematicians, researchers, engineers, designers, and students in the field of mathematics, information science, operations research, industrial engineering, computer science, artificial intelligence, and management science will find this work a stimulating and useful reference. (orig.)
Rothbart, Andrea
2012-01-01
An imaginative introduction to number theory and abstract algebra, this unique approach employs a pair of fictional characters whose dialogues explain theories and demonstrate applications in terms of football scoring, chess moves, and more.
[Mathematics and string theory
Jaffe, A.; Yau, Shing-Tung.
1993-01-01
Work on this grant was centered on connections between non- commutative geometry and physics. Topics covered included: cyclic cohomology, non-commutative manifolds, index theory, reflection positivity, space quantization, quantum groups, number theory, etc.
Henneaux, Marc; Vasiliev, Mikhail A
2017-01-01
Symmetries play a fundamental role in physics. Non-Abelian gauge symmetries are the symmetries behind theories for massless spin-1 particles, while the reparametrization symmetry is behind Einstein's gravity theory for massless spin-2 particles. In supersymmetric theories these particles can be connected also to massless fermionic particles. Does Nature stop at spin-2 or can there also be massless higher spin theories. In the past strong indications have been given that such theories do not exist. However, in recent times ways to evade those constraints have been found and higher spin gauge theories have been constructed. With the advent of the AdS/CFT duality correspondence even stronger indications have been given that higher spin gauge theories play an important role in fundamental physics. All these issues were discussed at an international workshop in Singapore in November 2015 where the leading scientists in the field participated. This volume presents an up-to-date, detailed overview of the theories i...
Exact exponent λ of the autocorrelation function for a soluble model of coarsening
Bray, A. J.; Derrida, B.
1995-03-01
The exponent λ that describes the decay of the autocorrelation function A(t) in a phase ordering system, A(t)~L-(d-λ), where d is the dimension and L the characteristic length scale at time t, is calculated exactly for the time-dependent Ginzburg-Landau equation in d=1. We find λ=0.3993835.... We also show explicitly that a small bias of positive domains over negative gives a magnetization which grows in time as M(t)~Lμ and prove that for the one-dimensional Ginzburg-Landau equation, μ=λ, exemplifying a general result.
Noncommutative Gauge Theories: Model for Hodge theory
Upadhyay, Sudhaker
2013-01-01
The nilpotent BRST, anti-BRST, dual-BRST and anti-dual-BRST symmetry transformations are constructed in the context of noncommutative (NC) 1-form as well as 2-form gauge theories. The corresponding Noether's charges for these symmetries on the Moyal plane are shown to satisfy the same algebra as by the de Rham cohomological operators of differential geometry. The Hodge decomposition theorem on compact manifold is also studied. We show that noncommutative gauge theories are field theoretic models for Hodge theory.
Linker, Patrick
2016-01-01
A couple of quantum gravity theories were proposed to make theoretical predictions about the behavior of gravity. The most recent approach to quantum gravity, called E-theory, is proposed mathematical, but there is not formulated much about what dynamics of gravity this theory proposes. This research paper treats the main results of the application of E-theory to General relativity involving conservation laws and scattering of particles in presence of gravity. Also the low-energy limit of thi...
Information theory and Thermodynamics
Kafri, Oded
2006-01-01
A communication theory for a transmitter broadcasting to many receivers is presented. In this case energetic considerations cannot be neglected as in Shannon theory. It is shown that, when energy is assigned to the information bit, information theory complies with classical thermodynamic and is part of it. To provide a thermodynamic theory of communication it is necessary to define equilibrium for informatics systems that are not in thermal equilibrium and to calculate temperature, heat, and ...
Quantum algorithmic information theory
Svozil, Karl
1995-01-01
The agenda of quantum algorithmic information theory, ordered `top-down,' is the quantum halting amplitude, followed by the quantum algorithmic information content, which in turn requires the theory of quantum computation. The fundamental atoms processed by quantum computation are the quantum bits which are dealt with in quantum information theory. The theory of quantum computation will be based upon a model of universal quantum computer whose elementary unit is a two-port interferometer capa...
Algorithmic information theory
Grünwald, P.D.; Vitányi, P.M.B.; Adriaans, P.; van Benthem, J.
2008-01-01
We introduce algorithmic information theory, also known as the theory of Kolmogorov complexity. We explain the main concepts of this quantitative approach to defining 'information'. We discuss the extent to which Kolmogorov's and Shannon's information theory have a common purpose, and where they are fundamentally different. We indicate how recent developments within the theory allow one to formally distinguish between 'structural' (meaningful) and 'random' information as measured by the Kolmo...
Algorithmic information theory
Grünwald, P.D.; Vitányi, P.M.B.
2008-01-01
We introduce algorithmic information theory, also known as the theory of Kolmogorov complexity. We explain the main concepts of this quantitative approach to defining `information'. We discuss the extent to which Kolmogorov's and Shannon's information theory have a common purpose, and where they are fundamentally different. We indicate how recent developments within the theory allow one to formally distinguish between `structural' (meaningful) and `random' information as measured by the Kolmo...
Philosophical theories of probability
Gillies, Donald
2000-01-01
The Twentieth Century has seen a dramatic rise in the use of probability and statistics in almost all fields of research. This has stimulated many new philosophical ideas on probability. Philosophical Theories of Probability is the first book to present a clear, comprehensive and systematic account of these various theories and to explain how they relate to one another. Gillies also offers a distinctive version of the propensity theory of probability, and the intersubjective interpretation, which develops the subjective theory.
Matsumoto, Kohji
2002-01-01
The book includes several survey articles on prime numbers, divisor problems, and Diophantine equations, as well as research papers on various aspects of analytic number theory such as additive problems, Diophantine approximations and the theory of zeta and L-function Audience Researchers and graduate students interested in recent development of number theory
Iachello, F
1995-01-01
1. The Wave Mechanics of Diatomic Molecules. 2. Summary of Elements of Algebraic Theory. 3. Mechanics of Molecules. 4. Three-Body Algebraic Theory. 5. Four-Body Algebraic Theory. 6. Classical Limit and Coordinate Representation. 8. Prologue to the Future. Appendices. Properties of Lie Algebras; Coupling of Algebras; Hamiltonian Parameters
Vazzana, Anthony; Garth, David
2007-01-01
One of the oldest branches of mathematics, number theory is a vast field devoted to studying the properties of whole numbers. Offering a flexible format for a one- or two-semester course, Introduction to Number Theory uses worked examples, numerous exercises, and two popular software packages to describe a diverse array of number theory topics.
Pais, Alexandre; Valero, Paola
2014-01-01
What is the place of social theory in mathematics education research, and what is it for? This special issue of "Educational Studies in Mathematics" offers insights on what could be the role of some sociological theories in a field that has historically privileged learning theories coming from psychology and mathematics as the main…
Building theory through design
Markussen, Thomas
2017-01-01
This chapter deals with a fundamental matter of concern in research through design: how can design work lead to the building of new theory? Controversy exists about the balance between theory and design work in research through design. While some researchers see theory production as the scientific...
Davis, Philip W.
This volume explores objectively the essential characteristic of nine twentieth-century linguistic theories with the theoretical variant for discussion based on one closely representative of work within a given approach or usually associated with the name of the theory. First, the theory of Ferdinand de Saussure is discussed based on his book,…
Peim, Nick
2009-01-01
This paper seeks to re-examine Yrio Engestrom's activity theory as a technology of knowledge designed to enable positive transformations of specific practices. The paper focuses on a key paper where Engestrom defines the nature and present state of activity theory. Beginning with a brief account of the relations between activity theory and…