Related papers: Optimal anisotropic three-phase conducting composi…
We investigate the behavior of shear viscosity in the presence of small anisotropy and a finite chemical potential. First, we construct an anisotropic Reissner Nordstr{\"o}m blackbrane in 5 dimensions in a simple Einstein-Maxwell theory…
Electromagnetic materials with a uniaxial effective permittivity tensor, characterized by its transverse ($\epsilon_\perp$) and axial ($\epsilon_\parallel$) components, play a central role in the design of advanced photonic and…
For a composite containing one isotropic elastic material, with positive Lame moduli, and void, with the elastic material occupying a prescribed volume fraction $f$, and with the composite being subject to an average stress, ${{…
The purpose of this paper is to set out optimal gradient estimates for solutions to the isotropic conductivity problem in the presence of adjacent conductivity inclusions as the distance between the inclusions goes to zero and their…
The paper investigates two-phase microstructures of optimal 3D composites that store minimal elastic energy in a given strain field. The composite is made of two linear isotropic materials which differ in elastic moduli and self-strains. We…
A methodology is presented for bounding all higher moments of the local hydrostatic stress field inside random two phase linear thermoelastic media undergoing macroscopic thermomechanical loading. The method also provides a lower bound on…
We present an alternative derivation of upper-bounds for the bulk modulus of both two-dimensional and three-dimensional cellular materials. For two-dimensional materials, we recover exactly the expression of the Hashin-Shtrikman (HS)…
Two-phase heterogeneous materials arising in a variety of natural and synthetic situations exhibit a wide-variety of microstructures and thus display a broad-spectrum effective physical properties. Given that such properties of disordered…
Relying on our theoretical approach for the superconducting critical state problem in 3D magnetic field configurations, we present an exhaustive analysis of the electrodynamic response for the so-called longitudinal transport problem in the…
We consider the inverse conductivity problem in a strictly convex domain whose boundary is not known. Usually the numerical reconstruction from the measured current and voltage data is done assuming the domain has a known fixed geometry.…
We propose and analyze a combined finite volume--nonconforming finite element scheme on general meshes to simulate the two compressible phase flow in porous media. The diffusion term, which can be anisotropic and heterogeneous, is…
We propose a decomposition of constitutive relations into crack-driving and persistent portions, specifically designed for materials with anisotropic/orthotropic behavior in the phase field approach to fracture to account for the…
The effective transport coefficients and figure of merit ZT for anisotropic systems are derived from a macroscopic formalism. The full tensorial structure of the transport coefficients and the effect of the sample boundaries are included.…
Shrinking CMOS interconnect dimensions to the nanometer scale intensifies electron scattering at surfaces, interfaces, and grain boundaries, causing severe conductivity loss and challenging copper-based designs. Here we present a…
Macroscopic assemblies of one- and two-dimensional materials promise to translate nanoscale electronic properties into device-scale performance, yet the microscopic principles governing charge transport in such networks remain unresolved.…
This paper is concerned with six variational problems and their mutual connections: The quadratic Monge-Kantorovich optimal transport, the Schr\"odinger problem, Brenier's relaxed model for incompressible fluids, the so-called Br\"odinger…
We present numerical reconstructions of anisotropic conductivity tensors in three dimensions, from knowledge of a finite family of power density functionals. Such a problem arises in the coupled-physics imaging modality Ultrasound Modulated…
We study angular-dependent magnetoresistance in a low $T_c$ layered cuprate Bi$_{2.15}$Sr$_{1.9}$CuO$_{6+\delta}$. The low $T_c$ ~ 4 K allows complete suppression of superconductivity by modest magnetic fields and facilitate accurate…
In this chapter of the book entitled, "Extending the Theory of Composites to Other Areas of Science" [edited by Graeme W. Milton, 2016] we give a rigorous derivation of the field equation recursion method in the abstract theory of…
We characterize the lower and upper attainability of the Wiener bound (also known as the conductive analogue of the Voigt-Reuss-Hill bound in elasticity theory) for singularly distributed conductive material mixtures. For the lower…