Related papers: Uphill in reaction-diffusion multi-species interac…
The dynamics of a coupled two-component nonequilibrium system is examined by means of continuum field theory representing the corresponding master equation. Particles of species A may perform hopping processes only when particles of…
For a large class of fluids exhibiting ultrasoft bounded pair potentials, particles form crystals consisting of clusters located in the lattice sites, with a density-independent lattice constant. Here we present an investigation on the…
In this paper, we are concerned with a class of conservative systems including asymmetric exclusion processes and zero-range processes as examples, where some particles are initially placed on $N$ positions. A particle jumps from a position…
Domain growth is a key process in many areas of biology, including embryonic development, the growth of tissue, and limb regeneration. As a result, mechanisms for incorporating it into traditional models for cell movement, interaction, and…
We study the large scale behavior of a collection of hard core run and tumble particles on a one dimensional lattice with periodic boundary conditions. Each particle has persistent motion in one direction decided by an associated spin…
At finite concentrations of reacting molecules, kinetics of diffusion-controlled reactions is affected by intra-reactant interactions. As a result, multi-particle reaction statistics cannot be deduced from single-particle results. Here we…
Collective motion is often modeled within the framework of active fluids, where the constituent active particles, when interactions with other particles are switched off, perform normal diffusion at long times. However, in biology,…
We consider the hydrodynamic behavior of some conservative particle systems with degenerate jump rates without exclusive constraints. More precisely, we study the particle systems without restrictions on the total number of particles per…
Diffusion of colloidal particles in a complex environment such as polymer networks or biological cells is a topic of high complexity with significant biological and medical relevance. In such situations, the interaction between the…
We consider a single species reaction diffusion system on a two dimensional lattice where the particles $A$ are biased to move towards their nearest neighbours and annihilate as they meet; $A + A \to \emptyset$. Allowing the bias to take…
Considering the dynamics of non-interacting particles randomly moving on a lattice, the occurrence of a discontinuous transition in the values of the lattice parameters (lattice spacing and hopping times) determines the uprisal of two…
Reaction-diffusion equations are widely used as the governing evolution equations for modeling many physical, chemical, and biological processes. Here we derive reaction-diffusion equations to model transport with reactions on a…
We consider a reaction-diffusion system where some components react and diffuse on the boundary of a region, while other components diffuse in the interior and react with those on the boundary through mass transport. We establish criteria…
Pour sand into a container and only the grains near the top surface move. The collective motion associated with the translational and rotational energy of the grains in a thin flowing layer is quickly dissipated as friction through…
We discuss diffusion properties of a dynamical system, which is characterised by long-tail distributions and finite correlations. The particle velocity has the stable L\'evy distribution; it is assumed as a jumping process (the kangaroo…
Reaction-diffusion systems, which consist of the reacting particles subject to diffusion process, constitute one of the common examples of non-linear statistical systems. In low space dimensions $d \leq 2$ the usual description by means of…
The particle diffusion in a fluid is a classical topic that dates back to more than one century ago. However, a full solution to this issue still lacks. In this work the velocity autocorrelation function and the diffusion constant are…
We introduce two discrete models of a collection of colliding particles with stored momentum and study the asymptotic growth of the mean-square displacement of an active particle. We prove that the models are superdiffusive in one dimension…
An autocatalytic reacting system with particles interacting at a finite distance is studied. We investigate the effects of the discrete-particle character of the model on properties like reaction rate, quenching phenomenon and front…
We consider a one-dimensional exclusion dynamics in mild contact with boundary reservoirs. In the diffusive scale, the particles' density evolves as the solution of the heat equation with non-linear Robin boundary conditions. For…