Related papers: Reaction-diffusion with stochastic decay rates
Among the main actors of organism development there are morphogens, which are signaling molecules diffusing in the developing organism and acting on cells to produce local responses. Growth is thus determined by the distribution of such…
We propose a model of sub-diffusion in which an external force is acting on a particle at all times not only at the moment of jump. The implication of this assumption is the dependence of the random trapping time on the force with the…
The motion of self-propelled particles is modeled as a persistent random walk. An analytical framework is developed that allows the derivation of exact expressions for the time evolution of arbitrary moments of the persistent walk's…
In this article we address the problem of the nonlinear interaction of subdiffusive particles. We introduce the random walk model in which statistical characteristics of a random walker such as escape rate and jump distribution depend on…
The A+B --> C reaction-diffusion process is studied in a system where the reagents are separated by a semipermeable wall. We use reaction-diffusion equations to describe the process and to derive a scaling description for the long-time…
We study the problem of diffusing particles which coalesce upon contact. With the aid of a non-perturbative renormalization group, we first analyze the dynamics emerging below the critical dimension two, where strong fluctuations imply…
Cells and organisms follow aligned structures in their environment, a process that can generate persistent migration paths. Kinetic transport equations are a popular modelling tool for describing biological movements at the mesoscopic…
Mathematical modeling is now used commonly in the analysis of signaling networks. With advances in high resolution microscopy, the spatial location of different signaling molecules and the spatio-temporal dynamics of signaling microdomains…
We show that the generalized diffusion coefficient of a subdiffusive intermittent map is a fractal function of control parameters. A modified continuous time random walk theory yields its coarse functional form and correctly describes a…
We study Fluctuation Relations (FRs) for dynamics that are anomalous, in the sense that the diffusive properties strongly deviate from the ones of standard Brownian motion. We first briefly review the concept of transient work FRs for…
The fundamental insight into Brownian motion by Einstein is that all substances exhibit continual fluctuations due to thermal agitation balancing with the frictional resistance. However, even at thermal equilibrium, biological activity can…
We study the contribution of advection by thermal velocity fluctuations to the effective diffusion coefficient in a mixture of two indistinguishable fluids. The enhancement of the diffusive transport depends on the system size L and grows…
We consider a simple linear reversible isomerization reaction A <--> B under subdiffusion described by continuous time random walks (CTRW). The reactants' transformations take place independently on the motion and are described by constant…
We investigate the relation between an applied potential and the corresponding stationary state occupation for nonequilibrium and overdamped diffusion processes. This relation typically becomes long ranged resulting in global changes for…
The long-time behavior of a reaction-diffusion front between one static (e.g. porous solid) reactant A and one initially separated diffusing reactant B is analyzed for the mean-field reaction-rate density R(\rho_A,\rho_B) =…
The diffusive transport of biased Brownian particles in a two-dimensional symmetric channel is investigated numerically considering both the no-flow and the reflection boundary conditions at the channel boundaries. Here, the geometrical…
We discuss a method by which quantum fluctuations can be included in microscopic transport models based on wave packets that are not energy eigenstates. By including the next-to-leading order term in the cumulant expansion of the…
The nucleus-nucleus potential and energy dissipation in fusion reactions are obtained from microscopic mean-field dynamics. The deduced potentials nicely reproduce the one extracted from experimental data. Energy dissipation shows a…
We present a one-dimensional model for diffusion in a fluctuating lattice; that is a lattice which can be in two or more states. Transitions between the lattice states are induced by a combination of two processes: one periodic…
The problem of velocity selection of reaction-diffusion fronts has been widely investigated. While the mean field limit results are well known theoretically, there is a lack of analytic progress in those cases in which fluctuations are to…