homogenization of two phase elasto plastic composite materials and structures study of tangent operators cyclic plasticity and numerical algorithms we develop homogenization schemes and numerical algorithms for two phase elasto plastic composite materials and structures a hill type incremental formulation enables the simulation of unloading and cyclic loadings it also allows to handle any rate independent model for each phase we study the crucial issue of tangent operators elasto plastic or continuum versus algorithmic or consistent and anisotropic versus isotropic we apply two methods of extraction of isotropic tangent moduli we compare mathematically the stiffnesses of various tangent operators all rate equations are discretized in time using implicit integration we implemented two homogenization schemes mori tanaka and a double inclusion model and two plasticity models classical j 2 plasticity and chaboche s model with non linear kinematic and isotropic hardenings we consider composites with different properties and present several discriminating numerical simulations in many cases the results are validated against finite element fe or experimental data we integrated our homogenization code into the fe program abaqus using a user material interface umat a two scale procedure allows to compute realistic structures made of non linear composite materials within reasonable cpu time and memory usage examples are shown c 2002 elsevier science ltd all rights reserved

a remark on regularity criterion for the 3d hall mhd equations based on the vorticity in this paper we investigate the regularity criterion for the local in time classical solution to the three dimensional 3d incompressible hall magnetohydrodynamic equations hall mhd it is proved that the control of the vorticity alone can ensure the smoothness of the solution

global existence and asymptotic behavior for the 3d generalized hall mhd system abstract in this paper we consider the global existence for the 3d generalized hall mhd equations with fractional dissipative terms u and b under small initial data in the setting of sobolev norms with lower regularity for the global existence we enlarge the range of dissipative exponents from 1 7 6 to 1 3 2 which established in a recent work in addition the long time behavior and rates of decay for both the solutions and higher derivatives in different sobolev spaces are obtained by using the fourier splitting method which extends the previous work by chae and schonbek

on global existence energy decay and blow up criteria for the hall mhd system in this paper we obtain global existence and energy decay for 3d hall magnetohydrodynamics hall mhd system with u and b besides the classical energy method and besov space techniques the interpolating inequalities are crucial in the proof of decay estimates then two osgood type blow up criteria are established our results improve the corresponding theorems in 3 and 4 in addition we establish two beale kato majda blow up criterion for the generalized version of hall mhd with u and b 1

global wellposedness for hall mhd equations abstract this paper concerns the wellposedness problem of hall mhd system the mild solution of hall mhd equations exists globally in the nonhomogeneous lei lin space setting provided that the initial data satisfies u 0 x 1 x 0 b 0 x 1 x 0 min 2 4 where is the viscosity of the fluid and is the magnetic diffusion coefficient our global existence result covers rougher initial data and improves the previous results

global well posedness for navier stokes equations in critical fourier herz spaces abstract we prove the global well posedness for the 3d navier stokes equations in critical fourier herz spaces by making use of the fourier localization method and the littlewood paley theory the advantage of working in fourier herz spaces lies in that they are more adapted than classical besov spaces for estimating the bilinear paraproduct of two distributions with the summation of their regularity indexes exactly zero our result is an improvement of a recent theorem by lei and lin 2011 10

a finite strain incremental secant homogenization model for elasto plastic composites abstract this paper presents a finite strain extension of the incremental secant mean field homogenization mfh formulation for two phase elasto plastic composites the formulation of the local finite strain elasto plastic constitutive equations of each phase is based on a multiplicative decomposition of the deformation gradient as suggested by simo in computer methods in applied mechanics and engineering 99 1 61 112 1992 the latter has proposed algorithms which preserve the classical return mapping schemes of the infinitesimal theory by using principal kirchhoff stresses and logarithmic eigenvalues of the left elastic cauchy green strain relying on this property we show that by considering a quadratic logarithmic free energy and j2 flow theory at the local level infinitesimal strain incremental secant mfh is readily extended to finite strains the proposed formulation and corresponding numerical algorithms are then presented finally the predictions are illustrated with several numerical simulations which are verified against full field finite element simulations of composite cells demonstrating that the micro mechanically based approach is able to predict the influence of the micro structure and of its evolution on the macroscopic properties in a very cost effective manner

a regularity criterion for a generalized hall mhd system abstract this paper proves a regularity criterion for a 3d generalized hall mhd system in terms of velocity gradient in negative besov spaces

on the blow up criterion and small data global existence for the hall magnetohydrodynamics abstract in this paper we establish an optimal blow up criterion for classical solutions to the incompressible resistive hall magnetohydrodynamic equations we also prove two global in time existence results of the classical solutions for small initial data the smallness conditions of which are given by the suitable sobolev and the besov norms respectively although the sobolev space version is already an improvement of the corresponding result in 4 the optimality in terms of the scaling property is achieved via the besov space estimate the special property of the energy estimate in terms of b 2 1 s norm is essential for this result contrary to the usual mhd the global well posedness in the 2 1 2 dimensional hall mhd is wide open

on the temporal decay for the hall magnetohydrodynamic equations abstract we establish temporal decay estimates for weak solutions to the hall magnetohydrodynamic equations with these estimates in hand we obtain algebraic time decay for higher order sobolev norms of small initial data solutions

regularity criterion for the 3d hall magneto hydrodynamics abstract this paper studies the regularity problem for the 3d incompressible resistive viscous hall magneto hydrodynamic hall mhd system the kolmogorov 41 phenomenological theory of turbulence 14 predicts that there exists a critical wavenumber above which the high frequency part is dominated by the dissipation term in the fluid equation inspired by this idea we apply an approach of splitting the wavenumber combined with an estimate of the energy flux to obtain a new regularity criterion the regularity condition presented here is weaker than conditions in the existing criteria prodi serrin type criteria for the 3d hall mhd system

global well posedness and ill posedness for the navier stokes equations with the coriolis force in function spaces of besov type abstract we consider the initial value problems for the navier stokes equations in the rotational framework we introduce function spaces b p q s r 3 of besov type and prove the global in time existence and the uniqueness of the mild solution for small initial data in our space b 1 2 1 r 3 near bmo 1 r 3 furthermore we also discuss the ill posedness for the navier stokes equations with the coriolis force which implies the optimality of our function space b 1 2 1 r 3 for the global well posedness

a remark on the blow up criterion for the 3d hall mhd system in besov spaces abstract in this paper we consider the three dimensional hall magnetohydrodynamic system and show that if the velocity and the magnetic fields belong to some critical besov spaces on 0 t then the solution can be extended smoothly beyond t this improves previous results

regularity criteria and small data global existence to the generalized viscous hall magnetohydrodynamics in this paper we establish the regularity criteria of solutions to the three space dimensions generalized viscous hall magnetohydrodynamics moreover we also prove that there exist classical solutions globally in time to the generalized viscous hall mhd if the initial data is small enough or the fractional laplacian dissipation powers and are suitably large these results are some improvements of very recent work chae and lee 2014 established by chae and lee

solving coupled composite monotone inclusions by successive fejer approximations of their kuhn tucker set we propose a new class of primal dual fejer monotone algorithms for solving systems of composite monotone inclusions our construction is inspired by a framework used by eckstein and svaiter for the basic problem of finding a zero of the sum of two monotone operators at each iteration points in the graph of the monotone operators present in the model are used to construct a half space containing the kuhn tucker set associated with the system the primal dual update is then obtained via a relaxed projection of the current iterate onto this half space an important feature that distinguishes the resulting splitting algorithms from existing ones is that they do not require prior knowledge of bounds on the linear operators involved or the inversion of linear operators

beale kato madja type criteria of smooth solutions to 3d hall mhd flows in this article we study the initial value problem for the impressible hall mhd flows in three space dimensions several beale kato madja type blow up criteria of smooth solutions in term of the vorticity in homogeneous besov space are established

global mild solutions of navier stokes equations we establish a global well posedness of mild solutions to the three dimensional incompressible navier stokes equations if the initial data are in the space x 1 defined by x 1 f e d r 3 3 1 f d and if the norms of the initial data in x 1 are bounded exactly by the viscosity coefficient

variable metric quasi fejer monotonicity the notion of quasi fejer monotonicity has proven to be an efficient tool to simplify and unify the convergence analysis of various algorithms arising in applied nonlinear analysis in this paper we extend this notion in the context of variable metric algorithms whereby the underlying norm is allowed to vary at each iteration applications to convex optimization and inverse problems are demonstrated

rate of convergence analysis of decomposition methods based on the proximal method of multipliers for convex minimization this paper presents two classes of decomposition algorithms based on the proximal method of multipliers pmm introduced in the mid 1970s by rockafellar for convex minimization we first show that

regularity criteria for the incompressible hall magnetohydrodynamic equations abstract we establish some new regularity criteria for the three dimensional incompressible hall magnetohydrodynamic equations

a new regularity criterion for the 3d generalized hall mhd system with β 12 1 abstract in this paper we consider the generalized hall mhd system in dimension three a new regularity criterion is established for 1 2 1

a proximal based decomposition method for convex minimization problems this paper presents a decomposition method for solving convex minimization problems at each iteration the algorithm computes two proximal steps in the dual variables and one proximal step in the primal variables we derive this algorithm from rockafellar s proximal method of multipliers which involves an augmented lagrangian with an additional quadratic proximal term the algorithm preserves the good features of the proximal method of multipliers with the additional advantage that it leads to a decoupling of the constraints and is thus suitable for parallel implementation we allow for computing approximately the proximal minimization steps and we prove that under mild assumptions on the problem s data the method is globally convergent and at a linear rate the method is compared with alternating direction type methods and applied to the particular case of minimizing a convex function over a finite intersection of closed convex sets

a primal dual dynamical approach to structured convex minimization problems abstract in this paper we propose a primal dual dynamical approach to the minimization of a structured convex function consisting of a smooth term a nonsmooth term and the composition of another nonsmooth term with a linear continuous operator in this scope we introduce a dynamical system for which we prove that its trajectories asymptotically converge to a saddle point of the lagrangian of the underlying convex minimization problem as time tends to infinity in addition we provide rates for both the violation of the feasibility condition by the ergodic trajectories and the convergence of the objective function along these ergodic trajectories to its minimal value explicit time discretization of the dynamical system results in a numerical algorithm which is a combination of the linearized proximal method of multipliers and the proximal admm algorithm