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The fully discrete problem for convection-diffusion equation is considered. It comprises compact approximations for spatial discretization, and Crank-Nicolson scheme for temporal discretization. The expressions for the entries of inverse of…
The most common mathematical models for electrolyte flows are based on the dilute solution assumption, leading to a coupled system of the Nernst--Planck--Poisson drift-diffusion equations for ion transport and the Stokes resp.…
A quasi-two-dimensional system of hard spheres strongly confined between two parallel plates is considered. The attention is focussed on the macroscopic self-diffusion process observed when the system is looked from above or from below. The…
The crucial problem for better understanding the nature of glass transition and related relaxation phenomena is to find proper interrelations between molecular dynamics and thermodynamics of viscous systems. To gain this aim the recently…
In order to describe the dynamics of crowded ions (charged particles), we use an energetic variation approach to derive a modified Poisson-Nernst-Planck (PNP) system which includes an extra dissipation due to the effective velocity…
A model is presented for the solution of electrokinetic phenomena of colloidal suspensions in fluid mixtures. We solve the discrete Boltzmann equation with a BGK collision operator using the lattice Boltzmann method to simulate binary fluid…
We report the key findings from numerical solutions of a model of transport within an established perfusion bioreactor design. The model includes a complete formulation of transport with fully coupled convection-diffusion and scaffold cell…
We develop a theoretical and computational approach to deal with systems that involve a disparate range of spatio-temporal scales, such as those comprised of colloidal particles or polymers moving in a fluidic molecular environment. Our…
A semi-implicit Lax-Wendroff kinetic scheme is developed for hydrodynamic phonon transport in solid materials based on the Boltzmann transport equation under the double relaxation time approximation, in which both the normal and resistive…
In this paper we propose and validate a multiscale model for the description of particle diffusion in presence of trapping boundaries. We start from a drift-diffusion equation in which the drift term describes the effect of bubble traps,…
Anisotropic diffusion is imperative in understanding cosmic ray diffusion across the Galaxy, the heliosphere, and the interplay of cosmic rays with the Galactic magnetic field. This diffusion term contributes to the highly stiff nature of…
This article investigates the non-stationary reaction-diffusion-advection equation, emphasizing solutions with internal layers and the associated inverse problems. We examine a nonlinear singularly perturbed partial differential equation…
In this paper, we studied phase-space analysis of a certain mathematical model of tumor growth with an immune responses and chemotherapy therapy. Mathematical modelling of this process is viewed as a potentially powerful tool in the…
Astrophysical fluids under the influence of magnetic fields are often subjected to single-fluid or two-fluid approximations. In the case of weakly ionized plasmas however, this can be inappropriate due to distinct responses from the…
Particle transport, acceleration and energisation are phenomena of major importance for both space and laboratory plasmas. Despite years of study, an accurate theoretical description of these effects is still lacking. Validating models with…
In this paper, we consider mathematical modeling and numerical simulation of non-isothermal compressible multi-component diffuse-interface two-phase flows with realistic equations of state. A general model with general reference velocity is…
In this paper, we start from a very natural system of cross-diffusion equations, which can be seen as a gradient flow for the Wasserstein distance of a certain functional. Unfortunately, the cross-diffusion system is not well-posed, as a…
Sampling from flat energy or density distributions has proven useful in equilibrating complex systems with large energy barriers. Several thermostats and barostats are presented to sample these flat distributions by molecular dynamics.…
We study a system of nonlinear partial differential equations modeling the electrokinetics of a nematic electrolyte material consisting of various ion species suspended in a nematic liquid crystal within a bounded domain in two or three…
We study the consequences of different realizations of diffusion processes in relativistic Langevin simulations. We elaborate on the Ito-Stratonovich dilemma by showing how microscopically calculated transport coefficients as obtained from…