Related papers: Mixing in Reaction-Diffusion Systems: Large Phase …

We show that an analogy between crowding in fluid and jammed phases of hard spheres captures the density dependence of the kissing number for a family of numerically generated jammed states. We extend this analogy to jams of mixtures of…

We investigate the nonparametric, composite hypothesis testing problem for arbitrary unknown distributions in the asymptotic regime where both the sample size and the number of hypotheses grow exponentially large. Such asymptotic analysis…

In this paper we perform a formal asymptotic analysis on a kinetic model for reactive mixtures in order to derive a reaction-diffusion system of Maxwell-Stefan type. More specifically, we start from the kinetic model of simple reacting…

We study diffusion of hardcore particles on a one dimensional periodic lattice subjected to a constraint that the separation between any two consecutive particles does not increase beyond a fixed value $(n+1);$ initial separation larger…

In reaction-diffusion models of annihilation reactions in low dimensions, single-particle dynamics provides a bottleneck for reactions, leading to an anomalously slow approach to the empty state. Here, we construct a reaction model with a…

In this paper, we develop asymptotic theory for the mixing detection methodology proposed by M. Magdziarz and A. Weron [Physical Review E, 84:051138 (2011)]. The assumptions cover a broad family of Gaussian stochastic processes including…

Particle filtering is a Bayesian inference method and a fundamental tool in state estimation for dynamic systems, but its effectiveness is often limited by the constraints of the initial prior distribution, a phenomenon we define as the…

We construct a kinetic model for matter-radiation interactions whose hydrodynamic gradient expansion can be computed analytically up to infinite order in derivatives, in the fully nonlinear regime, and for arbitrary flows. The frequency…

We study a large class of 1D reaction diffusion models with quenched disorder using a real space renormalization group method (RSRG) which yields exact results at large time. Particles (e.g. of several species) undergo diffusion with random…

Coarsening of two-phase systems is crucial for the stability of dense particle packings such as alloys, foams, emulsions or supersaturated solutions. Mean field theories predict an asymptotic scaling state with a broad particle size…

We examine the long-time behaviour of A+B \to 0 reaction-diffusion systems with initially separated species A and B. All of our analysis is carried out for arbitrary (positive) values of the diffusion constant D_A of particles A and initial…

We study nonlinear stability of spatially homogeneous oscillations in reaction-diffusion systems. Assuming absence of unstable linear modes and linear diffusive behavior for the neutral phase, we prove that spatially localized perturbations…

Pattern formation mechanisms of a reaction-diffusion-advection system, with one diffusivity, differential advection, and (Robin) boundary conditions of Danckwerts type, are being studied. Pattern selection requires mapping the domains of…

We study the steady state of a stochastic particle system on a two-dimensional lattice, with particle influx, diffusion and desorption, and the formation of a dimer when particles meet. Surface processes are thermally activated, with…

We carry out a comprehensive linear stability analysis of active Brownian particle systems around a constant homogeneous state. These scalar models, being important prototypes for the continuous description of active matter, are…

Diffusive dynamics abound in nature and have been especially studied in physical, biological, and financial systems. These dynamics are characterised by a linear growth of the mean squared displacement (MSD) with time. Often, the conditions…

This is a pedagogical account on reaction-diffusion systems and their relationship with integrable quantum spin chains. Reaction-diffusion systems are paradigmatic examples of non-equilibrium systems. Their long-time behaviour is strongly…

Models of reaction diffusion processes usually employ discrete lattice models with particles interacting at the same site, resulting in localized reactions in the continuum limit. Here, various non-local interactions are considered, and two…

A driven diffusive model of three types of particles that exhibits phase separation on a ring is introduced. The dynamics is local and comprises nearest neighbor exchanges that conserve each of the three species. For the case in which the…

We consider a coupled reaction-advection-diffusion system based on the Fisher-KPP and Burgers equations. These equations serve as a one-dimensional version of a model for a reacting fluid in which the arising density differences induce a…