Related papers: On the effective conductivity of flat random two-p…
A model is developed for the transport of heat and solute in a system of double-diffusive layers under astrophysical conditions (viscosity and solute diffusivity low compared with the thermal diffusivity). The process of formation of the…
In this study, we develop a probabilistic approach to map the parametric uncertainty to the output state uncertainty in first-order hyperbolic conservation laws. We analyze this problem for nonlinear immiscible two-phase transport in…
We study the effect of nonuniform transverse couplings on a quasi-one dimensional superconductor. We show that inhomogeneous couplings quite generally increase the superconducting (pairing) gap relative to the uniform system, but that…
A spinless two-band model is studied in infinite dimension limit. Starting from the atomic limit, the formal exact solution of the model is obtained by means a perturbative treatment of the hopping and hybridisation terms. The model is…
We consider a two-dimensional singularly perturbed transmission problem with two different diffusion coefficients, in a domain with smooth (analytic) boundary. The solution will contain boundary layers only in the part of the domain where…
The statistical mechanics of flexible two-dimensional surfaces (membranes) appears in a wide variety of physical settings. In this talk we discuss the simplest case of fixed-connectivity surfaces. We first review the current theoretical…
This work investigates finite element approximations for a general class of elliptic hemivariational inequalities arising in semipermeable media. The proposed model incorporates non-isotropic and heterogeneous diffusion coefficients,…
This article concerns the mathematical justification of an averaged system of partial differential equations governing the evolution of a two-phase mixture of compressible ideal fluids, with viscosity and without conductivity, in space…
We study a diffusion model of phase field type, consisting of a system of two partial differential equations encoding the balances of microforces and microenergy; the two unknowns are the order parameter and the chemical potential. By a…
We consider the conductivity $\sigma_{xx}$ of graphene with negligible intervalley scattering at half filling. We derive the effective field theory, which, for the case of a potential disorder, is a symplectic-class $\sigma$-model including…
We consider equilibrium statistical mechanics of a simplified model for the ideal conductor electrode in an interface contact with a classical semi-infinite electrolyte, modeled by the two-dimensional Coulomb gas of pointlike $\pm$ unit…
We prove strong convergence to singular limits for a linearized fully inhomogeneous Stefan problem subject to surface tension and kinetic undercooling effects. Different combinations of $\sigma \to \sigma_0$ and $\delta \to\delta_0$, where…
This paper presents and analyses a Constraint Energy Minimization Generalized Multiscale Finite Element Method (CEM-GMsFEM) for solving single-phase non-linear compressible flows in highly heterogeneous media. The construction of CEM-GMsFEM…
We solve elliptic systems of equations posed on highly heterogeneous materials. Examples of this class of problems are composite structures and geological processes. We focus on a model problem which is a second-order elliptic equation with…
Homogenization method is used to analyse the equivalent behavior of transient flow of a passive solute through highly heterogeneous porous media. The flow is governed by a coupled system which includes an elliptic equation and a linear…
A non-equilibrium theory of optical conductivity of dirty-limit superconductors and commensurate charge density wave is presented. We discuss the current response to different experimentally relevant light-field probe pulses and show that a…
We study the effective behavior of random, heterogeneous, anisotropic, second order phase transitions energies that arise in the study of pattern formations in physical-chemical systems. Specifically, we study the asymptotic behavior, as…
We study the optical conductivity of a pristine two-dimensional electron system near an Ising-nematic quantum critical point. We discuss the relation between the frequency scaling of the conductivity and the shape of the Fermi surface,…
The effective quasistatic conductivity of composite polymeric electrolytes is studied in terms of a hard-core--penetrable-layer model. Used to incorporate the interface phenomena (such as amorphization of the polymer matrix around filler…
High-frequency (HF) conductivity ($\sigma_{hf}$) measured by an acoustical method has been studied in GaAs/AlGaAs heterostructures in a linear and nonlinear regime on acoustic power. It has been shown that in the quantum Hall regime at…