Related papers: Nonlocal competition and logistic growth: patterns…
We study the competition interface between two growing clusters in a growth model associated to last-passage percolation. When the initial unoccupied set is approximately a cone, we show that this interface has an asymptotic direction with…
This work analyzes bifurcation delay and front propagation in the one-dimensional real Ginzburg-Landau equation (RGLE) with periodic boundary conditions on monotonically growing or shrinking domains. First, we obtain closed-form expressions…
This paper investigates a class of reaction-diffusion population models defined on a bounded domain, characterized by a general time-delayed per capita growth rate and a general advection term. Notably, the growth rate encompasses both…
We consider a stochastic individual-based model of adaptive dynamics for an asexually reproducing population with mutation, with linear birth and death rates, as well as a density-dependent competition. To depict repeating changes of the…
We analyze the competitive evolution of codimension one and two morphologies within the $H^{-1}$ gradient flow of the strong Functionalized Cahn-Hilliard equation. On a slow time scale a sharp hypersurface reduction yields a degenerate…
Directed Percolation (DP) is a classic model for nonequilibrium phase transitions into a single absorbing state (fixation). It has been extensively studied by analytical and numerical techniques in diverse contexts. Recently, DP has…
The competition between deformation twinning and dislocation slip underpins the evolution of mesoscale plasticity in face-centered cubic materials. While competition between these mechanisms is known to be related to the critical features…
The current paper is concerned with the existence of spreading speeds and linear determinacy for two species competition systems with nonlocal dispersal in time and space periodic habitats. The notion of spreading speed intervals for such a…
Extinction is the ultimate absorbing state of any stochastic birth-death process, hence the time to extinction is an important characteristic of any natural population. Here we consider logistic and logistic-like systems under the combined…
Via hydrodynamics preserving molecular dynamics simulations we study growth phenomena in a phase separating symmetric binary mixture model. We quench high-temperature homogeneous configurations to state points inside the miscibility gap,…
This paper is concerned with the existence and qualitative properties of pulsating fronts for spatially periodic reaction-diffusion equations with bistable nonlinearities. We focus especially on the influence of the spatial period and,…
We study the evolution of a localized perturbation in a chemical system with multiple homogeneous steady states, in the presence of stirring by a fluid flow. Two distinct regimes are found as the rate of stirring is varied relative to the…
We consider a two-component competition-diffusion system with equal diffusion coefficients and inhomogeneous Dirichlet boundary conditions. When the interspecific competition parameter tends to infinity, the system solution converges to…
Both community ecology and conservation biology seek further understanding of factors governing the advance of an invasive species. We model biological invasion as an individual-based, stochastic process on a two-dimensional landscape. An…
Many fibrous materials are modeled as elastic networks featuring a substantial separation between the stiffness scales that characterize different microscopic deformation modes of the network's constituents. This scale separation has been…
Fluid--fluid interfacial instability and subsequent fluid mixing are ubiquitous in nature and engineering. The hydrodynamic instability of fluid interfaces has long centered on the pressure gradient-driven long-wavelength Rayleigh--Taylor…
This paper is concerned with the limit, as the interspecific competition rate goes to infinity, of pulsating front solutions in space-periodic media for a bistable two-species competition--diffusion Lotka--Volterra system. We distinguish…
Dispersal is an important strategy that allows organisms to locate and exploit favorable habitats. The question arises: given competition in a spatially heterogeneous landscape, what is the optimal rate of dispersal? Continuous population…
A limited mobility nonequilibrium solid-on-solid dynamical model for kinetic surface growth is introduced as a simple description for the morphological evolution of a growing interface under random vapor deposition and surface diffusion…
In this paper, we consider the diffusive Nicholson's blowflies model in spatially heterogeneous environment when the diffusion rate is large. We show that the ratio of the average of the maximum per capita egg production rate to that of the…