Related papers: Series, Index and Threshold for Random 2D Composit…
We consider the problem of isotropic effective conductivity $\sigma_e(\sigma_1,\ldots,\sigma_n)$ in two-dimensional three- and four-phase symmetric composites with a partial isotropic conductivity $\sigma_j$ of the $j$-th phase. The upper…
We show that the compositions of positive integers may be interpreted in terms of powers of some power series, over arbitrary commutative ring. As consequences, several closed formulas for the compositions as well as for the generalized…
We consider a large number of randomly dispersed spherical, identical, perfectly conducting inclusions (of infinite conductivity) in a bounded domain. The host medium's conductivity is finite and can be inhomogeneous. In the dilute limit,…
In this article we recover the distribution function (and possible density) of an arbitrary random variable that is subject to an additive measurement error. This problem is also known as deconvolution and has a long tradition in…
We consider the fluctuation conductivity in the critical region of a disorder induced quantum phase transition in layered d-wave superconductors. We specifically address the fluctuation contribution to the system's conductivity in the limit…
This paper provides two characterizations of regularity for near-vector spaces: first, by expressing them as a direct sum of vector spaces over division rings formed by distributive elements; second, by expressing their dimension in term of…
We prove the tightness of radially-symmetric solutions to 2D aggregation-diffusion equations, where the pairwise attraction force is possibly degenerate at large distance. We first reduce the problem into the finiteness of a time integral…
A selection of open problems in the theory of composites is presented. Particular attention is drawn to the question of whether two-dimensional, two-phase, composites with general geometries have the same set of possible effective tensors…
We present large scale simulations of the diffusion constant $D$ of a random composite consisting of aligned platelets with aspect ratio $a/b>>1$ in a matrix (with diffusion constant $D_0$) and find that $D/D_0 = 1/(1+ c_1 x + c_2 x^2)$,…
We propose a "decomposition method" to prove non-asymptotic bound for the convergence of empirical measures in various dual norms. The main point is to show that if one measures convergence in duality with sufficiently regular observables,…
The near-threshold clustering phenomenon is well understood by the low-energy universality, for shallow bound states below the threshold. Nevertheless, the characteristics of resonances slightly above the threshold still lack thorough…
The conductance of a normal-metal mesoscopic system in proximity to superconducting electrode(s) is calculated. The normal-metal part may have a general geometry, and is described as a ``circuit'' with ``leads'' and ``junctions''. The…
Reproducibility is essential to reliable scientific discovery in high-throughput experiments. In this work we propose a unified approach to measure the reproducibility of findings identified from replicate experiments and identify putative…
In the framework of the perturbation theory an expression suitable for calculation of the effective conductivity of 3-D inhomogeneous metals in uniform magnetic field $H$ is derived. For polycrystals of metals with closed Fermi surfaces in…
Based on a recent proposal [O.P. Sushkov, Phys. Rev. B 64, 155319 (2001)], we relate the quantum conductance through a sample in which electrons are strongly correlated to the persistent current of a large ring, composed of the sample and a…
We want to approximate general multivariate probability density functions by deterministic sample sets. For optimal sampling, the closeness to the given continuous density has to be assessed. This is a difficult challenge in multivariate…
We study certain properties of modules over 1-dimensional local integral domains. First, we examine the order of the conductor ideal and its expected relationship with multiplicity. Next, we investigate the reflexivity of certain…
The theory of weak localization is generalized for multilevel 2D systems taking into account intersubband scattering. It is shown that weak intersubband scattering which is negligible in a classical transport, affects strongly the…
The size estimation problem in electrical impedance tomography is considered when the conductivity is a complex number and the body is two-dimensional. Upper and lower bounds on the volume fraction of the unknown inclusion embedded in the…
A key optical parameter characterizing the existence of negative refraction in a thin layer of a composite material is the effective refractive index of an equivalent, homogenized layer with the same physical thickness as the initial…