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The aim of this paper is to establish the framework of the enclosure method for some class of inverse problems whose governing equations are given by parabolic equations with discontinuous coefficients. The framework is given by considering…

We design a class of spatially inhomogeneous heat spreaders in the context of steady-state thermal conduction leading to spatially uniform thermal fields across a large convective surface. Each spreader has a funnel-shaped design, either in…

Diffusion processes with boundaries are models of transport phenomena with wide applicability across many fields. These processes are described by their probability density functions (PDFs), which often obey Fokker-Planck equations (FPEs).…

This paper introduces the use of statistical distributions based on transport differential equations for clear distinction of transport modes within transient kinetic experiments. More specifically,novel techniques are developed for the…

Energy-transport equations for the transport of fermions in optical lattices are formally derived from a Boltzmann transport equation with a periodic lattice potential in the diffusive limit. The limit model possesses a formal gradient-flow…

This work is aimed at the study and analysis of the heat transport on a metal bar of length $L$ with a solid-solid interface. The process is assumed to be developed along one direction, across two homogeneous and isotropic materials.…

A simple finite element formulation of the outlet gradient boundary condition is presented in the general context of convective-diffusive transport processes. Basically, the method is based on an upstream evaluation of the dependent…

An anisotropic random barrier model is presented, in which the transition probabilities in different directions have different probability density functions. At low temperatures, the anisotropic long--time diffusion coefficients, obtained…

The conventional assumption that the self-diffusion coefficient of a small tracer can be obtained by a local and instantaneous application of Einstein's relation in a temperature field with spatial and temporal heterogeneity is revisited.…

In this paper we investigate a sub-diffusion equation for simulating the anomalous diffusion phenomenon in real physical environment. Based on an equivalent transformation of the original sub-diffusion equation followed by the use of a…

We present a new multi-fluid, multi-temperature plasma solver with adaptive Cartesian mesh (ACM) based on a full-Newton (non-linear, implicit) scheme for collisional low-temperature plasma. The particle transport is described using the…

We propose a new model to describe diffusion processes within active deformable media. Our general theoretical framework is based on physical and mathematical considerations, and it suggests to use diffusion tensors directly coupled to…

We develop a curvilinear invariant set of the diffusion tensor which may be applied to Diffusion Tensor Imaging measurements on tissues and porous media. This new set is an alternative to the more common invariants such as fractional…

We study an inverse boundary value problem on the determination of principal order coefficients in isotropic nonautonomous heat flows stated as follows; given a medium, and in the absence of heat sources and sinks, can the time-dependent…

This paper is devoted to the study of some nonlinear parabolic equations with discontinuous diffusion intensities. Such problems appear naturally in physical and biological models. Our analysis is based on variational techniques and in…

Turbulent flows under transcritical conditions are present in regenerative cooling systems of rocker engines and extraction processes in chemical engineering. The turbulent flows and the corresponding heat transfer phenomena in these…

We study the heat equation on a half-space with a linear dynamical boundary condition. Our main aim is to show that, if the diffusion coefficient tends to infinity, then the solutions converge (in a suitable sense) to solutions of the…

The present article proposes a diffuse interface model for compressible multicomponent flows with transport phenomena of mass, momentum and energy (i.e., mass diffusion, viscous dissipation and heat conduction). The model is reduced from…

This work deals with an inverse boundary value problem arising from the equation of heat conduction. We reconstruct small perturbations of the (isotropic) heat conductivity distribution from partial (on accessible part of the boundary)…

We present a comprehensive analytical study of radiative transfer using the method of moments and include the effects of non-isotropic scattering in the coherent limit. Within this unified formalism, we derive the governing equations and…