Related papers: Unbounded autocatalytic growth on diffusive substr…
Evolution of a system of diffusing and proliferating mortal reactants is analyzed in the presence of randomly moving catalysts. While the continuum description of the problem predicts reactant extinction as the average growth rate becomes…
The extinction transition on a one dimensional heterogeneous substrate with diffusive correlations is studied. Diffusively correlated heterogeneity is shown to affect the location of the transition point, as the reactants adapt to the…
Logistic growth on a static heterogenous substrate is studied both above and below the drift-induced delocalization transition. Using stochastic, agent-based simulations the delocalization of the highest eigenfunction is connected with the…
We study a system of self-propelled, proliferating finite-size disks with game-theoretical interactions, where growth rates depend on local population composition. We analyze how these interactions influence spatial distribution,…
The dynamics of linear stochastic growth equations on growing substrates is studied. The substrate is assumed to grow in time following the power law $t^\gamma$, where the growth index $\gamma$ is an arbitrary positive number. Two different…
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…
This short paper concerns a diffusive logistic equation with the heterogeneous environment and a free boundary, which is formulated to study the spread of an invasive species, where the free boundary represents the expanding front. A…
A Markov chain model for spatially distributed autocatalytic systems with a quadratic reaction rate is considered. An approximate solution for the local probability distribution is obtained in the form of a perturbation expansion for the…
We study the non-equilibrium phase transition between survival and extinction of spatially extended biological populations using an agent-based model. We especially focus on the effects of global temporal fluctuations of the environmental…
Motivated by modeling the dynamics of a population living in a flowing medium where the environmental factors are random in space, we have studied an asymmetric variant of the one-dimensional contact process, where the quenched random…
We characterize the influence that external noise, with both spatial and temporal correlations, has on the scale dependence of the reaction parameters of a cubic autocatalytic reaction diffusion (CARD) system. Interpreting the CARD model as…
The kinetic processes in nanoparticle-based catalysis are dominated by large fluctuations and spatiotemporal heterogeneities, in particular for diffusion-influenced reactions which are far from equilibrium. Here, we report results from…
In this paper we consider the diffusive competition model with free boundary in the heterogeneous time-periodic environment, in which the variable intrinsic growth rates of invasive and native species may change signs and be "very negative"…
A finite-time fluctuation theorem is proved for the diffusion-influenced surface reaction A<->B in a domain with any geometry where the species A and B undergo diffusive transport between the reservoir and the catalytic surface. A…
Stochastic chemical reaction or population dynamics in finite systems often terminates in an absorbing state. Yet in large spatially extended systems, the time to reach species extinction (or fixation) becomes exceedingly long. Tuning…
Understanding anomalous transport and reaction kinetics due to microscopic physical and chemical disorder is a long-standing goal in many fields including geophysics, biology, and engineering. We consider reaction-diffusion characterized by…
The kinetics of encounter-controlled processes in growing domains is markedly different from that in a static domain. Here, we consider the specific example of diffusion limited coalescence and annihilation reactions in one-dimensional…
We propose a generalized diffusion equation for a flat Euclidean space subjected to a continuous infinitesimal scale transform. For the special cases of an algebraic or exponential expansion/contraction, governed by time-dependent scale…
The family of autonomous reaction-diffusion models on a one-dimensional lattice with boundaries is studied. By autonomous, it is meant that the evolution equation for n-point functions contain only n- or less- point functions. It is shown…
This paper concerns a diffusive logistic equation with a free boundary and sign-changing intrinsic growth rate in heterogeneous time-periodic environment, in which the variable intrinsic growth rate may be "very negative" in a "suitable…