Related papers: Reaction Diffusion patterns in Pseudoplatystoma fi…
We discuss the diffusion phenomenon in the parabolic and hyperbolic regimes. New effects related to the finite velocity of the diffusion process are predicted, that can partially explain the strange behavior associated to adsorption…
Plasmas in which there is a threshold for a dominant reaction to take place (such as recombination or attachment) will have particle distributions that evolve as the reaction progresses. The form of the Boltzmann collision term in such a…
Anomalous diffusion, manifest as a nonlinear temporal evolution of the position mean square displacement, and/or non-Gaussian features of the position statistics, is prevalent in biological transport processes. Likewise, collective behavior…
Hyperbolic reaction-diffusion equations have recently attracted attention both for their application to a variety of biological and chemical phenomena, and for their distinct features in terms of propagation speed and novel instabilities…
At finite concentrations of reacting molecules, kinetics of diffusion-controlled reactions is affected by intra-reactant interactions. As a result, multi-particle reaction statistics cannot be deduced from single-particle results. Here we…
Spatio-temporal biochemical signaling in a large class of protein-protein interaction networks is well modeled by a reaction-diffusion system. The global existence of the solution to the reaction-diffusion system is determined by the…
A key problem in modelling the evolution dynamics of infectious diseases is the mathematical representation of the mechanism of transmission of the contagion. Models with a finite number of subpopulations can be described via systems of…
Reaction-Diffusion (RD) systems provide a computational framework that governs many pattern formation processes in nature. Current RD system design practices boil down to trial-and-error parameter search. We propose a differentiable…
Q-conditional symmetries (nonclassical symmetries) for a general class of two-component reaction-diffusion systems with constant diffusivities are studied. Using the recently introduced notion of Q-conditional symmetries of the first type…
We study a hybrid impulsive reaction-advection-diffusion model given by a reaction-advection-diffusion equation composed with a discrete-time map in space dimension $n\in\mathbb N$. The reaction-advection-diffusion equation takes the form…
The use of reaction-diffusion models rests on the key assumption that the underlying diffusive process is Gaussian. However, a growing number of studies have pointed out the prevalence of anomalous diffusion, and there is a need to…
This paper investigates pattern formation in reaction--diffusion systems with both diffusive and nondiffusive components, providing necessary and sufficient conditions for diffusion-driven instability (DDI) and establishing the existence of…
Intracellular protein patterns govern essential cellular functions by dynamically redistributing proteins between membrane-bound and cytosolic states, conserving their total numbers. This review presents a theoretical framework for…
Using the methods of computer modeling this scientific paper studies the special features of diffusion of the particles subjected to the external periodic force in the crystal lattice. The particle motion is described by a Langevin…
The study of pattern emergence together with exploration of the exemplar Turing model is enjoying a renaissance both from theoretical and experimental perspective. Here, we implement a stability analysis of spatially dependent reaction…
Abridged abstract: Inert interactions between randomly moving entities and spatial disorder play a crucial role in quantifying the diffusive properties of a system. These interactions affect only the movement of the entities, and examples…
This work presents algebraic closure models associated with advective transport and nonlinear reactions in a Reynolds-averaged Navier-Stokes context for a system of species subject to binary reactions and transport by advection and…
Density-dependent diffusion is a widespread phenomenon in nature. We have examined the density-dependent diffusion behavior of some biological processes such as tumor growth and invasion [23]. Here, we extend our previous work by developing…
Spatio-temporal patterns emerging from an initial quiescent, uniform state is a phenomenon observed in many dynamical systems sustained far from thermodynamic equilibrium, the practical application of which has only recently begun to be…
We consider particle systems that are perturbations of the voter model and show that when space and time are rescaled the system converges to a solution of a reaction diffusion equation in dimensions $d \ge 3$. Combining this result with…