Related papers: Single Transition Layer in Mass-Conserving Reactio…
A thermodynamic approach to rapid phase transformations within a diffuse interface in a binary system is developed. Assuming an extended set of independent thermodynamic variables formed by the union of the classic set of slow variables and…
This paper investigates the propagation phenomena of a monotone bistable reaction-diffusion system in an exterior domain of R2. By constructing suitable sub- and supersolutions, we establish the existence and monotonicity of an entire…
We consider general reaction diffusion systems posed on rectangular lattices in two or more spatial dimensions. We show that travelling wave solutions to such systems that propagate in rational directions are nonlinearly stable under small…
We establish the existence of solutions to a class of non-linear stochastic differential equation of reaction-diffusion type in an infinite-dimensional space, with diffusion corresponding to a given transition kernel. The solution obtained…
Self-diffusion and radial distribution functions are studied in a strongly confined Lennard-Jones fluid. Surprisingly, in the solid-liquid phase transition region, where the system exhibits dynamic coexistence, the self-diffusion constants…
In the past the study of reaction-diffusion systems has greatly contributed to our understanding of the behavior of many-body systems far from equilibrium. In this paper we aim at characterizing the properties of diffusion limited reactions…
A Rayleigh B\'enard instability study using the energy conserving dissipative particle dynamics method is presented here for the first time. The simulation is performed on an ideal dissipative particle dynamics fluid in a three dimensional…
Transition waves in mechanical metamaterials manifest themselves as propagating interfaces between different stable states in lattices composed of arrays of coupled, intrinsically bistable elements. Here, we show experimentally and…
Many mathematical models for biological phenomena, such as the spread of diseases, are based on reaction-diffusion equations for densities of interacting cell populations. We present a consistent derivation of reaction-diffusion equations…
The emergence of stable disordered patterns in reactive system on spatially homogenous substrate is studied in the context of vegetation patterns in the semi-arid climatic zone. It is shown that reaction-diffusion systems that allow for…
Numerous experimental data on the rapid solidification of binary systems exhibit the formation of metastable solid phases with the initial (nominal) chemical composition. This fact is explained by complete solute trapping leading to…
We study thermal instability in NbN superconducting stripline resonators. The system exhibits extreme nonlinearity near a bifurcation, which separates a monostable zone and an astable one. The lifetime of the metastable state, which is…
Protein aggregation on the plasma membrane (PM) is of critical importance to many cellular processes such as cell adhesion, endocytosis, fibrillar conformation, and vesicle transport. Lateral diffusion of protein aggregates or clusters on…
The aim of this work is to study the effect of diffusion on the stability of the equilibria in a general two-components reaction-diffusion system with Neumann boundary conditions in the space of continuous functions. As by product, we…
In many plasma systems, introducing a small background shear flow is enough to stabilize the system linearly. The nonlinear dynamics are much less sensitive to sheared flows than the average linear growthrates, and very small amplitude…
We study a one dimensional metastable dynamics of internal interfaces for the initial boundary value problem for the following convection-reaction-diffusion equation \begin{equation*} \partial_t u = \varepsilon \partial_x^2 u -\partial_x…
We consider reaction-diffusion equations that are stochastically forced by a small multiplicative noise term. We show that spectrally stable travelling wave solutions to the deterministic system retain their orbital stability if the…
Noise-induced transitions between metastable fixed points in systems evolving on multiple time scales are analyzed in situations where the time scale separation gives rise to a slow manifold with bifurcation. This analysis is performed…
We study a system of all-to-all weakly coupled uniformly expanding circle maps in the thermodynamic limit. The state of the system is described by a probability measure and its evolution is given by the action of a nonlinear operator, also…
We study pattern formation in a chemotaxis model of bacteria and soil carbon dynamics as an example system where transient dynamics can give rise to pattern formation outside of Turing unstable regimes. We use a detailed analysis of the…