Related papers: Gas-filled pore in bounded particle
We obtain the local well-posedness of a moving boundary problem that describes the swelling of a pocket of water within an infinitely thin elongated pore. Our result involves fine a priori estimates of the moving boundary evolution, Banach…
Diffusion rates through a membrane can be asymmetric, if the diffusing particles are spatially extended and the pores in the membrane have asymmetric structure. This phenomenon is demonstrated here via a deterministic simulation of a…
The macroscopic behavior of the solution of a coupled system of partial differential equations arising in the modeling of reaction-diffusion processes in periodic porous media is analyzed. Our mathematical model can be used for studying…
This study investigates the steady Boltzmann equation in one spatial variable for a polyatomic single-component gas in a half-space. Inflow boundary conditions are assumed at the half-space boundary, where particles entering the half-space…
Phase transitions of systems confined in long cylindrical pores (capillary condensation, wetting, crystallization, etc.) are intrinsically not sharply defined but rounded. The finite size of the cross section causes destruction of long…
The diffusion in two dimensions of non-interacting active particles that follow an arbitrary motility pattern is considered for analysis. Accordingly, the transport equation is generalized to take into account an arbitrary distribution of…
A model of randomly distributed overlapping spheres of different radii is represented to describe a heterogeneous porous medium. Two-particle correlation function of the relative position of pores of different radii in the medium space was…
We consider nonlinear diffusive evolution equations posed on bounded space domains, governed by fractional Laplace-type operators, and involving porous medium type nonlinearities. We establish existence and uniqueness results in a suitable…
The problem of deriving a gradient flow structure for the porous medium equation which is {\em thermodynamic}, in that it arises from the large deviations of some microscopic particle system, is studied. To this end, a rescaled zero-range…
Understanding gas transport in porous media and its mechanism has broad applications in various research areas, such as carbon sequestration in deep saline aquifers and gas explorations in reservoir rocks. Gas transport is mainly controlled…
We consider a one-dimensional gas of hard point particles in a finite box that are in thermal equilibrium and evolving under Hamiltonian dynamics. Tagged particle correlation functions of the middle particle are studied. For the special…
We consider aspects of the population dynamics, inside a bound domain, of diffusing agents carrying an attribute which is stochastically destroyed upon contact with the boundary. The normal mode analysis of the relevant Helmholtz equation…
A new approach to the modeling of nonfree particle diffusion is presented. The approach uses a general setup based on geometric graphs (networks of curves), which means that particle diffusion in anything from arrays of barriers and pore…
A one-dimensional model on a line of the length L is investigated, which involves particle diffusion as well as single particle annihilation. There are also creation and annihilation at the boundaries. The static and dynamical behaviors of…
We investigate mathematical properties of the system of nonlinear partial differential equations that describe, under certain simplifying assumptions, evolutionary processes in water-saturated granular materials. The unconsolidated solid…
We perform a linear perturbation analysis of expanding shells driven by expansions of HII regions. The ambient gas is assumed to be uniform. As an unperturbed state, we develop a semi-analytic method for deriving the time evolution of the…
A mathematical model for the evolution of, and deposition from, a thin particle-laden droplet on an infinitely thick, isotropic, flooded, porous substrate with interconnected pores undergoing simultaneous evaporation and imbibition is…
Liquid-gas phase coexistence in a boundary-driven diffusive system is studied by analyzing fluctuating hydrodynamics of a density field defined on a one-dimensional lattice with a space interval $\Lambda$. When an interface width $\ell$ is…
We investigate the motion of a particle around a low mass planet embedded in a non-turbulent gaseous disk. We take into account the effect of the gas structure that is modified by the gravitational interaction between the planet. We derive…
A biomimetic model of cell-cell communication was developed to probe the passive molecular transport across ion channels inserted in synthetic lipid bilayers formed between contacting droplets arranged in a linear array. Diffusion of a…