Related papers: Large-time behavior of solutions to a thermo-diffu…
Convection-driven cooling in porous media influences thermo-poro-mechanical stresses, thereby causing deformation. These processes are strongly influenced by the presence of fractures, which dominate flow and heat transfer. At the same…
This paper establishes explicit solutions for fractional diffusion problems on bounded domains. It also gives stochastic solutions, in terms of Markov processes time-changed by an inverse stable subordinator whose index equals the order of…
This work studies the heat equation in a two-phase material with spherical inclusions. Under some appropriate scaling on the size, volume fraction and heat capacity of the inclusions, we derive a coupled system of partial differential…
Steric or attractive interactions among reactants or between reactants and inert crowders can substantially influence the total rate of a diffusion-influenced reaction in the liquid phase. However, the role of the product species, that has…
We study the motion of a Brownian particle in a medium with inhomogeneous temperature. In the overdamped regime of low Reynolds numbers, the probability distribution function (PDF) of the particle is obtained from the van Kampen diffusion…
A mixture of solvent particles with short-range, directional interactions and solute particles with short-range, isotropic interactions that can bond multiple times is of fundamental interest in understanding liquids and colloidal mixtures.…
We consider the long time behavior of solutions to a nonlocal reaction diffusion equation that arises in the study of directed polymers. The model is characterized by convolution with a kernel $R$ and an $L^2$ inner product. In one spatial…
The reciprocity principle governs the symmetry in transmission of electromagnetic and acoustic waves, as well as the diffusion of heat between two points in space, with important consequences for thermal management and energy harvesting.…
Theoretical and experimental investigations of water vapor interaction with porous materials are carried out both at the macro level and at the micro level. At the macro level, the influence of the arrangement structure of individual pores…
We discuss a failure of the wide-spread method of images solution to describe the time evolution of probability distribution in diffusive processes with memory. For a path that touches a target during stochastic evolution, we define its…
In the first paper of this series, I investigated whether a wavefunction model of a heavy particle and a collection of light particles might generate "Brownian-Motion-Like" trajectories of the heavy particle. I concluded that it was…
The problem of diffusion in a porous medium with a spatially varying porosity is considered. The particular microstructure analyzed comprises a collection of impenetrable spheres, though the methods developed are general. Two different…
We present several numerical results on granular mixtures. In particular, we examine the efficiency of diffusion as a mixing mechanism in these systems. The collisions are inelastic and to compensate the energy loss, we thermalize the…
Stimuli-responsive materials that modify their shape in response to changes in environmental conditions -- such as solute concentration, temperature, pH, and stress -- are widespread in nature and technology. Applications include micro- and…
The paper deals with the fundamental problem of a modeling of the physical, in particular, thermal hydraulic processes, in various media of fractal structure of the natural, technological and technical systems and devices. The examples of a…
Using information theory we derive a thermodynamics for systems evolving under a collective motion, i.e. under a time-odd constraint. An illustration within the Lattice gas Model is given for two model cases: a collision between two complex…
This work investigates the two-dimensional thermal behavior of a bilayer medium subject to both internal and external heat sources. The model incorporates diffusion, advection, and temperature-dependent volumetric heat generation or…
The established macroscopic equations of motion for two phase immiscible displacement in porous media are known to be physically incomplete because they do not contain the surface tension and surface areas governing capillary phenomena.…
The strong friction regime at low temperatures is analyzed systematically starting from the formally exact path integral expression for the reduced dynamics. This quantum Smoluchowski regime allows for a type of semiclassical treatment in…
The equations of motion in a macroscopically inhomogeneous porous medium saturated by a fluid are derived. As a first verification of the validity of these equations, a two-layer rigid frame porous system considered as one single porous…