grid generation techniques in computational fluid dynamics revue des differentes methodes on montre que les regions tridimensionnelles sont mieux traitees par fragmentation du champ en sous regions avec generation de grilles dans chaque sous region interet des grilles adaptatives couplees a des solutions physiques

correlation of power variables frequency domain abstract this publication is a third paper in a series considering the concept of power correlation power correlation is treated herein from a frequency domain viewpoint with major emphasis being placed on the power frequency response function pfrf a pfrf relates power at a driving point to power at another point in a vibratory system a theoretical formula for power frequency response function is derived and experimentally determined pfrf s are presented a pfrf is complex valued the real part relating the transfer of real power from one point in a system to another this function provides further insight into power flow in a vibratory system

correlation of power variables abstract cross correlation functions between input power fluctuations and system power fluctuations are derived for a gaussian process and sine wave process these cross correlation functions are referred to as power correlations and they contain both a constant term plus a fluctuating quantity the derivations show that for a linear system with no uncorrelated noise normalized correlations of squared fluctuations between the input and output should be equal to one experimental data obtained from tests on an electrical circuit validated analytically derived power correlation formulas power correlation functions can be used for determination of propagation times for power transmission and for other applications such as resonance testing

partial regularity of the landau de gennes energy model for liquid crystals abstract we discuss the partial regularity of non trivial minimizers for the landau de gennes energy functional in a bounded domain of r 3 off some relatively closed subset z whose 1 dimensional hausdorff measure is zero we prove that the minimizers are analytic

singularities of energy minimizing maps from the ball to the sphere we study maps from the unit ball b in r3 to the unit sphere s2 in r3 which minimize dirichlet s energy integral varepsilon varphi int b nabla varphi 2 dv

a general comparison theorem for p harmonic maps in homotopy class abstract we prove a general comparison result for homotopic finite p energy c 1 p harmonic maps u v m n between riemannian manifolds assuming that m is p parabolic and n is complete and nonpositively curved in particular we construct a homotopy through constant p energy maps which turn out to be p harmonic when n is compact moreover we obtain uniqueness in the case of negatively curved n this generalizes a well known result in the harmonic setting due to r schoen and s t yau

a quantization property for static ginzburg landau vortices for any critical point of the complex ginzburg landau functional in dimension 3 we prove that for large coupling constants if the energy of this critical point on a ball of a given radius r is relatively small compared to r log then the ball of half radius contains no vortex the modulus of the solution is larger than we then show how this property can be applied to describe limiting vortices as e 0 2001 john wiley sons inc

a relaxation of the intrinsic biharmonic energy the tension field u of a map u from a domain omega subset mathbb r m into a manifold n is the negative l2 gradient of the dirichlet energy in this paper we study the intrinsic biharmonic energy functional t u int omega tau u 2 in order to overcome the lack of coercivity of t we extend it to a larger space we construct minimizers of the extended functional via the direct method and we study the relation between these minimizers and critical points of t our results are restricted to dimensions m 4

homotopy classes in sobolev spaces and the existence of energy minimizing maps consider the problem of finding maps f m n that are stationary for an energy functional such as fm idfl p where m and n are compact riemannian manifolds and p l such maps may be found by minimizing the functional but if we minimize among all maps from m to n then the minimum is 0 and is attained only by constant maps thus in order to find nontrivial stationary maps we would like to use the topology of m and n to define classes of maps from m to n in which we can minimize the functional for instance one could try to minimize among maps in a given homotopy class but this is not possible in general unless p dimm since a minimizing sequence of mappings in one homotopy class can converge in the appropriate weak topology to a map in another homotopy class however in this paper we show that it is possible to minimize among maps fwhose restrictions to a lower dimensional skeleton of a triangulation of m belong to a given homotopy class to state the results precisely we need to refer to certain sobolev spaces and norms we will assume without loss of generality that m and n are submanifolds of euclidean spaces r m and r respectively and we let lip m n denote the space of lipschitz maps from m to n we define li p m r to be the space of all functions fe lp m r n such that there exist functions

a time frequency formulation of optimum detection a time frequency formulation is proposed for the optimum detection of gaussian signals in white gaussian noise by choosing the wigner ville distribution as the basic time frequency tool it is shown that the corresponding receivers generally take the form of a correlation between time frequency structures matching mathematical optimality with a physically meaningful interpretation the case of low snr is examined and various examples are considered deterministic signal rayleigh fading signal random jitter and random time varying channel a general class of time frequency receivers is proposed which admits as limiting cases different known structures and its suboptimum performance is evaluated possible extensions to more elaborate situations including parameter estimation are mentioned

dirichlet and neumann boundary value problems for yang mills connections the yang mills equations have been extensively studied on compact riemannian manifolds without boundary a substantial amount of work has also been done on non compact examples with a boundary component at infinity see 5 10 11 14 15 here we define and describe a solution of dirichlet and neumann boundary value problems for yang mills connections on a compact four dimensional manifold with smooth boundary the equations in the interior are the full yang mills equations we do not restrict ourselves to self dual or anti self dual solutions in the case where the structure group in the gauge theory is abelian our results are contained in the hodge de rham theory for manifolds with boundary see 6 9 4 3 in the general case our results describe a non linear version of this theory the base manifold m of the theory is a compact orientable four dimensional manifold with smooth boundary m we assume that m is endowed with a riemannian metric we consider a principal fiber bundle p over m with structure group g a compact lie group which will have a metric invariant under the adjoint action in the usual example this comes from trace the unknown in the problem is the connection a i e a differential form in p ad g where g is the lie algebra of g there are two natural boundary value problems one of them requires fixing the tangential part of the connection a on the bundle restricted to m if m is locally described as x 0 this amounts to prescribing a1 x dx a2 x dx 2 a3 x dx 3 on m the connection is fixed in the sense that a particular choice is fixed in the gauge equivalence class of a on the boundary the yang mills equations are satisfied in the interior this corresponds to the dirichlet problem in the other boundary value problem we consider a is free at the boundary but the normal part of the curvature is set equal to zero we call this the neumann problem for the dirichlet problem we consider a sequence of l1 connections that minimizes the yang mills functional with prescribed admissible tangential boundary data we show that there exists a weak limiting connection a by finding local good gauges the limiting connection is only locally defined we show that a solves the yang mills equations and satisfies the boundary conditions up to

partial regularity to the landau lifshitz equation with spin accumulation abstract in this paper we consider a model for the spin magnetization system that takes into account the diffusion process of the spin accumulation this model consists of the landau lifshitz equation describing the precession of the magnetization coupled with a quasi linear parabolic equation describing the diffusion of the spin accumulation this paper establishes the global existence and uniqueness of weak solutions for large initial data in r 2 moreover partial regularity is shown in particular the solution is regular on r 2 0 with the exception of at most finite singular points

smoothness of harmonic maps for hypoelliptic diffusions harmonic maps are viewed as maps sending a fixed diffusion to manifold valued martingales under a convexity condition we prove that the continuity of real valued harmonic functions implies the continuity of harmonic maps then we prove with a probabilistic method that continuous harmonic maps are smooth under hormander s condition the proof relies on the study of martingales with values in the tangent bundle

regularity for the approximated harmonic map equation and application to the heat flow for harmonic maps let omega subset mathbb r n n ge 2 be open and n subset mathbb r k a smooth compact riemannian manifold without boundary we consider the approximated harmonic map equation delta u a u nabla u nabla u f for maps u in h 1 omega n where f in l p omega mathbb r k for p frac n 2 we prove holder continuity for weak solution s which satisfy a certain smallness condition for p frac n 2 we derive an energy estimate which allows to prove partial regularity for stationary solutions of the heat flow for harmonic maps in dimension n le 4

convex functionals and the stratification of the singular set of their stationary points abstract we prove partial regularity of stationary solutions and minimizers u from a set r n to a riemannian manifold n for the functional f x u u 2 d x the integrand f is convex and satisfies some ellipticity and boundedness assumptions we also develop a new monotonicity formula and an regularity theorem for such stationary solutions with no restriction on their images we then use the idea of quantitative stratification to show that the k th strata of the singular set of such solutions are k rectifiable

liquid crystals and the monotonicity formula abstract we give numerical evidence that the monotonicity formula holds for the liquid crystal functional and study part of the associated bifurcation diagram

frequency response functions for power power transfer ratio and coherence abstract the concept of frequency response functions for power variables was proposed in reference 3 where a convolution integral formula in the frequency domain was used to relate fluctuating power variables and to give the frequency response function for power this convolution integral is simplified in the present paper for several cases of varying bandwidth random force inputs and cosine wave force input to an oscillator which results in frequency response functions for power which are dependent on the type of force input coherence functions for power variables are also determined from theory theoretically derived results compare well to those obtained from experiments and these results are used to demonstrate the bandwidth sensitivity of coherence between power and velocity squared the zero frequency or d c value of the frequency response function for power is shown to be related to the system damping and system damping can be determined from an examination of this term several formulas are given for the calculation of system damping for different types of force input and degrees of freedom of a system also power transfer is associated with the zero frequency term of the frequency response function for power and other frequencies are associated with power fluctuations given the mobility functions of a system the power transfer and effective damping can be determined for any force bandwidth by the formulas given in this paper

numerical analysis of a finite element scheme for the approximation of harmonic maps into surfaces this article studies the numerical approximation of harmonic maps mto surfaces i e critical pomts for the dirichlet energy among weakly differentiable vector fields that are constrained to attain their pointwise values in a given manifold an iterative algorithm that is based on a linearization of the constraint about the current iterate at the nodes of a triangulation is devised and its global convergence to a discrete harmonic map is proved under general conditions weak accumulation of discrete harmonic maps at harmonic maps as discretization parameters tend to zero is established in two dimensions under certain assumptions on the underlying sequence of triangulations numerical simulations illustrate the performance of the algorithm for curved domains

flux vector splitting algorithm for chain rule conservation law form a flux vector splitting algorithm with newton raphson iteration was developed for the full compressible navier stokes equations cast in chain rule conservation law form the algorithm is intended for problems with deforming spatial domains and for problems whose governing equations cannot be cast in strong conservationlaw form the usefulness of the algorithm for such problems was demonstrated by applying it to analyze the unsteady two and three dimensional flows inside one combustion chamber of a wankel engine under nonfiring conditions solutions were obtained to examine the algorithm in terms of conservation error robustness and ability to handle complex flows on time dependent grid systems

brownian motion and the formation of singularities in the heat flow for harmonic maps we develop a general framework for a stochastic interpretation of certain nonlinear pdes on manifolds the linear operation of takin expectations is replaced by the concept of martingale means namely the notion of deterministic starting points of martingales with respect to the levi civita connection ending up at a prescribed state we formulate a monotonicity condition for the riemannian quadratic variation of such martingales that allows us to turn smallness of the quadratic variation into a priori gradient bounds for solutions of the nonlinear heat equation such estimates lead to simple criteria for blow ups in the nonlinear heat flow for harmonic maps with small initial energy

stability and asymptotics in nematic liquid crystals under a small dirichlet data and a non constant magnetic field abstract we consider the stability of a critical point and asymptotics of the minimizers of the free energy functional with a small dirichlet boundary data under a non constant exterior magnetic field in nematic liquid crystals in the author s previous papers we studied the stability of a critical point under the more general hypotheses but we had to assume the curl free condition on the critical point for technical reason however in this paper without the curl free condition we can get the similar result in the special case where the elastic coefficients are equal

correlation of power variables normalized results abstract correlation of fluctuating power input to a system and a fluctuating system field variable squared was examined in reference 1 in this paper the power correlation function is normalized for gaussian field variables and is shown to be the product of two normalized field correlation function and a weighting factor which is dependent upon statistics of force velocity and power at a driving point experiments on a rlc circuit validated results of derivations given in this paper and that given in reference 1 several relationships are derived in this paper associated with the force excitation of a structure and power flow at a driving point one gives the relationship between the variance of power mean power flow and the variances of force and velocity at a driving point another equation shows the mean power transferred for wide band random force is equal to the value of the impulse response function at zero time multiplied by the mean square value of the driving force

removability of singular sets of harmonic maps it is proved that a harmonic map with small energy and the monotonicity property is smooth if its singular set is rectifiable and has a finite uniform density moreover the monotonicity property holds if the singular set has a lower dimension or its gradient has higher integrability this work generalizes the results in cl df lg12 which were proved under the assumption that the singular sets are isolated points or smooth submanifolds

partial regularity for weak heat flows into spheres in this paper we show that a weak heat flow of harmonic maps from a compact riemannian manifold possibly with boundary into a sphere satisfying the monotonicity inequality and the energy inequality is regular off a closed set of m dimensional hausdorff measure zero

numerical methods for p harmonic flows and applications to image processing we propose in this paper an alternative approach for computing p harmonic maps and flows instead of solving a constrained minimization problem on sn 1 we solve an unconstrained minimization problem on the entire space of functions this is possible using the projection on the sphere of any arbitrary function then we show how this formulation can be used in practice for problems with both isotropic and anisotropic diffusion with applications to image processing using a new finite difference scheme

an elementary partial regularity proof for vector valued obstacle problems soit r n et m r n des ensembles ouverts bornes on suppose n 3 n 2 et on requiert que la frontiere de m est une hyper surface lisse de classe c 2 l espace de fonction h 1 2 m des fonctions de comparaison consiste en toutes les fonctions de sobolev v h 1 2 r n avec la propriete v x m pour presque tous les points x dans si u h 1 2 m minimise localement l energie alors il y a un sous ensemble ouvert 0 de tel que u c 1 0 r n pour tout 0 1 h n 2 0 0 et x 0 si et seulement si lim 1 0 r 2 n br x du 2 dz 0

improved partial regularity for manifold constrained minimisers of subquadratic energies we consider minimising p harmonic maps from three dimensional domains to the real projective plane for 1 p 2 these maps arise as least energy configurations in variational models for nematic liquid crystals we show that the singular set of such a map decomposes into a 1 dimensional set which can be physically interpreted as a non orientable line defect and a locally finite set i e a collection of point defects

the singular set of minima of integral functionals in this paper we provide upper bounds for the hausdorff dimension of the singular set of minima of general variational integrals open image in new window where f is suitably convex with respect to dv and holder continuous with respect to x v in particular we prove that the hausdorff dimension of the singular set is always strictly less than n where open image in new window

quaternionic maps between hyperkahler manifolds quaternionic maps q maps between hyperkahler manifolds are quaternionic analogue of cauchy riemann equations between kahler manifolds we provide a necessary and sufficient condition on when a quaternionic map becomes holomorphic with respect to some complex structures in the hyperkahler 2 spheres and give examples of q maps which cannot be holomorphic when the domain is real 4 dimensional we analyze the structure of the blow up set of a sequence of q maps and show that the singular set of a stationary q map is h1 rectifiable

on the regularity of harmonic functions and spherical harmonic maps defined on lattices abstract a growth lemma for certain discrete symmetric laplacians defined on a lattice z d zd rd with spacing is proved the lemma implies a de giorgi theorem that the harmonic functions for these laplacians are equi holder continuous 0 these results are then applied to establish regularity properties for the harmonic maps defined on zd and taking values in an n dimensional sphere sn uniform in questions of the convergence 0 and the dirichlet problem for these discrete harmonic maps are also addressed

partial regularity for stationary harmonic maps at a free boundary let and be smooth riemannian manifolds of the dimension n 2 with nonempty boundary and compact without boundary we consider stationary harmonic maps u h 1 with a free boundary condition of the type u given a submanifold we prove partial boundary regularity namely sing u 0 a result that was until now only known in the interior of the domain see b the key of the proof is a new lemma that allows an extension of u by a reflection construction once the partial regularity theorem is known it is possible to reduce the dimension of the singular set further under additional assumptions on the target manifold and the submanifold

on a fractional ginzburg landau equation and 1 2 harmonic maps into spheres this paper is devoted to the asymptotic analysis of a fractional version of the ginzburg landau equation in bounded domains where the laplacian is replaced by an integro differential operator related to the square root laplacian as defined in fourier space in the singular ginzburg landau limit we show that solutions with uniformly bounded energy converge weakly to sphere valued 1 2 harmonic maps i e the fractional analogues of the usual harmonic maps in addition the convergence holds in smooth functions spaces away from a n 1 rectifiable closed set of finite n 1 hausdorff measure the proof relies on the representation of the square root laplacian as a dirichlet to neumann operator in one more dimension and on the analysis of a boundary version of the ginzburg landau equation besides the analysis of the fractional ginzburg landau equation we also give a general partial regularity result for stationary 1 2 harmonic maps in arbitrary dimension

regularity of a fourth order nonlinear pde with critical exponent in this paper we demonstrate the regularity of minimizers for a variational problem a special case of which arises in spectral theory and conformal geometry the associated euler lagrange equation is fourth order semilinear the leading term is the bilaplacian and lower order terms appear at critical powers

the singular set of stationary solution for semilinear elliptic equations with supercritical growth abstract in this paper we are concerned with the partial regularity of the stationary solution to semilinear elliptic equations for almost all supercritical exponents we improve the upper bounds of the hausdorff dimension of the singular set which are derived by pacard to the optimal ones

remarks on the regularity of biharmonic maps in four dimensions we study intrinsic biharmonic maps on a four dimensional domain into a smooth compact riemannian manifold we prove a partial regularity result without the assumption that the second derivatives are square integrable

neohookean deformations of annuli existence uniqueness and radial symmetry let mathbb x x in mathbb r 2 r x r and mathbb y y in mathbb r 2 r ast y r ast be annuli in the plane we consider the class fancyscript f mathbb x mathbb y of all orientation preserving homeomorphisms h mathbb x overset textnormal tiny onto longrightarrow mathbb y in the sobolev space fancyscript w 1 2 mathbb x mathbb y which keep the boundary circles in the same order this means that lim x searrow r h x r ast and lim x nearrow r h x r ast we study the neohookean energy integral mathcal e h int limits mathbb x dh 2 phi rm det dh quad rm for h in fancyscript f mathbb x mathbb y quad quad quad 1 where phi in fancyscript c infty 0 infty is positive and strictly convex we assume in addition that the function psi z 1 ddot phi z and its derivative extend continuously to 0 with 0 0 then we prove

harmonic maps from noncompact riemannian manifolds with non negative ricci curvature outside a compact set in this paper we prove the uniqueness and existence of harmonic maps of finite energy from a complete noncompact riemannian manifold m g with sobolev constant s2 m 0 and ricci curvature ric m 0 outside some compact subset into a complete manifold of nonpositive curvature or a regular ball in particular we prove the uniqueness and existence of bounded harmonic functions on m g

phase transition for potentials of high dimensional wells for a potential function f w r k rc that attains its global minimum value at two disjoint compact connected submanifolds n in r k we discuss the asymptotics as 0 of minimizers u of the singular perturbed functional e u d r jruj 2 c 1 2 f u dx under suitable dirichlet boundary data g w r k in the expansion of e u with respect to 1 we identify the first order term by the area of the sharp interface between the two phases an area minimizing hypersurfacea and the energyc f of minimal connecting orbits between n c and n and the zerothorder term by the energy of minimizing harmonic maps into n both under the dirichlet boundary condition on and a very interesting partially constrained boundary condition on the sharp interfacea 2011 wiley periodicals inc

the uniqueness of tangent cones for yang mills connections with isolated singularities we proved a uniqueness theorem of tangent connections for a yang mills connection with an isolated singularity with a quadratic growth of the curvature at the singularity we also obtained control over the rate of the asymptotic convergence of the connection to the tangent connection if furthermore the connection is stationary or the tangent connection is integrable with a stronger result in the latter case there are parallel results for the cones at infinity of a yang mills connection on an asymptotically flat manifold we also gave an application of our methods to the yang mills flow and proved that the yang mills flow exists for all time and has asymptotic limit if the initial value is close to a smooth local minimizer of the yang mills functional

some regularity results for p harmonic mappings between riemannian manifolds abstract let m be a c 2 smooth riemannian manifold with boundary and n a complete c 2 smooth riemannian manifold we show that each stationary p harmonic mapping u m n whose image lies in a compact subset of n is locally c 1 for some 0 1 provided that n is simply connected and has non positive sectional curvature we also prove similar results for minimizing p harmonic mappings with image being contained in a regular geodesic ball moreover when m has non negative ricci curvature and n is simply connected with non positive sectional curvature we deduce a gradient estimate for c 1 smooth weakly p harmonic mappings from which follows a liouville type theorem in the same setting

energy concentration for almost harmonic maps and the willmore functional let be an open domain in 3 or 4 and n a smooth compact riemannian manifold we consider the dirichlet energy e u for maps u n and its negative l2 gradient the tension field u we study sequences of maps ui n with open image in new window if the maps are sufficiently regular we find strong h1 subconvergence away from a generalized submanifold in if the limit map is regular too we can estimate a willmore type energy of this generalized submanifold

on global singularities of sobolev mappings we define various invariants for sobolev mappings defined between manifolds which are stable under perturbation with respect to the strong sobolev topology we show that these invariants classify various types of global singularities of sobolev maps these invariants are used to give a simple characterization of the strong closure of the set of smooth maps in the sobolev space

rigidity of teichmuller space we prove the holomorphic rigidity conjecture of teichmuller space which loosely speaking states that the action of the mapping class group uniquely determines the teichmuller space as a complex manifold the method of proof is through harmonic maps we prove that the singular set of a harmonic map from a smooth n dimensional riemannian domain to the weil petersson completion overline mathcal t of teichmuller space has hausdorff dimension at most n 2 and moreover u has certain decay near the singular set combining this with the earlier work of schumacher siu and jost yau we provide a proof of the holomorphic rigidity of teichmuller space in addition our results provide as a byproduct a harmonic maps proof of both the high rank and the rank one superrigidity of the mapping class group proved via other methods by farb masur and yeung

regularity of harmonic maps with prescribed singularities in this paper we studied the regularity problem for harmonic maps into hyperbolic spaces with prescribed singularities along codimension two submanifolds this is motivated from one of hawking s conjectures on the uniqueness of kerr solutions among all axially symmetric asymptotically flat stationary solutions to the vacuum einstein equation in general relativity

on the evolution of harmonic maps in higher dimensions on etablit des resultats de regularite partielle et l existence de solutions regulieres globales pour le probleme d evolution pour des applications harmoniques avec des donnees petites

partially constrained boundary conditions with energy minimizing mappings on considere la regularite a la frontiere pour une application minimisant l energie u m n pour deux types de conditions aux limites frontiere libre et condition limite partiellement contrainte

biaxial escape in nematics at low temperature abstract in the present work we study minimizers of the landau de gennes free energy in a bounded domain r 3 we prove that at low temperature minimizers do not vanish even for topologically non trivial boundary conditions this is in contrast with a simplified ginzburg landau model for superconductivity studied by bethuel brezis and helein merging this with an observation of canevari we obtain as a corollary the occurrence of biaxial escape the tensorial order parameter must become strongly biaxial at some point in in particular while it is known that minimizers cannot be purely uniaxial we prove the much stronger and physically relevant fact that they lie in a different homotopy class

compactness theorems for coupled yang mills fields in this paper we consider coupled yang mills fields on vector bundle e over compact riemannian manifold m under appropriate conditions on the curvature and the higgs field two compactness theorems are proved

an l p regularity theory for harmonic maps motivated by the harmonic map heat flow we consider maps between riemannian manifolds such that the tension field belongs to an lp space under an appropriate smallness condition a certain degree of regularity follows for suitable solutions of the harmonic map heat flow we have a partial regularity result as a consequence

parabolic theory as a high dimensional limit of elliptic theory the aim of this article is to show how certain parabolic theorems follow from their elliptic counterparts this technique is demonstrated through new proofs of five important theorems in parabolic unique continuation and the regularity theory of parabolic equations and geometric flows specifically we give new proofs of an l 2 carleman estimate for the heat operator and the monotonicity formulas for the frequency function associated to the heat operator the two phase free boundary problem the flow of harmonic maps and the mean curvature flow the proofs rely only on the underlying elliptic theorems and limiting procedures belonging essentially to probability theory in particular each parabolic theorem is proved by taking a high dimensional limit of the related elliptic result

monotonicity formulas for extrinsic triharmonic maps and the triharmonic lane emden equation abstract we derive monotonicity formulas and e regularity results for extrinsic triharmonic maps and triharmonic lane emden equations as an application we prove partial regularity results for both types of equations in the supercritical regime

singular points of harmonic maps from 4 dimensional domains into 3 spheres in this article we show that if a stable stationary harmonic map u from a domain in r4 into s3 has an isolated singular point then the mapping degree deg u of u at is 1 or 1 furthermore the complete characterization of stable stationary tangent maps from b4 to s3 is given