Related papers: Alternative interdiffusion theory of many componen…
We show that propagation speeds in invasion processes modeled by reaction-diffusion systems are determined by marginal spectral stability conditions, as predicted by the marginal stability conjecture. This conjecture was recently settled in…
Under ideal MHD conditions the magnetic field strength should be correlated with density in the interstellar medium (ISM). However, observations indicate that this correlation is weak. Ambipolar diffusion can decrease the flux-to-mass ratio…
Dilute granular flows are routinely described by collisional kinetic theory, but dense flows require a fundamentally different approach, due to long-lasting, many-body contacts. In the case of silo drainage, many continuum models have been…
A new diffuse interface model has been proposed in this study for simulating binary alloy solidification under universal cooling conditions, involving both equilibrium and non-equilibrium solute partitioning. Starting from the Gibbs-Thomson…
We consider planar traveling fronts between stable steady states in two-component singularly perturbed reaction-diffusion-advection equations, where a small quantity $\delta^2$ represents the ratio of diffusion coefficients. The fronts…
A new semi-analytical solution to the advection-dispersion-reaction equation for modelling solute transport in layered porous media is derived using the Laplace transform. Our solution approach involves introducing unknown functions…
We establish global-in-time existence results for thermodynamically consistent reaction-(cross-)diffusion systems coupled to an equation describing heat transfer. Our main interest is to model species-dependent diffusivities, while at the…
This work describes three diffuse-interface methods for the simulation of immiscible, compressible multiphase fluid flows and elastic-plastic deformation in solids. The first method is the localized-artificial-diffusivity approach of Cook…
Experimental studies of systems containing active proteins that undergo conformational changes driven by catalytic chemical reactions have shown that the diffusion coefficients of passive tracer particles and active molecules are larger…
Intermittency is an essential property of astrophysical fluids, which demonstrate an extended inertial range. As intermittency violates self-similarity of motions, it gets impossible to naively extrapolate the properties of fluid obtained…
Interacting particles diffusing in single-file is a fundamental model of transport in narrow channels where particles cannot bypass each other. An important result has been obtained by Kollmann [Phys. Rev. Lett. 90, 180602 (2003)] for the…
The problem of mass diffusion in layered systems has relevance to applications in different scientific disciplines, e.g., chemistry, material science, soil science, and biomedical engineering. The mathematical challenge in these type of…
Diffusion of small particles is omnipresent in a plentiful number of processes occurring in Nature. As such, it is widely studied and exerted in almost all branches of sciences. It constitutes such a broad and often rather complex subject…
We analyze diffusion-driven (Turing) instability of a reaction-diffusion system. The innovation is that we replace the traditional Laplacian diffusion operator with a combination of the fourth order bi-Laplacian operator and the second…
Understanding particle motion in narrow channels is essential to guide progress in numerous applications, from filtration to vascular transport. Thermal or active fluctuations of channel walls for fluid-filled channels can slow down or…
The diffusion of elements is a key process in understanding the unusual surface composition of white dwarfs stars and their spectral evolution. The diffusion coefficients of Paquette et al. (1986) have been widely used to model diffusion in…
Diffusion, a ubiquitous phenomenon in nature, is a consequence of particle number conservation and locality, in systems with sufficient damping. In this paper we consider diffusive processes in the bulk of Weyl semimetals, which are exotic…
We discuss the molecular diffusion transport in infinitely dilute liquid solutions under non-isothermal conditions. This discussion is motivated by an occurring misinterpretation of thermodynamic transport equations written in terms of…
The paper is devoted to further development of the new approach in equilibrium statistical mechanics the basis of which was worked out in a series of articles by the author. The approach proceeds on the use of a hierarchy of equations for…
The alleged existence of sluggish diffusion in high entropy alloys has drawn controversy. In high entropy alloys, and in general in all solids, transport properties are controlled by point defect concentration, which must be known before…