time dependent ginzburg landau equations of superconductivity abstract we study in this article the existence uniqueness and long time behavior of the solutions of a nonstationary ginzburg landau superconductivity model we first prove the existence and uniqueness of solutions with h 1 initial data which are crucial for the study of the global attractor we also obtain for the first time the existence of global weak solutions of the model with l 2 initial data it is then proved that the ginzburg landau system admits a global attractor which represents exactly all the long time dynamics of the system the global attractor obtained consists of exactly the set of steady state solutions and its unstable manifold its hausdorff and fractal dimensions are estimated in terms of the physically relevant ginzburg landau parameter diffusion parameter and applied magnetic field we construct explicitly absorbing sets for some abstract semigroups having a lyapunov functional and consequently prove the existence of global attractors this abstract result is applied to the ginzburg landau system for which the existence of global attractor does not seem to be the direct consequence of some a priori estimates of solutions

numerical studies of discrete approximations to the allen cahn equation in the sharp interface limit the numerical approximations to the allen cahn type diffuse interface models are studied with a particular focus on their performance in the sharp interface limit and the effectiveness of high order discretization schemes different spatial discretizations of an energy functional in the diffuse interface framework are compared first discretizations of the time dependent equation using various different time stepping schemes and an adaptive finite element spatial approximations are then analyzed assessments of the numerical accuracy in different parameter regimes are carried out the analysis and computational findings provide insight on the effectiveness of the discretization schemes and offer guidance to parameter choices when numerical simulations are conducted within the diffuse interface framework

quasilinear elliptic system arising in a three dimensional type ii superconductor for infinite κ abstract we study a quasilinear elliptic system arising in a three dimensional superconductor this model is formally derived from the ginzburg landau energy at for a meissner solution if the tangential trace of the magnetic field h is given on we prove the existence of a unique solution for small data and nonexistence for large data on the other hand we prove that the current j curl h is such that j 2 is maximum on the boundary

approximations of a ginzburg landau model for superconducting hollow spheres based on spherical centroidal voronoi tessellations in this paper the numerical approximations of the ginzburg landau model for a superconducting hollow spheres are constructed using a gauge invariant discretization on spherical centroidal voronoi tessellations a reduced model equation is used on the surface of the sphere which is valid in the thin spherical shell limit we present the numerical algorithms and their theoretical convergence as well as interesting numerical results on the vortex configurations properties of the spherical centroidal voronoi tessellations are also utilized to provide a high resolution scheme for computing the supercurrent and the induced magnetic field

symmetric vortices for the ginzberg landau equations of superconductivity and the nonlinear desingularization phenomenon abstract the existence of countably many distinct symmetric vortices for the nonlinear ginzberg landau equations of superconductivity with an arbitrary positive parameter is proven we then prove the existence of a linearization phenomenon as the parameter in this case the linearized equations contain an appropriate dirac delta function these equations are known as the london equations

convergence analysis of a numerical method for a mean field model of superconducting vortices in the mean field models of superconductivity the individual vortex like structures occurring in practical type ii superconductors are averaged and a vortex density is solved for them the numerical solution of the mean field models makes large scale simulations of vortex phenomena possible in this paper we present a simple convergence analysis for a numerical method based on hybrid finite element finite volume finite difference approximations in the two dimensional case by providing various different interpretations to the discretization scheme

on decomposition numbers of the cyclotomic q schur algebras abstract let s be the cyclotomic q schur algebra associated to the ariki koike algebra h we construct a certain subalgebra s 0 of s and show that it is a standardly based algebra in the sense of du and rui s 0 has a natural quotient s 0 which turns out to be a cellular algebra in the case where the modified ariki koike algebra h is defined s 0 coincides with the cyclotomic q schur algebra associated to h in this paper we discuss a relationship among the decomposition numbers of s s 0 and s 0 in particular we show that some important part of the decomposition matrix of s coincides with a part of the decomposition matrix of s 0

superconductivity near the normal state in a half plane under the action of a perpendicular electric current and an induced magnetic field we consider the linearization of the time dependent ginzburg landau system near the normal state we assume that a constant magnetic field and an electric current are applied through the sample which captures half of the plane inducing thereby a linearly varying magnetic field in the limit of small normal conductivity we prove that if the electric current is lower than some critical value the normal state loses its stability for currents stronger than this critical value the normal state is stable to obtain this stability result we analyze both the spectrum and the pseudo spectrum of the linearized operator the critical current tends in this small conductivity limit to another critical current which had been obtained for a reduced model which neglects magnetic field effects

on double centralizer properties between quantum groups and ariki koike algebras abstract in this paper the double centralizer properties for tensor spaces as bimodules over quantum groups and ariki koike algebras as well as their relations with shoji s algebra h h see j algebra 226 2000 818 856 are studied we proved that under the separation condition see j reine angew math 513 1999 53 69 the natural homomorphism from the ariki koike algebra to the endomorphism algebra of tensor space as module over quantum group is surjective we also show that the natural homomorphism from shoji s algebra h h to that endomorphism algebra is always surjective and h h is actually isomorphic to a direct sum of some matrix algebras over some hecke algebras of type a

spectral methods for nonlinear parabolic systems many physical problems are naturally formulated as nonlinear parabolic systems of partial differential equations in periodic geometry in this paper a simple efficient spectrally accurate numerical method for these problems is described and implemented the method combines stiff extrapolation with fast solvers for elliptic systems theory and numerical results show that the method solves even difficult problems including phase field models and mean curvature flows

stability and convergence of finite element approximation schemes for harmonic maps this article discusses stability and convergence of approximation schemes for harmonic maps a finite element discretization of an iterative algorithm due to f alouges is introduced and shown to be stable and convergent in general only on acute type triangulations an break a posteriori criterion is proposed which allows us to monitor sufficient conditions for weak convergence to a harmonic map on general triangulations and for adaptive mesh refinement numerical break experiments show that an adaptive strategy automatically refines triangulations in neighborhoods of typical point singularities and thereby underline its efficiency

product formulas for the cyclotomic v schur algebra and for the canonical bases of the fock space abstract let f q s be the q deformed fock space of level l with multi charge s s 1 s l uglov defined canonical bases g s of f q s for l partitions and the polynomials q z q are defined as the coefficients of the transition matrix between the canonical bases and the standard basis of f q s in this paper we prove a product formula for q for certain l partitions which expresses q as a product of such polynomials related to various smaller fock spaces f q s i yvonne conjectures that q are related to the q decomposition numbers d q of the cyclotomic v schur algebra s where the parameters v q 1 q l are roots of unity in c determined from s in our earlier work we have proved a product formula for d q of s and the product formula for q is regarded as a counter part of that formula for the case of the fock space

nucleation of instability of the meissner state of 3 dimensional superconductors this paper concerns a nonlinear partial differential system in a 3 dimensional domain involving the operator curl2 which is a simplified model used to examine nucleation of instability of the meissner state of a superconductor as the applied magnetic field reaches the superheating field we derive a priori c 2 estimates for a weak solution h the curl of the magnetic potential and determine the location of the maximal points of curlh which correspond to the nucleation of instability of the meissner state we show that if the penetration length is small the solution exhibits a boundary layer if the applied magnetic field is homogeneous curlh is maximal around the points on the boundary where the applied field is tangential to the surface

adaptive galerkin methods with error control for a dynamical ginzburg landau model in superconductivity the time dependent ginzburg landau model which describes the phase transitions taking place in superconductors is a coupled system of nonlinear parabolic equations it is discretized semi implicitly in time and in space via continuous piecewise linear finite elements a posteriori error estimates are derived for the l infty l 2 norm by studying a dual problem of the linearization of the original system other than the dual of error equations numerical simulations are included which illustrate the reliability of the estimators and the flexibility of the proposed adaptive method

slim cyclotomic q schur algebras abstract we construct a new basis for a slim cyclotomic q schur algebra s m n r via symmetric polynomials in jucys murphy operators of the cyclotomic hecke algebra h m r we show that this basis labelled by matrices is not the double coset basis when h m r is the hecke algebra of a coxeter group but coincides with the double coset basis for the corresponding group algebra the hecke algebra at q 1 as further applications we then discuss the cyclotomic schur weyl duality at the integral level this also includes a category equivalence and a classification of simple objects

vortex filaments pinning for inhomogeneous ginzburg landau equations abstract in this paper the structure of vortices of the ginzburg landau system with impurity in higher dimensions was studied this functional has been proposed as a model for vortex pinning we show that vortices are localized near the set of minimum of impurity this is the pinning phenomenon predicted in the physics literature it was also proven that the limiting vortices is n 2 dimensional rectifiable set

blocks of affine quantum schur algebras abstract the affine quantum schur algebra is a certain important infinite dimensional algebra whose representation theory is closely related to that of quantum affine gl n finite dimensional irreducible modules for the affine quantum schur algebra s n r v were classified in 15 where v c is not a root of unity we will classify blocks of the affine quantum schur algebra s n r v in this paper

modified ariki koike algebras and cyclotomic q schur algebras the modified ariki koike algebra open image in new window is a variation of the original ariki koike algebra open image in new window over an integral domain r when r is a rational function field over the independent parameters open image in new window but for general r open image in new window is not isomorphic to open image in new window and has a simpler structure than open image in new window in this paper we construct a cellular basis of open image in new window which has a similar property as the cellular basis of open image in new window introduced by dipper james mathas by comparing these two cellular bases we obtain some estimate on the decomposition numbers of open image in new window in terms of the decomposition numbers of open image in new window we also prove the integral form of the schur weyl reciprocity between a certain quantum algebra u q and open image in new window on the tensor space open image in new window

schur weyl reciprocity between quantum groups and hecke algebras of type g p p n abstract let u q gl m p be the quantized universal enveloping algebra of gl m p let be the automorphism of u q gl m p which is defined on generators by e i e i m f i f i m k j k j m for any i z p m z 0 m p 1 m and any j z p m z let h p p n be the hecke algebra of type g p p n with parameters q e where e is a primitive pth root of unity in this paper we establish a schur weyl reciprocity between h p p n and a twisted tensor product of u q gl m p and the group algebra for a cyclic group of order p by using the results in j hu j algebra 274 2004 446 490

numerical methods for simulating ginzburg landau vortices numerical solution to the ginzburg landau gl equation becomes infeasible as the gl parameter kappa and the number of gl vortices increase to a physically interesting regime it is in this regime that we focus our attention to design a simulated annealing approach for minimizing the associated renormalized energy to study the gl vortex configurations this approach applied to a commonly used model produces vortex configurations which are of interest in recent studies

on the action of ariki koike algebras on tensor space the action of the ariki koike algebra on tensor space is used to show an isomorphism theorem between the ariki koike algebra and a direct sum of matrix rings over tensorproducts of smaller ariki koike algebras as an application we get schur weyl duality for the action of the ariki koike algebra and the levi subalgebra of the q schur algebra when separation conditions holds mit hilfe der operation der ariki koike algebra auf dem tensorraum wird ein isomorphismus zwischen der ariki koike algebra und einer direkten summe von matrizenringen uber tensorprodukten kleinerer ariki koike algebren gezeigt als anwendung ergibt sich das die ariki koike algebra und die leviunteralgebra der q schur algebra schur weyl dualitat erfullen falls die separationsbedingung erfullt ist

numerical solution of the three dimensional ginzburg landau models using artificial boundary for three dimensional simulations of the vortex phenomena in superconductors based on the ginzburg landau gl theory the physical variables must be solved in the whole space in general exact boundary conditions on an artificial boundary are discussed to reformulate the problem in a finite domain approximations of these boundary conditions with high accuracy are given and their convergence properties are examined error estimates are derived for the finite element approximations with the approximate boundary conditions

schur weyl reciprocity for ariki koike algebras let g glm1 glmr be a levi subalgebra of glm with m ri 1mi and v the natural representation of the quantum group uq g we construct a representation of the ariki koike algebra hn r on the n fold tensor space of v commuting with the action of uq g and prove the schur weyl reciprocity for the actions of uq g and hn r on it

yang baxter bases of 0 hecke algebras and representation theory of 0 ariki koike shoji algebras after reformulating the representation theory of 0 hecke algebras in an appropriate family of yang baxter bases we investigate certain specializations of the ariki koike algebras obtained by setting q 0 in a suitably normalized version of shoji s presentation we classify the simple and projective modules and describe restrictions induction products cartan invariants and decomposition matrices this allows us to identify the grothendieck rings of the towers of algebras in terms of certain graded hopf algebras known as the mantaci reutenauer descent algebras and poirier quasi symmetric functions we also describe the ext quivers and conclude with numerical tables

analysis and approximation of the ginzburg landau model of superconductivity the authors consider the ginzburg landau model for superconductivity first some well known features of superconducting materials are reviewed and then various results concerning the model the resultant differential equations and their solution on bounded domains are derived then finite element approximations of the solutions of the ginzburg landau equations are considered and error estimates of optimal order are derived

asymptotic stability for tracking control of nonlinear uncertain dynamical systems described by differential inclusions in this paper we will study the tracking control problem for nonlinear uncertain dynamical systems two generalized feedback control inputs have been proposed such that the feedback controlled systems satisfy the complete tracking control property with exponential asymptotic stability and the trajectories of the systems are steered to the pre specified observation map with an exponential convergence rate moreover an estimate of the tracking time of the trajectories attaining the observation map has also been given an example inspired from a guided missile problem illustrates the use of our main results

a model for superconducting thin films having variable thickness abstract a two dimensional macroscopic model for superconductivity in thin films having variable thickness is derived through an averaging process across the film thickness the resulting model is similar to the well known ginzburg landau equations for homogeneous isotropic materials except that a function that describes the variations in the thickness of the film now appears in the coefficients of the differential equations some results about solutions of the variable thickness model are then given including existence of solutions and boundedness of the order parameter it is also shown that the model is consistent in the sense that solutions obtained from the new model are an appropriate limit of a sequence of averages of solutions of the three dimensional ginzburg landau model as the thickness of the film tends to zero an application of the variable thickness thin film model to flux pinning is then provided in particular the results of numerical calculations are given that show that the vortex like structures that are present in certain superconductors are attracted re relatively thin regions in a material sample finally extensions of the model to other settings are discussed

sweeping algorithms for inverting the discrete ginzburg landau operator the ginzburg landau equations we study arise in the modeling of superconductivity one widely used method of discretizing the equations together with the associated periodic boundary conditions in the case of a rectangle of dimension 2 leads to a five point stencil solving the system means inverting a sparse matrix of dimension n 2 where n is the number of grid points on each side of the rectangle we propose a method that is similar to the shooting technique in the numerical solution of ordinary differential equations for small n the method requires inverting a full matrix of dimension 2n when n is large an iterative procedure combining partial sweeping and the technique of divide and conquer domain decomposition is appropriate

on the transition to the normal phase for superconductors surrounded by normal conductors abstract for a cylindrical superconductor surrounded by a normal material we discuss transition to the normal phase of stable locally stable and critical configurations associated with those phase transitions we define critical magnetic fields and we provide a sufficient condition for which those critical fields coincide in particular when the conductivity ratio of the superconducting and the normal material is large we show that the aforementioned critical magnetic fields coincide thereby proving that the transition to the normal phase is sharp one key ingredient in the paper is the analysis of an elliptic boundary value problem involving transmission boundary conditions another key ingredient involves a monotonicity result with respect to the magnetic field strength of the first eigenvalue of a magnetic schrodinger operator with discontinuous coefficients

implicit integration of the time dependent ginzburg landau equations of superconductivity this article is concerned with the integration of the time dependent ginzburg landau tdgl equations of superconductivity four algorithms ranging from fully explicit to nonlinearly implicit are presented and evaluated for stability accuracy and compute time the benchmark problem for the evaluation is the equilibration of a vortex configuration in a superconductor that is embedded in a thin insulator and subject to an applied magnetic field

feedback controlled differential inclusions and stabilization of uncertain dynamical systems deterministic design of stabilizing feedback controls for a class of uncertain dynamical systems is considered adopting a problem formulation based on differential inclusions to encompass all possible realizations of uncertainty the authors describe a class of generalized feedback controls with practical analogues in the form of discontinuous feedbacks that guarantees global uniform ultimate boundedness moreover under a matched uncertainty hypothesis this class of controls guarantees global uniform asymptotic stability of the zero state and ultimate attainment of prescribed model behaviour

finite element methods for the time dependent ginzburg landau model of superconductivity abstract the initial boundary value problem for the time dependent ginzburg landau equations that model the macroscopic behavior of superconductors is considered the convergence of finite dimensional semidiscrete galerkin approximations is studied as is a fully discrete scheme the results of some computational experiments are presented

on the discretization error of parametrized nonlinear equations many applications lead to nonlinear parameter dependent equations h y t y 0 where h y times t to y y 0 in operatorname rge h and the state space y is infinite dimensional while the parameter space t has finite dimension the case dim t 1 is of special interest in connection with continuation methods for this case a general theory is developed which provides for the existence of solution paths of a rather general class of such equations and of their finite dimensional approximations and which allows for an assessment of the error between these paths a principal tool in this analysis is the theory of nonlinear fredholm operators the results cover a more general class of operators than the mildly nonlinear mappings to which other approaches appear to be restricted

stability radius optimization a geometric approach abstract the subject of this paper is a geometric approach to the robustness optimization problem for uncertain finite dimensional linear systems for the structurally perturbed stabilizable pair a b we show that optimally robust feedback stabilization is possible via the class of feedbacks parameterizing a b feedback invariant subspaces of codimension rk b a direct consequence of this geometric approach is a reduction in dimension of the optimization problem

homotopy classification of minimizers of the ginzburg landau energy and the existence of permanent currents our objective is to explain the phenomenon of permanent currents within the context of the ginzburg landau model for superconductors using variational techniques we make a connection between the formation of permanent currents and the topology of the superconducting sample

a frobenius formula for the characters of ariki koike algebras abstract let h n r be the ariki koike algebra associated to the complex reflection group wn r g r 1 n in this paper we give a new presentation of h n r by making use of the schur weyl reciprocity for h n r established by m sakamoto and t shoji 1999 j algebra 221 293 314 this allows us to construct various non parabolic subalgebras of h n r we construct all the irreducible representations of h n r as induced modules from such subalgebras we show the existence of a partition of unity in h n r which is specialized to a partition of unity in the group algebra c wn r then we prove a frobenius formula for the characters of h n r which is an analogy of the frobenius formula proved by a ram 1991 invent math 106 461 488 for the iwahori hecke algebra of type a

integral affine schur weyl reciprocity abstract let d n be the double ringel hall algebra of the cyclic quiver n and let d n be the modified quantum affine algebra of d n we will construct an integral form d n z for d n such that the natural algebra homomorphism from d n z to the integral affine quantum schur algebra is surjective furthermore we will use hall algebras to construct the integral form u z g l n of the universal enveloping algebra u g l n of the loop algebra g l n g l n q q t t 1 and prove that the natural algebra homomorphism from u z g l n to the affine schur algebra over z is surjective in a subsequent paper fu 10 we will use affine schur algebras to give blm realization of u z g l n and this enables us to give a new proof of the statements about u z g l n given in this paper

bifurcation analysis for phase transitions in superconducting rings with nonuniform thickness we perform an analytic study of the problem of transitions between normal and superconducting phases for a sample which encloses a magnetic flux as in the classic little parks experiment for a sample of uniform thickness the order parameter is uniform but even infinitesimal deviations from uniform thickness give rise to a mixed state which avoids enclosing the magnetic field the stability domain of this mixed state is a line segment in the magnetic field temperature plane delimited by two critical points the phase diagram contains several bifurcation lines which are systematically analyzed

spinor ginzburg landau equation and mean curvature flow abstract recent papers in the physics literature have introduced spin coupled or spinor ginzburg landau models for complex vector valued order parameters in order to account for ferromagnetic or antiferromagnetic effects in high temperature superconductors in this paper we study the asymptotic behavior of solutions of the evolutionary spinor ginzburg landau equation in three dimensions we prove also that asymptotically the singularities evolve according to mean curvature flow in the sense of weak formulation

numerical approximations of the ginzburg landau models for superconductivity in this paper we review various methods for the numerical approximations of the ginzburg landau models of superconductivity particular attention is given to the different treatment of gauge invariance in both the finite element finite difference and finite volume settings representative theoretical results typical numerical simulations and computational challenges are presented generalizations to other relevant models are also discussed

output feedback control of uncertain coupled systems the stabilization of uncertain dynamical systems on n that admit a decomposition into two coupled subsystems of dimension nc and nr respectively is studied we refer to the nc dimensional sybsystem as the reduced order system and to the nr dimensional subsystem as the residual system the overall n dimensional system is termed the full system the prototype for which is a mechanical model arising in the study of the active control of structures each subsystem is modelled by a differential equation with a linear nominal part and a nonlinear perturbation of a specified class the output available for feedback purposes is an nc valued linear combination of the state components of the full system and is subject to bounded measurement noise with known bound an output feedback strategy is described and sufficient conditions are obtained for the existence of a calculable global uniform compact attractor containing the state origin for controlled systems of this class

mixed finite element methods for a dynamical ginzburg landau model in superconductivity in this paper we consider the numerical solutions of the nonlinear time dependent ginzburg landau model which describes the phase transitions taking place in superconducting films we propose a semi implicit finite element scheme which is based on a linear finite element approximation of the order parameter psi and a mixed finite element discretization for the equation involving the magnetic potential a the error estimates of the scheme are derived

sobolev gradients and the ginzburg landau functional we describe a sobolev gradient method for finding minima of the ginzburg landau functional for superconductivity this method leads to a particularly simple algorithm which avoids consideration of the nonlinear boundary conditions associated with the ginzburg landau equations

finite dimensional approximation of nonlinear problems in the first two papers of this series 4 5 we have studied a general method of approximation of nonsingular solutions and simple limit points of nonlinear equations in a banach space we derive here general approximation results of the branches of solutions in the neighborhood of a simple bifurcation point the abstract theory is applied to the galerkin approximation of nonlinear variational problems and to a mixed finite element approximation of the von karman equations

finite element approximation of a periodic ginzburg landau model for type ii superconductors we consider efficient finite element algorithms for the computational simulation of type ii superconductors the algorithms are based on discretizations of a periodic ginzburg landau model periodicity is defined with respect to a non orthogonal lattice that is not necessarily aligned with the coordinate axes also the primary dependent variables employed in the model satisfy non standard quasi periodic boundary conditions after introducing the model we define finite element schemes derive error estimates of optimal order and present the results of some numerical calculations for a similar quality of simulation the resulting algorithms seem to be significantly less costly than are previously used numerical approximation methods

on tensor spaces over hecke algebras of type bn abstract let w b n be the weyl group of type b n and h b n be the associated iwahori hecke algebra in this paper we study the n tensor space v n where dim v 2 m with natural actions introduced in r m green hyperoctahedral schur algebras j algebra 192 1997 418 438 of w b n and of h b n for each composition 1 m of n let e be the corresponding initial basis element of v n see 3 8 for definition we show that if d is a distinguished right coset representative of s in w b n then the action of the natural basis element t d on e coincides with the permutation action of d up to a scalar as an application we prove that the n tensor space decomposes at the integral level into a direct sum of some permutation modules over hecke algebra h b n with respect to certain standard parabolic subalgebras

minimization of the ginzburg landau energy functional by a sobolev gradient trust region method we describe a generalized levenberg marquardt method for computing critical points of the ginzburg landau energy functional which models superconductivity the algorithm is a blend of a newton iteration with a sobolev gradient descent method and is equivalent to a trust region method in which the trust region radius is defined by a sobolev metric numerical test results demonstrate the method to be remarkably effective

radial solutions for the ginzburg landau equation with applied magnetic field abstract the purpose of this work is a systematic study of symmetric vortices for the ginzburg landau model of superconductivity along a cylinder with applied magnetic field parallel to its axis the ginzburg landau constant of the material and the degree d of the vortex are fixed for any given parameters r the radius of the cylinder and h the intensity of the applied magnetic field one can find a symmetric vortex a which satisfies the boundary conditions b r e i d and curl a b r he 3 it is then shown that symmetric vortices form a family depending continuously on two real parameters and c which describe the behaviour at the center of the vortex as the boundary conditions depend smoothly on those parameters one can distinguish two main connected domains of vortices the first one defined by the boundary conditions b r e i d and ra r b r is a zone of stability where remains increasing the second one defined by the boundary conditions b r e i d and ra r b r d is a zone where some instability can occur attention is focused on the smooth branch of vortices which separates those two domains it is indexed by the parameter running from some l 0 to and the limit as decreases to l corresponds to a berger and chen type vortex

schrodinger operators with non degenerately vanishing magnetic fields in bounded domains we establish an asymptotic estimate of the lowest eigenvalue bf of the schrodinger operator 2 bf with a magnetic field in a bounded 2 dimensional domain where curl f vanishes non degenerately and b is a large parameter our study is based on an analysis on an eigenvalue variation problem for the sturm liouville problem using the estimate we determine the value of the upper critical field for superconductors subject to non homogeneous applied magnetic fields and localize the nucleation of superconductivity

attractors and inertial manifolds for finite difference approximations of the complex ginzburg landau equation a semidiscrete spatial finite difference approximation and two fully discrete finite difference approximations to the complex ginzburg landau equation are considered in this paper the existence of an inertial manifold is proved inside a discrete h1 absorbing ball for the semi discrete approximation by showing that certain spectral properties hold for the linear operator and certain lipschitz properties hold for the nonlinear term convergence of the true and discrete inertial manifolds is then shown by considering the contraction mappings used to construct the inertial manifolds a fully implicit scheme is shown to form a continuous semigroup in a discrete l2 space and absorbing balls of radii independent of the spatial and temporal mesh sizes in discrete l2 and h1 spaces are constructed existence of a global attractor follows furthermore the existence of an inertial manifold is proved by showing that certain spectral and lipschitz properties hold for a semi implicit scheme existence of absorbing balls in the discrete space l2 of radii independent of the spatial and temporal mesh is proved existence of a global attractor follows

a geometric schur weyl duality for quotients of affine hecke algebras abstract after establishing a geometric schur weyl duality in a general setting we recall this duality in type a in the finite and affine case we extend the duality in the affine case to positive parts of the affine algebras the positive parts have nice ideals coming from geometry allowing duality for quotients some of the quotients of the positive affine hecke algebra are then identified to some cyclotomic hecke algebras and the geometric setting allows the construction of canonical bases

viable control for uncertain nonlinear dynamical systems described by differential inclusions in this paper we will study the viable control problem for a class of uncertain nonlinear dynamical systems described by a differential inclusion the goal is to construct a feedback control such that all trajectories of the system are viable in a map moreover for any initial states no viable in the map under the feedback control all solutions of the system are steered to the map with an exponential convergence rate and viable in the map after a finite time t in this case an estimate of the time t of all trajectories attaining the map is given in the nanomedicine system an example inspired from cerebral embolism and cerebral thrombosis problems illustrates the use of our main results

green functions associated to complex reflection groups ii green functions associated to complex reflection groups g e 1 n were discussed in the author s previous paper in this paper we consider the case of complex reflection groups w g e p n schur functions and hall littlewood functions associated to w are introduced and green functions are described as the transition matrix between those two symmetric functions furthermore it is shown that these green functions are determined by means of green functions associated to various g e 1 n our result involves as a special case a combinatorial approach to the green functions of type dn

a finite element method with mesh adaptivity for computing vortex states in fast rotating bose einstein condensates numerical computations of stationary states of fast rotating bose einstein condensates require high spatial resolution due to the presence of a large number of quantized vortices in this paper we propose a low order finite element method with mesh adaptivity by metric control as an alternative approach to the commonly used high order finite difference or spectral approximation methods the mesh adaptivity is used with two different numerical algorithms to compute stationary vortex states an imaginary time propagation method and a sobolev gradient descent method we first address the basic issue of the choice of the variable used to compute new metrics for the mesh adaptivity and show that refinement using simultaneously the real and imaginary part of the solution is successful mesh refinement using only the modulus of the solution as adaptivity variable fails for complicated test cases then we suggest an optimized algorithm for adapting the mesh during the evolution of the solution towards the equilibrium state considerable computational time saving is obtained compared to uniform mesh computations the new method is applied to compute difficult cases relevant for physical experiments large nonlinear interaction constant and high rotation rates

virtual algebraic lie theory tilting modules and ringel duals for blob algebras in this paper we construct a representation of the blob algebra 22 over a ring allowing base change to every interesting i e non semisimple specialisation which in quasihereditary specialisations passes to a full tilting module the temperley lieb algebras are a tower t0 q t1 q of one parameter finite dimensional algebras 28 each with a basis independent of q these algebras are quasihereditary 3 8 except in case q q 0 accordingly one may in principle construct tilting modules full tilting modules and corresponding ringel duals in fact if v is a free module of rank 2 over the ground ring then tn q has an action on v and it is straightforward to show see later that v n is a full tilting module in the quasihereditary cases since v n exists over the ground ring the ringel dual can be constructed without having to pick a specialisation the cases of n finite of this dual are a nested sequence of quotients of the quantum group uqsl2 17 11 this q deformable duality and glorious limit structure 16 more usually observed with uqsl2 as the starting point provides the mechanism for massive exchange of representation theoretic information between the two sides 26 10 13 4 18 in particular the weight theory of uqsl2 controls the representation theory of tn q for all n simultaneously as localisations of a global limit the blob algebras are a tower b0 b1 of two parameter finite dimensional algebras and bn tn q they are quasihereditary except at a finite set of parameter values accordingly one may in principle construct tilting modules and so on ab initio one would have to expect such a construction to depend on the specialisation as indecomposable tilting modules do 24 on the other hand it turns out 23 that bn has an action on v and in this paper we show that v 2n is a full tilting module in the quasihereditary cases historically tn q and uqsl2 were studied extensively separately before the full tilting module ringel duality connection was known but if one side and the appropriate full tilting module had been discovered first the passage to the ringel dual would rightly have been regarded as quite a significant spin off the bn tilting property of v 2n is a striking result in as much as it places us in a position analogous to this as it were before the discovery of quantum groups

existence of periodic solutions for ginzburg landau equations of superconductivity abstract in an earlier paper b wang 1999 j math anal appl 232 394 412 the author proved the existence of periodic solutions to the ginzburg landau equations of superconductivity in two dimensions here we will show that the ginzburg landau equations admit periodic solutions in three dimensions as well we also prove the existence of periodic solutions to the phase lock equations introduced by the author in press j nonlinear anal

on the solutions of the one dimensional ginzburg landau equations for superconductivity this paper gives a complete description of the solutions of the one dimensional ginzburg landau equations which model superconductivity phenomena in infinite slabs we investigate this problem over the entire range of physically important parameters a the size of the slab the ginzburg landau parameter and h0 the exterior magnetic field we do extensive numerical computations using the software auto and determine the number symmetry and stability of solutions for all values of the parameters in particular our experiments reveal the existence of two key points in parameter space which play a central role in the formation of the complicated patterns by means of bifurcation phenomena our global description also allows us to separate the various physically important regimes to classify previous results in each regime according to the values of the parameters and to derive new open problems in addition our investigation provides new insight into the problem of differentiating between the types of superconductors in terms of the parameters

boundary concentration for eigenvalue problems related to the onset of superconductivity we examine the asymptotic behavior of the eigenvalue h and corresponding eigenfunction associated with the variational problem in the regime h 1 here a is any vector field with curl equal to 1 the problem arises within the ginzburg landau model for superconductivity with the function h yielding the relationship between the critical temperature vs applied magnetic field strength in the transition from normal to superconducting state in a thin mesoscopic sample with cross section omega subset r 2 we first carry out a rigorous analysis of the associated problem on a half plane and then rigorously justify some of the formal arguments of bs obtaining an expansion for while also proving that the first eigenfunction decays to zero somewhere along the sample boundary when is not a disc for interior decay we demonstrate that the rate is exponential

superconductivity near the normal state under the action of electric currents and induced magnetic fields in mathbb r 2 we consider the linearization of the time dependent ginzburg landau system near the normal state we assume that an electric current is applied through the sample which captures the whole plane inducing thereby a magnetic field we show that independently of the current the normal state is always stable using fourier analysis the detailed behaviour of solutions is obtained as well relying on semi group theory we then obtain the spectral properties of the steady state elliptic operator

directional curl spaces and applications to the meissner states of anisotropic superconductors the directional curl spaces are introduced which consist of vector fields that have directional curl along the given unit length vector fields the basic properties of these spaces are derived including the trace theorem and the representation of the dual spaces the directional curl spaces are used to analyze the asymptotic behavior of the meissner states of strongly anisotropic superconductors where the limiting energy functionals are non coercive in the usual sobolev spaces

analysis and convergence of a covolume approximation of the ginzburg landau model of superconductivity in this paper we present the mathematical analysis of a covolume method for the approximations of the ginzburg landau gl model for superconductivity a nice feature of this approach is that the gauge invariance properties are retained in discrete approximations based on triangular grids we also use properties of discrete vector fields to study issues such as the gauge choices and their enforcement