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Network Approximation in the Limit of¶Small Interparticle Distance of the¶Effective Properties of a High-Contrast¶Random Dispersed Composite
Abstract We consider a high-contrast two-phase composite such as a ceramic/polymer composite or a fiberglass composite. Our objective is to determine the dependence of the effective conductivity (orExpand
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Generalized Clausius–Mossotti Formula for Random Composite with Circular Fibers
An important area of materials science is the study of effective dielectric, thermal and electrical properties of two phase composite materials with very different properties of the constituents. TheExpand
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Large time asymptotics of solutions to a model combustion system with critical nonlinearity
We consider a model semilinear reaction-diffusion system with cubic nonlinear reaction terms and small spatially decaying initial data on R1. The model system is motivated by the thermal-diffusiveExpand
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Polyharmonic homogenization, rough polyharmonic splines and sparse super-localization
We introduce a new variational method for the numerical homogenization of divergence form elliptic, parabolic and hyperbolic equations with arbitrary rough (L^∞) coefficients. Our method does notExpand
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Increase and Decrease of the Effective Conductivity of Two Phase Composites due to Polydispersity
We present a two-dimensional mathematical model of a composite material with conducting inclusions (fibers) embedded in a matrix. Our main objective is to study how polydispersity (two differentExpand
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On uniqueness of vector-valued minimizers of the Ginzburg-Landau functional in annular domains
Abstract. Consider a class of Sobolev functions satisfying a prescribed degree condition on the boundary of a planar annular domain. It is shown that, within this class, the Ginzburg-LandauExpand
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Solutions with vortices of a semi-stiff boundary value problem for the Ginzburg–Landau equation
We study solutions of the 2D Ginzburg-Landau equation 1uC 1 "2 u.juj 2 1/D 0 subject to "semi-stiff" boundary conditions: Dirichlet conditions for the modulus,juj D 1, and homogeneous NeumannExpand
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Introduction to the Network Approximation Method for Materials Modeling
Preface 1. Review of mathematical notions used in the analysis of transport problems in dense-packed composite materials 2. Background and motivation for introduction of network models 3. NetworkExpand
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Effective shear viscosity and dynamics of suspensions of micro-swimmers from small to moderate concentrations
Recently, there has been a number of experimental studies convincingly demonstrating that a suspension of self-propelled bacteria (microswimmers in general) may have an effective viscosityExpand
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Ginzburg-Landau minimizers in perforated domains with prescribed degrees
This is a long and unpublished version of the paper "Ginzburg-Landau minimizers with prescribed degrees. Capacity of the domain and emergence of vortices" (J. Funct. Anal. 2006). It contains detailedExpand
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