相关论文: The Clausius-Mossotti formula
This review is devoted to the large-scale rheology of suspensions of rigid particles in Stokes fluid. After describing recent results on the definition of the effective viscosity of such systems in the framework of homogenization theory, we…
In this expository article, we present a systematic formal derivation of the Kubo formula for the linear-response current due to a time-harmonic electric field applied to non-interacting, spinless charged particles in a finite volume in the…
We consider fluctuations of the dissipated energy in nonlinear driven diffusive systems subject to bulk dissipation and boundary driving. With this aim, we extend the recently-introduced macroscopic fluctuation theory to nonlinear driven…
In this paper, we propose some algorithms for the simulation of the distribution of certain diffusions conditioned on terminal point. We prove that the conditional distribution is absolutely continuous with respect to the distribution of…
Consider a colloidal suspension of rigid particles in a steady Stokes flow. In a celebrated work, Einstein argued that in the regime of dilute particles the system behaves at leading order like a Stokes fluid with some explicit effective…
This paper is accountable only to explicitly stated physical assumptions and strict logical inference. Its goal is to run a rigorous stress test of second-law claims within the Clausius framework. We work directly with \textbf{Clausius's…
We present in this paper an analytical model for a cold bosonic gas on an optical lattice (with densities of the order of 1 particle per site) targeting the critical regime of the Bose - Einstein Condensate superfluid - Mott insulator…
This short note provides explicit solutions to the linearized Boussinesq equations around the stably stratified Couette flow posed on $\mathbb{T}\times\mathbb{R}$. We consider the long-time behavior of such solutions and prove inviscid…
In high-contrast composites, the electric (or stress) field may exhibit significant amplification in the narrow region between inclusions. The behavior of the solution depends on the distance $\epsilon$ between the inclusions, which tends…
Given a resistor network on $\mathbb Z^d$ with nearest-neighbor conductances, the effective conductance in a finite set with a given boundary condition is the the minimum of the Dirichlet energy over functions with the prescribed boundary…
On the basis of a quantum-statistical approach to the electrical conductivity of nonideal plasmas we derive analytical results in the classical low-density regime, in the degenerate Born limit, and for the contribution of the Debye-Onsager…
We derive from kinetic theory, fluid mechanics, and thermodynamics the minimal continuum-level equations governing the flow of a binary, non-electrolytic mixture in an isotropic porous medium with osmotic effects. For dilute mixtures, these…
We rigorously derive the quadrupole formula within the context of the Einstein-Vlasov system. The main contribution of this work is an estimate of the remainder terms, derived from well-defined assumptions, with explicitly stated error…
A numerical method to calculate optical conductivity based on a pump-probe setup is presented. Its validity and limits are tested and demonstrated via the concrete numerical simulations on the half-filled one-dimensional extended Hubbard…
The van de Hulst formula provides an expression for the effective refractive index or effective propagation constant of a suspension of particles of arbitrary shape, size and refractive index in an optically homogeneous medium. However, its…
The Maxwell approach from electrostatics is applied for calculation of transport coefficients in composites. The viscosity of a dilute emulsion is obtained as a function of the volume fraction of dispersed phase. The derived new formula is…
We discuss in this short note the local-in-time strong well-posedness of the compressible Navier-Stokes system for non-Newtonian fluids on the three dimensional torus. We show that the result established recently by Kalousek, M\'{a}cha, and…
We conclude our analysis of the linear response of charge transport in lattice systems of free fermions subjected to a random potential by deriving general mathematical properties of its conductivity at the macroscopic scale. The present…
In this paper, we rigorously derive the compressible one-fluid Navier-Stokes equation from the scaled compressible two-fluid Navier-Stokes-Maxwell equations locally in time under the assumption that the initial data are well prepared. We…
This note considers a finite dimensional statistical model for the Calder\'on problem with piecewise constant conductivities. In this setting it is shown that injectivity of the forward map and its linearisation suffice to prove the…