Related papers: Reaction-subdiffusion on moving fluids
In this work we are concerned with generating solutions of a class of Convection-Diffusion-Reaction equation from the solutions of another CDR equation through the Darboux transformations. The method is elucidated by cases with certain…
Reaction-diffusion systems, which consist of the reacting particles subject to diffusion process, constitute one of the common examples of non-linear statistical systems. In low space dimensions $d \leq 2$ the usual description by means of…
This paper proposes a novel reaction-diffusion system approximation tailored for singular diffusion problems, typified by the fast diffusion equation. While such approximation methods have been successfully applied to degenerate parabolic…
We consider a system of reaction-diffusion equations with passive advection term and Lewis number not equal to one. Such systems are used to describe chemical reactions in a flow in a situation where temperature and material diffusivities…
Multispecies reaction-diffusion systems, for which the time evolution equation of correlation functions become a closed set, are considered. A formal solution for the average densities is found. Some special interactions and the exact time…
Diffusion of a tagged particle near a constraining biological surface is examined numerically by modeling the surface-water interaction by an effective potential. The effective potential is assumed to be given by an asymmetric double well…
This paper proposes the Ricci-flow equation from Riemannian geometry as a general geometric framework for various nonlinear reaction-diffusion systems (and related dissipative solitons) in mathematical biology. More precisely, we propose a…
A mode-coupling theory for the slow single-particle dynamics in fluids adsorbed in disordered porous media is derived, which complements previous work on the collective dynamics [V. Krakoviack, Phys. Rev. E 75, 031503 (2007)]. Its…
We propose coupled evolution equations for the thickness of a liquid film and the density of an adsorbate layer on a partially wetting solid substrate. Therein, running droplets are studied assuming a chemical reaction underneath the…
Computing reaction rates in biomolecular systems is a common goal of molecular dynamics simulations. The reactions considered often involve conformational changes in the molecule, either changes in the structure of a protein or the relative…
Reaction-diffusion systems where transition rates exhibit quenched disorder are common in physical and chemical systems. We study pair reactions on a periodic two-dimensional lattice, including continuous deposition and spontaneous…
A new asymptotic method is presented for the analysis of the traveling waves in the one-dimensional reaction-diffusion system with the diffusion with a finite velocity and Kolmogorov-Petrovskii-Piskunov kinetics. The analysis makes use of…
Reaction-diffusion equations describe various spatially extended processes that unfold as traveling fronts moving at constant velocity. We introduce and solve analytically a model that, besides such fronts, supports solutions advancing as…
Diffusion is a central phenomenon in almost all fields of natural science revealing microscopic processes from the observation of macroscopic dynamics. Here, we consider the paradigmatic system of a single atom diffusing in a periodic…
The primary goal of this paper is to characterize solutions to coupled reaction-diffusion systems. Indeed, we use operators theory to show that under suitable assumptions, then the solutions to the reaction-diffusion equations exist. As…
A geometrically invariant concept of fast-slow vector fields perturbed by transport terms (describing molecular diffusion processes) is proposed in this paper. It is an extension of our concept of singularly perturbed vector fields to…
Stellar evolution is driven by the changing composition of a star from nuclear reactions. At the late stages of evolution and during explosive events, the timescale can be short and drive strong hydrodynamic flows, making simulations of…
A hybrid mesoscopic multi-particle collision model is used to study diffusion-influenced reaction kinetics. The mesoscopic particle dynamics conserves mass, momentum and energy so that hydrodynamic effects are fully taken into account.…
This study examines anomalous diffusion and dynamical phase transitions in a nonlinear bouncer model with short-range interactions leading to velocity-dependent (adiabatic) collisions. By varying a control parameter, transitions between…
Traditional chemical kinetics may be inappropriate to describe chemical reactions in micro-domains involving only a small number of substrate and reactant molecules. Starting with the stochastic dynamics of the molecules, we derive a…