gamma convergence of gradient flows with applications to ginzburg landau we present a method to prove convergence of gradient flows of families of energies that converge to a limiting energy it provides lower bound criteria to obtain the convergence that correspond to a sort of c1 order convergence of functionals we then apply this method to establish the limiting dynamical law of a finite number of vortices for the heat flow of the ginzburg landau energy in dimension 2 retrieving in a different way the existing results for the case without magnetic field and obtaining new results for the case with magnetic field 2004 wiley periodicals inc

root n consistent semiparametric regression on considere une variable aleatoire x z dans 7b r p 7b r q on construit un estimateur generalisant l estimateur des moindres carres ordinaires en inserant des estimateurs non parametriques de la regression dans la projection orthogonale non lineaire sur z

the γ limit of the two dimensional ohta kawasaki energy droplet arrangement via the renormalized energy this is the second in a series of papers in which we derive a expansion for the two dimensional non local ginzburg landau energy with coulomb repulsion known as the ohta kawasaki model in connection with diblock copolymer systems in this model two phases appear which interact via a nonlocal coulomb type energy here we focus on the sharp interface version of this energy in the regime where one of the phases has very small volume fraction thus creating small droplets of the minority phase in a sea of the majority phase in our previous paper we computed the limit of the leading order energy which yields the averaged behavior for almost minimizers namely that the density of droplets should be uniform here we go to the next order and derive a next order limit energy which is exactly the coulombian renormalized energy obtained by sandier and serfaty as a limiting interaction energy for vortices in the magnetic ginzburg landau model the derivation is based on the abstract scheme of sandier serfaty that serves to obtain lower bounds for 2 scale energies and express them through some probabilities on patterns via the multiparameter ergodic theorem thus without appealing to the euler lagrange equation we establish for all configurations which have almost minimal energy the asymptotic roundness and radius of the droplets and the fact that they asymptotically shrink to points whose arrangement minimizes the renormalized energy in some averaged sense via a kind of equivalence the obtained results also yield an expansion of the minimal energy and a characterization of the zero super level sets of the minimizers for the original ohta kawasaki energy this leads to the expectation of seeing triangular lattices of droplets as energy minimizers

bounds on the micromagnetic energy of a uniaxial ferromagnet we identify the optimal scaling law for a nonconvex nonlocal variational problem representing the magnetic energy of a uniaxial ferromagnet our analysis is restricted to a certain parameter regime in which the surface tension is sufficiently small relative to the other parameters of the problem 1998 john wiley sons inc

higher dimensional coulomb gases and renormalized energy functionals we consider a classical system of n charged particles in an external confining potential in any dimension d larger than 2 the particles interact via pairwise repulsive coulomb forces and the coupling parameter scales like the inverse of n mean field scaling by a suitable splitting of the hamiltonian we extract the next to leading order term in the ground state energy beyond the mean field limit we show that this next order term which characterizes the fluctuations of the system is governed by a new renormalized energy functional providing a way to compute the total coulomb energy of a jellium i e an infinite set of point charges screened by a uniform neutralizing background in any dimension the renormalization that cuts out the infinite part of the energy is achieved by smearing out the point charges at a small scale as in onsager s lemma we obtain consequences for the statistical mechanics of the coulomb gas next to leading order asymptotic expansion of the free energy or partition function characterizations of the gibbs measures estimates on the local charge fluctuations and factorization estimates for reduced densities this extends results of sandier and serfaty to dimension higher than two by an alternative approach

limiting behavior of the ginzburg landau functional we continue our study of the functional ee u u12 u 2 14e2 1 u 2 2dx for u h1 u r2 where u is a bounded open subset of r2 compactness results for the scaled jacobian of ue are proved under the assumption that ee ue is bounded uniformly by a function of e in addition the gamma limit of ee ue ln e 2 is shown to be e v 12 v 22 v m where v is the limit of j ue ln e j ue ue due and m is the total variation of a radon measure these results are applied to the ginzburg landau functionalfe u a hext u12 au 2 14e2 1 u 2 2 12 a hext dx with external magnetic field hext h ln e the gamma limit of fe ln e 2 is calculated to bef v a h 12 v a 22 v m a h 22 where v is as before and a is the limit of ae ln e

nonparametric tests for conditional symmetry in dynamic models this article proposes omnibus tests for conditional symmetry around a parametric function in a dynamic context conditional moments may not exist or may depend on the explanatory variables test statistics are suitable functionals of the empirical process of residuals and explanatory variables whose limiting distribution under the null is nonpivotal the tests are implemented with the assistance of a bootstrap method which is justified assuming very mild regularity conditions on the specification of the center of symmetry and the underlying serial dependence structure finite sample properties are examined by means of a monte carlo experiment

boundary regularity and the dirichlet problem for harmonic maps in a previous paper 10 we developed an interior regularity theory for energy minimizing harmonic maps into riemannian manifolds in the first two sections of this paper we prove boundary regularity for energy minimizing maps with prescribed dirichlet boundary condition we show that such maps are regular in a full neighborhood of the boundary assuming appropriate regularity on the manifolds the boundary and the data the reader may refer to theorem 2 7 for a statement of the precise result it is not surprising that the boundary regularity is actually stronger than the partial regularity we obtained for the interior this is due to the fact that there are no nontrivial smooth harmonic maps from hemispheres s which map the boundary s 9s to a point i j n 2 and is analogous to the fact that in certain cases we were able to obtain complete regularity in the interior many authors have worked on boundary regularity for this general type of problem we mention hildebrandt and widman 5 and hamilton 4 as having obtained important results specifically for harmonic maps morrey had obtained the boundary regularity for domain dimension n 2 in conjunction with his investigation of the plateau problem in riemannian manifolds 8 in 3 of this paper we observe that the direct method gives solvability of the dirichlet problem under reasonable hypotheses on the manifolds we give as an application an amusing proof of a theorem of sacks and uhlenbeck 9 on the existence of minimal 2 spheres representing the second homotopy group of a manifold the same method gives smooth harmonic representations for k n for a certain class of manifolds n these are characterized by the nonexistence of lower dimensional harmonic spheres whose homogeneous extensions are minimal see proposition 3 4 in the last section of the paper we discuss approximation of l maps by smooth maps we give a simple example of an l map from the three dimensional ball to the two sphere which is not an l limit of continuous maps we

testing for symmetry summary we introduce the characteristic symmetry function based on the characteristic function of the underlying distribution whose behaviour is indicative of symmetry or its absence a statistic is proposed for testing symmetry about an unspecified centre derived from the empirical characteristic symmetry function the statistic is readily computible it utilizes information in the empirical characteristic function over an interval and does not require the estimation of the centre of symmetry under general symmetry the asymptotic null distribution of the statistic is folded normal the empirical power for selected alternatives is studied by a small scale simulation and a numerical illustration is given

a product estimate for ginzburg landau and corollaries abstract we prove a new inequality for the jacobian or vorticity associated to the ginzburg landau energy in any dimension it allows to retrieve existing lower bounds on the energy to extend them to the case of unbounded vorticity and to get a few other corollaries it also provides a new estimate on the time variation for time dependent families which has applications for the study of ginzburg landau dynamics

fine properties of functions with bounded deformation the paper is concerned with the fine properties of functions in the space of functions with bounded deformation we analyse the set of lebesgue points and the set where these functions have one sided approximate limits moreover following the analogy with we decompose the symmetric distributional derivative into an absolutely continuous part a jump part and a cantor part the main result of the paper is a structure theorem for functions showing that these parts of the derivative can be recovered from the corresponding ones of the one dimensional sections moreover we prove that functions are approximately differentiable in almost every point of their domain

froth like minimizers of a non local free energy functional with competing interactions we investigate the ground and low energy states of a one dimensional non local free energy functional describing at a mean field level a spin system with both ferromagnetic and antiferromagnetic interactions in particular the antiferromagnetic interaction is assumed to have a range much larger than the ferromagnetic one the competition between these two effects is expected to lead to the spontaneous emergence of a regular alternation of long intervals on which the spin profile is magnetized either up or down with an oscillation scale intermediate between the range of the ferromagnetic and that of the antiferromagnetic interaction in this sense the optimal or quasi optimal profiles are froth like if seen on the scale of the antiferromagnetic potential they look neutral but if seen at the microscope they actually consist of big bubbles of two different phases alternating among each other in this paper we prove the validity of this picture we compute the oscillation scale of the quasi optimal profiles and we quantify their distance in norm from a reference periodic profile the proof consists of two main steps we first coarse grain the system on a scale intermediate between the range of the ferromagnetic potential and the expected optimal oscillation scale in this way we reduce the original functional to an effective sharp interface one next we study the latter by reflection positivity methods which require as a key ingredient the exact locality of the short range term our proof has the conceptual interest of combining coarse graining with reflection positivity methods an idea that is presumably useful in much more general contexts than the one studied here

dislocation microstructures and the effective behavior of single crystals we consider single crystal plasticity in the limiting case of infinite latent hardening which signifies that the crystal must deform in single slip at all material points this requirement introduces a nonconvex constraint and thereby induces the formation of fine scale structures we restrict attention throughout to linearized kinematics and deformation theory of plasticity which is appropriate for monotonic proportional loading and confers the boundary value problem of plasticity a well defined variational structure analogous to elasticity we first study a scale invariant local problem we show that by developing microstructures in the form of sequential laminates of finite depth crystals can beat the single slip constraint i e the macroscopic relaxed constitutive behavior is indistinguishable from multislip ideal plasticity in a second step we include dislocation line energies and hence a length scale into the model different regimes lead to several possible types of microstructure patterns we present constructions which achieve the various optimal scaling laws and discuss the relation with experimentally known scalings such as the hall petch law

branched microstructures scaling and asymptotic self similarity we address some properties of a scalar two dimensional model that has been proposed to describe microstructure in martensitic phase transformations consisting of minimizing the bulk energy where uy 1 a e and u 0 0 kohn and muller r v kohn and s muller comm pure and appl math 47 1994 405 proved the existence of a minimizer for 0 and obtained bounds on the total energy that suggested self similarity of the minimizer building upon their work we derive a local upper bound on the energy and on the minimizer itself and show that the minimizer u is asymptotically self similar in the sense that the sequence 0 1 has a strongly converging subsequence in w1 2 2000 john wiley sons inc

on u statistics and v mise statistics for weakly dependent processes some probabilistic limit theorems for hoeffding s u statistic 13 and v mises functional are established when the underlying processes are not necessarily independent we consider absolutely regular processes 24 and processes x n n 1 which are uniformly mixing 14 as well as their time reversal x n n 1 called uniformly mixing in both directions of time many authors have weakened the hypothesis of independence in statistical limit theorems and considered m dependent markov or weakly dependent processes in particular for u statistics under weak dependence sen 22 has considered mixing processes and derived a central limit theorem and a law of the iterated logarithm while yoshihara 26 proved central limit theorems and a s results in the absolutely regular and uniformly mixing case here we extend these results considerably and prove central limit theorems and their rate of convergence in the prohorov metric and a berry esseen type theorem functional central limit theorems and a s approximation by a brownian motion extensions to multisample versions and other extensions are briefly discussed

the complement of the path is determined by its spectrum abstract it is proved that a graph whose 0 1 adjacency matrix has the spectrum of p n the complement of the path on n vertices must be p n

singular kernels multiscale decomposition of microstructure and dislocation models we consider a model for dislocations in crystals introduced by koslowski cuitino and ortiz which includes elastic interactions via a singular kernel behaving as the h1 2 norm of the slip we obtain a sharp interface limit of the model within the framework of convergence from an analytical point of view our functional is a vector valued generalization of the one studied by alberti bouchitte and seppecher to which their rearrangement argument no longer applies instead we show that the microstructure must be approximately one dimensional on most length scales and we exploit this property to derive a sharp lower bound

a boundary value problem related to the ginzburg landau model we analyze the ginzburg landau equation for a superconductor in the case of a 2 dimensional model a cylindrical conductor with a magnetic field parallel to the axis this amounts to find the extrema of the free energy mathcal a kappa 1 2 int limits omega nabla ia phi 2 b a 2 kappa 4 phi 2 1 2 dx where is a bounded domain with smooth boundary in 2 a a1 a2 the vector potential ba 1a2 2a1 the magnetic field a complex field we describe the connected components of the maximal configuration space i e of the set of all a with components in the sobolev spaceh1 and such that 1 on the boundary modulo the action of the gauge group in the critical case 1 we give a complete description of the minimal configurations in each component

the spectral characterization of graphs abstract a graph b r s is a graph consisting of two cycles c r 1 and c s 1 with just a vertex in common fan and luo in theorem 4 4 8 alleged that a graph is determined by its adjacency spectrum if it contains no cycle c 4 however according to theorem 6 3 16 we find that the result in theorem 4 4 8 is not completely correct in this paper we prove that b r s s r 7 is das if and only if s r 2 and b r s s r 7 has a unique cospectral mate if s r 2

defects in nematic shells a γ convergence discrete to continuum approach in this paper we rigorously investigate the emergence of defects on nematic shells with a genus different from one this phenomenon is related to a non trivial interplay between the topology of the shell and the alignment of the director field to this end we consider a discrete xy system on the shell m described by a tangent vector field with unit norm sitting at the vertices of a triangulation of the shell defects emerge when we let the mesh size of the triangulation go to zero namely in the discrete to continuum limit in this paper we investigate the discrete to continuum limit in terms of convergence in two different asymptotic regimes the first scaling promotes the appearance of a finite number of defects whose charges are in accordance with the topology of shell m via the poincare hopf theorem the second scaling produces the so called renormalized energy that governs the equilibrium of the configurations with defects

lorentz space estimates for the ginzburg landau energy abstract in this paper we prove novel lower bounds for the ginzburg landau energy with or without magnetic field these bounds rely on an improvement of the vortex balls construction estimates by extracting a new positive term in the energy lower bounds this extra term can be conveniently estimated through a lorentz space norm on which it thus provides an upper bound the lorentz space l 2 we use is critical with respect to the expected vortex profiles and can serve to estimate the total number of vortices and get improved convergence results

weak anchoring for a two dimensional liquid crystal abstract we study the weak anchoring condition for nematic liquid crystals in the context of the landau de gennes model we restrict our attention to two dimensional samples and to nematic director fields lying in the plane for which the landau de gennes energy reduces to the ginzburg landau functional and the weak anchoring condition is realized via a penalized boundary term in the energy we study the singular limit as the length scale parameter e 0 assuming the weak anchoring parameter e at a prescribed rate we also consider a specific example of a bulk nematic liquid crystal with an included oil droplet and derive a precise description of the defect locations for this situation for e k e with 0 1 we show that defects lie on the weak anchoring boundary for 0 1 2 or for 1 2 and k small but they occur inside the bulk domain for 1 2 or 1 2 with k large

a new approach to counterexamples to l 1 estimates korn s inequality geometric rigidity and regularity for gradients of separately convex functions the derivation of counterexamples to l1 estimates can be reduced to a geometric decomposition procedure along rank one lines in matrix space we illustrate this concept in two concrete applications firstly we recover a celebrated and rather complex counterexample by ornstein proving the failure of korn s inequality and of the corresponding geometrically nonlinear rigidity result in l1 secondly we construct a function f 2 which is separately convex but whose gradient is not in bvloc in the sense that the mixed derivative 2f x1 x2 is not a bounded measure

rotating 2n vortex solutions to the gross pitaevskii equation on s2 we establish the existence of rotating solutions to the gross pitaevskii equation iut u 1 2 1 u 2 uposed on s2 that is for u s2 r c these solutions possess vortices that for all time follow the vortex paths of known relative equilibria to the point vortex problem on the two sphere in the asymptotic regime 1 the approach is variational based on minimization of the ginzburg landau energy subject to a momentum constraint we also establish orbital stability within a class of symmetric initial data

two modified wilcoxon tests for symmetry about an unknown location parameter summary two modifications of the wilcoxon test for symmetry about the sample median are proposed and their large sample distribution theory derived their pitman efficacies against contamination in the right tail are obtained both the asymptotic results and a monte carlo study show that the procedures are more powerful than the wilcoxon test about the median against many asymmetric alternatives while preserving its robustness of level shown by antille kersting 1977

metastability and dynamics of discrete topological singularities in two dimensions a γ convergence approach this paper aims at building a variational approach to the dynamics of discrete topological singularities in two dimensions based on convergence we consider discrete systems described by scalar functions defined on a square lattice and governed by periodic interaction potentials our main motivation comes from xy spin systems described by the phase parameter and screw dislocations described by the displacement function for these systems we introduce a discrete notion of vorticity as the lattice spacing tends to zero we derive the first order limit of the free energy which is referred to as renormalized energy and describes the interaction of vortices as a byproduct of this analysis we show that such systems exhibit increasingly many metastable configurations of singularities therefore we propose a variational approach to the depinning and dynamics of discrete vortices based on minimizing movements we show that letting first the lattice spacing and then the time step of the minimizing movements tend to zero the vortices move according with the gradient flow of the renormalized energy as in the continuous ginzburg landau framework

a consistent nonparametric test of symmetry in linear regression models abstract this article proposes a consistent nonparametric test of the hypothesis that the disturbance in a linear regression model is distributed symmetrically around zero simulation results show that the test has good size and power properties for sample sizes as small as 50 we illustrate the use of the test in a cross country model of inflation and monetary growth

note on the spectral characterization of some cubic graphs with maximum number of triangles abstract ubic graphs of given order with maximum number of triangles are characterized consequently it is proved that certain cubic graphs with maximum number of triangles are determined by their adjacency spectrum

on spatial and material covariant balance laws in elasticity this paper presents some developments related to the idea of covariance in elasticity the geometric point of view in continuum mechanics is briefly reviewed building on this regarding the reference configuration and the ambient space as riemannian manifolds with their own metrics a lagrangian field theory of elastic bodies with evolving reference configurations is developed it is shown that even in this general setting the euler lagrange equations resulting from horizontal referential variations are equivalent to those resulting from vertical spatial variations the classical green naghdi rivilin theorem is revisited and a material version of it is discussed it is shown that energy balance in general cannot be invariant under isometries of the reference configuration which in this case is identified with a subset of r 3 transformation properties of balance of energy under rigid translations and rotations of the reference configuration is obtained the spatial covariant theory of elasticity is also revisited the transformation of balance of energy under an arbitrary diffeomorphism of the reference configuration is obtained and it is shown that some nonstandard terms appear in the transformed balance of energy then conditions under which energy balance is materially covariant are obtained it is seen that material covariance of energy balance is equivalent to conservation of mass isotropy material doyle ericksen formula and an extra condition that we call configurational inviscidity in the last part of the paper the connection between noether s theorem and covariance is investigated it is shown that the doyleericksen formula can be obtained as a consequence of spatial covariance of lagrangian density similarly it is shown that the material doyle ericksen formula can be obtained from material covariance of lagrangian density 2006 american institute of physics doi 10 1063 1 2190827

on minimizers of a landau de gennes energy functional on planar domains we study tensor valued minimizers of the landau de gennes energy functional on a simply connected planar domain with non contractible boundary data here the tensorial field represents the second moment of a local orientational distribution of rod like molecules of a nematic liquid crystal under the assumption that the energy depends on a single parameter a dimensionless elastic constant varepsilon 0 we establish that as varepsilon to 0 the minimizers converge to a projection valued map that minimizes the dirichlet integral away from a single point in we also provide a description of the limiting map

non existence of vortices in the small density region of a condensate abstract in this paper we answer a question raised by lev pitaevskii and prove that the ground state of the gross pitaevskii energy describing a bose einstein condensate in a rotationally symmetric trap at low rotation does not have vortices in the low density region therefore the first ground state with vortices has its vortices in the bulk in fact we prove something stronger which is that the ground state for the model at low and moderate rotations is equal to the ground state in a condensate with no rotation this is obtained by proving that for small rotational velocities the ground state is multiple of the ground state with zero rotation we rely on sharp bounds of the decay of the wave function combined with weighted jacobian estimates

metamorphoses sudden jumps in basin boundaries in some invertible maps of the plane that depend on a parameter boundaries of basins of attraction are extremely sensitive to small changes in the parameter a basin boundary can jump suddenly and as it does change from being smooth to fractal such changes are calledbasin boundary metamorphoses we prove under certain non degeneracy assumptions that a metamorphosis occurs when the stable and unstable manifolds of a periodic saddle on the boundary undergo a homoclinic tangency

the line tension approximation as the dilute limit of linear elastic dislocations we prove that the classical line tension approximation for dislocations in crystals that is the approximation that neglects interactions at a distance between dislocation segments and accords dislocations energy in proportion to their length follows as the limit of regularized linear elasticity as the lattice parameter becomes increasingly small or equivalently as the dislocation measure becomes increasingly dilute we consider two regularizations of the theory of linear elastic dislocations a core cutoff and a mollification of the dislocation measure we show that both regularizations give the same energy in the limit namely an energy defined on matrix valued divergence free measures concentrated on lines the corresponding self energy per unit length b t which depends on the local burgers vector and orientation of the dislocation does not however necessarily coincide with the self energy per unit length 0 b t obtained from the classical theory of the prelogarithmic factor of linear elastic straight dislocations indeed microstructure can occur at small scales resulting in a further relaxation of the classical energy down to its h1 elliptic envelope

a consistent test for conditional symmetry in time series models the assumption of conditional symmetry is often invoked to validate adaptive estimation and consistent estimation of arch garch models by quasi maximum likelihood imposing conditional symmetry can increase the efficiency of bootstraps if the symmetry assumption is valid this paper proposes a procedure for testing conditional symmetry the proposed test does not require the data to be stationary or i i d and the dimension of the conditional variables can be infinite the proposed test is consistent and is asymptotically distribution free in addition the test is shown to have nontrivial power against root t local alternatives the size and power of the test are satisfactory even for small samples applying the test to various time series we reject conditional symmetry in inflation exchange rate and stock returns among the nonfinancial time series considered we find that investment the consumption of durables and manufacturing employment also reject conditional symmetry

analysis of nematic liquid crystals with disclination lines we investigate the structure of nematic liquid crystal thin films described by the landau de gennes tensor valued order parameter model with dirichlet boundary conditions on the sides of nonzero degree we prove that as the elasticity constant goes to zero in the energy a limiting uniaxial nematic texture forms with a finite number of defects all of degree frac 1 2 or all of degree frac 1 2 corresponding to vertical disclination lines at those locations we also state a result on the limiting behavior of minimizers of the chern simons higgs model without magnetic field that follows from a similar proof

vortices and pinning effects for the ginzburg landau model in multiply connected domains we consider the two dimensional ginzburg landau model with magnetic fi eld for a superconductor with a multiply connected cross section we study energy minimizers in the london limit as the ginzburg landau parameter 1 to determine the number and asymptotic location of vortices we show that the holes act as pinning sites acquiring nonzero winding for bounded fields and attracting all vortices away from the interior for fields up to a critica l value hex o ln at the critical level the pinning effect breaks down and vortices appear in the interior of the superconductor at locations that we id entify explicitly in terms of the solutions of an elliptic boundary value problem the method involves sharp upper and lower energy estimates and a careful analysis of the limiting problem that captures the interaction between the vortices and the holes c 2005 wiley periodicals inc

on the spectral characterization of t shape trees a graph g is said to be determined by its spectrum if any graph having the same spectrum as g is isomorphic to g a t shape is a tree with exactly one of its vertices having maximal degree 3 in this paper we show that all t shape trees are determined by their spectra except for a few well defined cases

energy estimates for the von karman model of thin film blistering we consider the behavior of buckling driven thin film blisterings using von karman s plate theory our focus is on the setting where the blistered region is the unit square with clamped boundary conditions at the vertical sides and periodic ones along the horizontal sides in this setting we prove rigorous upper and lower bounds for the elastic energy which are of the same order as the film thickness we also present a convincing argument for the necessity of branching of folds near the boundary as has been observed in experiments

domain branching in uniaxial ferromagnets a scaling law for the minimum energy we address the branching of magnetic domains in a uniaxial ferromagnet our thesis is that branching is required by energy minimization to show this we consider the nonlocal nonconvex variational problem of micromagnetics we identify the scaling law of the minimum energy by proving a rigorous lower bound which matches the already known upper bound we further show that any domain pattern achieving this scaling law must have average width of order l 2 3 where l is the length of the magnet in the easy direction finally we argue that branching is required by considering the constrained variational problem in which branching is prohibited and the domain structure is invariant in the easy direction its scaling law is different

gamma convergence of maxwell chern simons higgs energy in this article we derive the limit of the maxwell chern simons higgs energy with log 2 energy bound our interests focus on the case with external electro magnetic potentials similarly to the abelian ginzburg landau model the corresponding obstacle problems are derived

on approximation of ginzburg landau minimizers by s1 valued maps in domains with vanishingly small holes abstract we consider a two dimensional ginzburg landau problem on an arbitrary domain with a finite number of vanishingly small circular holes a special choice of scaling relation between the material and geometric parameters ginzburg landau parameter vs hole radius is motivated by a recently discovered phenomenon of vortex phase separation in superconducting composites we show that for each hole the degrees of minimizers of the ginzburg landau problems in the classes of s 1 valued and c valued maps respectively are the same the presence of two parameters that are widely separated on a logarithmic scale constitutes the principal difficulty of the analysis that is based on energy decomposition techniques

a variational model for dislocations in the line tension limit we study the interaction of a singularly perturbed multiwell energy with an anisotropic nonlocal regularizing term of h1 2 type and a pinning condition this functional arises in a phase field model for dislocations which was recently proposed by koslowski cuitino and ortiz but it is also of broader mathematical interest in the context of the dislocation model we identify the limit of the energy in all scaling regimes for the number n of obstacles the most interesting regime is n ln where is a nondimensional length scale related to the size of the crystal lattice in this case the limiting model is of line tension type one important feature of our model is that the set of energy wells is periodic and hence not compact thus a key ingredient in the proof is a compactness estimate up to a single translation for finite energy sequences which generalizes earlier results from alberti bouchitte and seppecher for the two well problem with a h1 2 regularization

generalized autoregressive conditional heteroskedasticity a natural generalization of the arch autoregressive conditional heteroskedastic process introduced in engle 1982 to allow for past conditional variances in the current conditional variance equation is proposed stationarity conditions and autocorrelation structure for this new class of parametric models are derived maximum likelihood estimation and testing are also considered finally an empirical example relating to the uncertainty of the inflation rate is presented

a data driven smooth test of symmetry in this paper we propose a data driven smooth test of symmetry we first transform the raw data via the probability integral transformation according to a symmetrized empirical distribution and show that under the null hypothesis of symmetry the transformed data has a limiting uniform distribution reducing testing for symmetry to testing for uniformity employing neyman s smooth test of uniformity we show that only odd ordered orthogonal moments of the transformed data are required in constructing the test statistic we present a standardized smooth test that is distribution free asymptotically and derive the asymptotic behavior of the test and establish its consistency extension to dependent data case is discussed we investigate the finite sample performance of the proposed tests on both homogeneous and mixed distributions with unobserved heterogeneity an empirical application on testing symmetry of wage adjustment process based on heterogeneous wage contracts with different durations is provided

ginzburg landau functionals and renormalized energy a revised γ convergence approach abstract we give short and self contained proofs of convergence results for ginzburg landau energy functionals in two dimensions in the logarithmic energetic regime in particular we derive the renormalized energy by convergence

pinning effects and their breakdown for a ginzburg landau model with normal inclusions we study a ginzburg landau model for an inhomogeneous superconductor in the singular limit as the ginzburg landau parameter 1 the inhomogeneity is represented by a potential term v 14 a x 2 2 with a given smooth function a x which is assumed to become negative in finitely many smooth subdomains the normally included regions for bounded applied fields independent of the ginzburg landau parameter 1 we show that the normal regions act as giant vortices acquiring large vorticity for large fixed applied field hex for hex o ln we show that this pinning effect eventually breaks down and free vortices begin to appear in the superconducting region where a x 0 at a point set which is determined by solving an elliptic boundary value problem the associated operators are strictly but not uniformly elliptic leading to some regularity questions to be resolved near the boundaries of the normal regions

spectral characterization of the hamming graphs abstract we show that the hamming graph h 3 q with diameter three is uniquely determined by its spectrum for q 36 moreover we show that for given integer d 2 any graph cospectral with the hamming graph h d q is locally the disjoint union of d copies of the complete graph of size q 1 for q large enough

energy estimates and cavity interaction for a critical exponent cavitation model we consider the minimization of in a perforated domain of among maps that are incompressible det and invertible and satisfy a dirichlet boundary condition u g on if the volume enclosed by g is greater than any such deformation u is forced to map the small holes be ai onto macroscopically visible cavities which do not disappear as e 0 we restrict our attention to the critical exponent p n where the energy required for cavitation is of the order of and the model is suited therefore for an asymptotic analysis v1 vm denote the volumes of the cavities in the spirit of the analysis of vortices in ginzburg landau theory we obtain estimates for the renormalized energy showing its dependence on the size and the shape of the cavities on the initial distance between the cavitation points a1 am and on the distance from these points to the outer boundary based on those estimates we conclude for the case of two cavities that either the cavities prefer to be spherical in shape and well separated or to be very close to each other and appear as a single equivalent round cavity this is in agreement with existing numerical simulations and is reminiscent of the interaction between cavities in the mechanism of ductile fracture by void growth and coalescence 2012 wiley periodicals inc

global existence results for viscoplasticity at finite strain we study a model for rate dependent gradient plasticity at finite strain based on the multiplicative decomposition of the strain tensor and investigate the existence of global in time solutions to the related pde system we reveal its underlying structure as a generalized gradient system where the driving energy functional is highly nonconvex and features the geometric nonlinearities related to finite strain elasticity as well as the multiplicative decomposition of finite strain plasticity moreover the dissipation potential depends on the left invariant plastic rate and thus depends on the plastic state variable the existence theory is developed for a class of abstract nonsmooth and nonconvex gradient systems for which we introduce suitable notions of solutions namely energy dissipation balance and energy dissipation inequality solutions hence we resort to the toolbox of the direct method of the calculus of variations to check that the specific energy and dissipation functionals for our viscoplastic models comply with the conditions of the general theory

nonparametric tests for conditional symmetry abstract we propose omnibus tests for symmetry of the conditional distribution of a time series process about a nonparametric regression function the test statistic is a weighted version of the integrated squared difference between the restricted and unrestricted estimators of the joint characteristic function of nonparametric residuals and explanatory variables whose critical values are estimated with the assistance of a bootstrap technique the test is sensitive to local alternatives converging to the null at the parametric rate t 1 2 with t the sample size we investigate the finite sample performance of the test by means of monte carlo experiments and two empirical applications to test whether losses are more likely than gains in financial markets and whether expansions and contractions are equally likely in business cycles given the relevant information

spectral characterization of graphs with index at most 2 5 abstract a graph is said to be determined by the adjacency spectrum ds for short if there is no other nonisomorphic graph with the same spectrum all connected graphs with index at most 2 5 are known in this paper we show that with few exceptions all of these graphs are ds

lower bounds for the energy of unit vector fields and applications we prove lower bounds for the dirichlet energy of a unit vector field defined in a perforated domain of r2with nonzero degree on the outer boundary in terms of the total diameter of the holes we use this to derive lower bounds and then compactness results for sequences ue of minimizers or almost minimizers of ginzburg landau functionals with coupling constant 1 e2tending to

on the variations of the vortex number in a periodic ginzburg landau model in this paper we study the variations of the number of vortices contained in the minimizer of a two dimensional ginzburg landau functional describing a type ii superconductor in the london limit with periodic conditions on the boundary of the sample we prove that under the assumption that the sample is rectangular with height small enough the number of vortices contained in the minimizer of the periodic ginzburg landau functional jumps by unit step as the applied magnetic field increases we convert the problem into the study of corresponding renormalized energy by using the convergence we reduce the two dimensional renormalized energy to one dimensional one then the result is obtained by analyzing the one dimensional model

energy scaling of compressed elastic films three dimensional elasticity and reduced theories we derive an optimal scaling law for the energy of thin elastic films under isotropic compression starting from three dimensional nonlinear elasticity as a consequence we show that any deformation with optimal energy scaling must exhibit fine scale oscillations along the boundary which coarsen in the interior this agrees with experimental observations of folds which refine as they approach the boundary

which graphs are determined by their spectrum for almost all graphs the answer to the question in the title is still unknown here we survey the cases for which the answer is known not only the adjacency matrix but also other types of matrices such as the laplacian matrix are considered

spectral characterizations of lollipop graphs abstract the lollipop graph denoted by h n p is obtained by appending a cycle c p to a pendant vertex of a path p n p we will show that no two non isomorphic lollipop graphs are cospectral with respect to the adjacency matrix it is proved that for p odd the lollipop graphs h n p and some related graphs h n p are determined by the adjacency spectrum and that all lollipop graphs are determined by its laplacian spectrum

γ convergence analysis of systems of edge dislocations the self energy regime this paper deals with the elastic energy induced by systems of straight edge dislocations in the framework of linearized plane elasticity the dislocations are introduced as point topological defects of the displacement gradient fields following the core radius approach we introduce a parameter varepsilon 0 representing the lattice spacing of the crystal we remove a disc of radius varepsilon around each dislocation and compute the elastic energy stored outside the union of such discs namely outside the core region then we analyze the asymptotic behaviour of the elastic energy as varepsilon rightarrow 0 in terms of convergence we focus on the self energy regime of order log frac 1 varepsilon we show that configurations with logarithmic diverging energy converge up to a subsequence to a finite number of multiple dislocations and we compute the corresponding limit

dynamics for systems of screw dislocations the goal of this paper is the analytical validation of a model of cermelli and gurtin arch ration mech anal 148 1999 pp 3 52 for an evolution law for systems of screw dislocations under the assumption of antiplane shear the motion of the dislocations is restricted to a discrete set of glide directions which are properties of the material the evolution law is given by a maximal dissipation criterion leading to a system of differential inclusions short time existence uniqueness cross slip and fine cross slip of solutions are proved

from the ginzburg landau model to vortex lattice problems we introduce a coulombian renormalized energy w which is a logarithmic type of interaction between points in the plane computed by a renormalization we prove various of its properties such as the existence of minimizers and show in particular using results from number theory that among lattice configurations the triangular lattice is the unique minimizer its minimization in general remains open

on a signless laplacian spectral characterization of t shape trees let m be an associated matrix of a graph g the adjacency laplacian and signless laplacian matrix two graphs are said to be cospectral with respect to m if they have the same m spectrum a graph is said to be determined by m spectrum if there is no other non isomorphic graph with the same spectrum with respect to m it is shown that t shape trees are determined by their laplacian spectra moreover among them those are determined by their adjacency spectra are characterized in this paper we identify graphs which are cospectral to a given t shape tree with respect to the signless laplacian matrix subsequently t shape trees which are determined by their signless laplacian spectra are identified

significance testing in nonparametric regression based on the bootstrap this paper proposes a test for selecting explanatory variables in nonparametric regression the test does not need to estimate the conditional expectation function given all the variables but only those which are significant under the null hypothesis this feature is computationally convenient and solves in part the problem of the curse of dimensionality when selecting regressors in a nonparametric context the proposed test statistic is based on functionals of a u process contiguous alternatives converging to the null at a rate n 1 2 can be detected the asymptotic null distribution of the statistic depends on certain features of the data generating process and asymptotic tests are difficult to implement except in rare circumstances we justify the consistency of two easy to implement bootstrap tests which exhibit good level accuracy for fairly small samples according to the reported monte carlo simulations these results are also applicable to test other interesting restrictions on nonparametric curves like partial linearity and conditional independence

gamma limit of the nonself dual chern simons higgs energy abstract we consider the gamma limit of the abelian chern simons higgs energy g csh 1 2 u a e u e 2 2 4 curl a e h ex 2 u e 2 1 e 2 u e 2 1 u e 2 2 d x on a bounded simply connected two dimensional domain under the e 0 limit as a first step we study the gamma limit of e csh 1 2 u u e 2 1 e 2 u e 2 1 u e 2 2 d x under two different scalings e csh log e and e csh log e 2 we apply the log e 2 scaling result to the full chern simons higgs energy g csh and as a consequence we are able to compute the first critical field h 1 h 1 u for the nucleation of a vortex the method entails estimating in certain weak topologies the jacobian j u e det u e in terms of the chern simons higgs energy e csh

the critical velocity for vortex existence in a two dimensional rotating bose einstein condensate we investigate a model corresponding to the experiments for a two dimensional rotating bose einstein condensate it consists in minimizing a gross pitaevskii functional defined in r 2 under the unit mass constraint we estimate the critical rotational speed 1 for vortex existence in the bulk of the condensate and we give some fundamental energy estimates for velocities close to 1

on the shape of interlayer vortices in the lawrence doniach model we consider the lawrence doniach model for layered superconductors in which stacks of parallel superconducting planes are coupled via the josephson effect to model experiments in which the superconductor is placed in an external magnetic field oriented parallel to the superconducting planes we study the structure of isolated vortices for a doubly periodic problem we consider a singular limit which simulates certain experimental regimes in which isolated vortices have been observed corresponding to letting the interlayer spacing of the superconducting planes tend to zero and the ginzburg landau parameter simultaneously but at a fixed relative rate