Related papers: Reaction-subdiffusion equations with species-depen…
Heat transfer in a fluid can be greatly enhanced by natural convection, giving rise to the nuanced relationship between the Nusselt number and Rayleigh number that has been a focus of modern fluid dynamics. Our work explores convection in…
Single-particle traces of the diffusive motion of molecules, cells, or animals are by-now routinely measured, similar to stochastic records of stock prices or weather data. Deciphering the stochastic mechanism behind the recorded dynamics…
We study reaction-diffusion processes with multi-species of particles and hard-core interaction. We add boundary driving to the system by means of external reservoirs which inject and remove particles, thus creating stationary currents. We…
Stochastic chemical systems with diffusion are modeled with a reaction-diffusion master equation. On a macroscopic level, the governing equation is a reaction-diffusion equation for the averages of the chemical species. On a mesoscopic…
We propose a reaction-transport model for CTRW with non-linear reactions and non-exponential waiting time distributions. We derive non-linear evolution equation for mesoscopic density of particles. We apply this equation to the problem of…
We briefly review some aspects of the anomalous diffusion, and its relevance in reactive systems. In particular we consider {\it strong anomalous} diffusion characterized by the moment behaviour $\langle x(t)^q \rangle \sim t^{q \nu(q)}$,…
The diffusion equation and its time-fractional counterpart can be obtained via the diffusion limit of continuous-time random walks with exponential and heavy-tailed waiting time distributions. The space dependent variable-order…
The reaction-diffusion master equation is a stochastic model often utilized in the study of biochemical reaction networks in living cells. It is applied when the spatial distribution of molecules is important to the dynamics of the system.…
The dispersive optical-model is applied to transfer reactions. A systematic study of $(d,p)$ reactions on closed-shell nuclei using the finite-range adiabatic reaction model is performed at several beam energies and results are compared to…
The fractional Fokker-Planck equation for subdiffusion in time-dependent force fields is derived from the underlying continuous time random walk. Its limitations are discussed and it is then applied to the study of subdiffusion under the…
We present a spatially-extended system of chemical reactions exhibiting adaptation to time-dependent influxes of reactants. Here adaptation is defined as improved reproductive success, namely the ability of one of the many locally stable…
Several stochastic simulation algorithms (SSAs) have been recently proposed for modelling reaction-diffusion processes in cellular and molecular biology. In this paper, two commonly used SSAs are studied. The first SSA is an on-lattice…
In this paper Gaussian models of retarded and accelerated anomalous diffusion are considered. Stochastic differential equations of fractional order driven by single or multiple fractional Gaussian noise terms are introduced to describe…
Complex biological and physical transport processes are often described through systems of interacting particles. Excluded-volume effects on these transport processes are well studied, however the interplay between volume exclusion and…
Reaction-diffusion equations appear in biology and chemistry, and combine linear diffusion with different kind of reaction terms. Some of them are remarkable from the mathematical point of view, since they admit families of travelling waves…
Distributed order fractional Langevin-like equations are introduced and applied to describe anomalous diffusion without unique diffusion or scaling exponent. It is shown that these fractional Langevin equations of distributed order can be…
We propose two nonlinear random walk models which are suitable for the analysis of both chemotaxis and anomalous transport. We derive the balance equations for the population density for the case when the transition rate for a random walk…
Reaction-diffusion systems have been proposed as a model for pattern formation and morphogenesis. The Fickian diffusion typically employed in these constructions model the Brownian motion of particles. The biological and chemical elements…
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…
We investigate evolution equations for anomalous diffusion employing fractional derivatives in space and time. Linkage between the space-time variables leads to a new type of fractional derivative operator. Fractional diffusion equations…