Related papers: Effective conductivity of a random suspension of h…
Consider a 2D composites with non-overlapping equal inclusions imbedded in a host material of the normalized unit conductivity. The conductivity of inclusions takes two values $\sigma_1$ and $\sigma_2$ with the probabilities $p$ and $1-p$,…
We determine the effective conductivity of a two-dimensional composite consisting of a doubly periodic array of identical circular cylinders within a homogeneous matrix. We obtain an exact analytic expression for the effective conductivity…
A conducting two-dimensional periodic composite of two anisotropic phases with anisotropic, not necessarily symmetric, conductivity tensors is considered. By finding approximate representations for the relevant operators, an approximation…
Iterative Fast Fourier Transform methods are useful for calculating the fields in composite materials and their macroscopic response. By iterating back and forth until convergence, the differential constraints are satisfied in Fourier…
We study concentration inequalities for structured weighted sums of random data, including (i) tensor inner products and (ii) sequential matrix sums. We are interested in tail bounds and concentration inequalities for those structured…
Effective conductivity of a 2D composite corresponding to the regular hexagonal arrangement of superconducting disks is expressed in the form of a long series in the volume fraction of ideally conducting disks. According to our calculations…
In the framework of the perturbation theory an expression suitable for calculation of the effective conductivity of 3-D inhomogeneous metals is derived. Formally, the final expression is an exact result, however, a function written as a…
In the work, a modified effective medium theory is constructed for calculating the effective properties of thermoelectric composites with different values of percolation thresholds. It is shown that even at concentrations beyond the…
Two-phase composites with non-overlapping inclusions randomly embedded in matrix are investigated. A straight forward approach is applied to estimate the effective properties of random 2D composites. First, deterministic boundary value…
Jeffery's equation with diffusion is widely used to predict the motion of concentrated fiber suspensions in flows with low Reynold's numbers. Unfortunately, the evaluation of the fiber orientation distribution can require excessive…
A composite conductive material, which consists of fibers of a high conductivity in a matrix of low conductivity, is discussed. The effective conductivity of the system considered is calculated in Clausius-Mossotti approximation. Obtained…
In this work we continue the investigation of different approaches to conception and modeling of composite materials. The global method we focus on, is called 'stochastic homogenization'. In this approach, the classical deterministic…
The main goal of this paper is to present the application of structural sums, mathematical objects originating from the computational materials science, in construction of a feature space vector of 2D random composites simulated by…
Effective conductivity of a 2D random composite is expressed in the form of long series in the volume fraction of ideally conducting disks. The problem of a {\it direct} reconstruction of the critical index for superconductivity from the…
We investigate the effective thermal conductivity of a two-phase composite with thermal resistance at the interface. The composite is obtained by introducing into an infinite homogeneous matrix a periodic set of inclusions of a different…
A method is presented for approximating the effective conductivity of composite media with thin interphase regions, which is exact to first order in the interphase thickness. The approximations are computationally efficient in the sense the…
We present an effective-medium model for calculating the frequency-dependent effective permittivity $\epsilon(\omega)$ and permeability $\mu(\omega)$ of metamaterial composites containing spherical particles with arbitrary permittivity and…
We investigate the dispersion of a passive scalar such as the concentration of a chemical species, or temperature, in homogeneous bubbly suspensions, by determining an effective diffusivity tensor. Defining the longitudinal and transverse…
We consider the conductivity tensor for composite fermions in a close to half-filled Landau band in the temperature regime where the scattering off the potential and the trapped gauge field of random impurities dominates. The Boltzmann…
We propose an improved effective-medium theory to obtain the concentration dependence of the viscosity of particle suspensions at arbitrary volume fractions. Our methodology can be applied, in principle, to any particle shape as long as the…