Related papers: Cluster geometry and survival probability in syste…
The cluster distributions of different systems are examined to search for signatures of a continuous phase transition. In a system known to possess such a phase transition, both sensitive and insensitive signatures are present; while in…
Dynamical reaction-diffusion processes and meta-population models are standard modeling approaches for a wide variety of phenomena in which local quantities - such as density, potential and particles - diffuse and interact according to the…
We investigate an extremal dynamics model of evolution with a variable number of units. Due to addition and removal of the units, the topology of the network evolves and the network splits into several clusters. The activity is mostly…
Understanding the statistical properties of a collection of individuals subject to random displacements and birth-and-death events is key to several applications in physics and life sciences, encompassing the diagnostic of nuclear reactors…
We use a one-dimensional random walk on $D$-dimensional hyper-spheres to determine the critical behavior of statistical systems in hyper-spherical geometries. First, we demonstrate the properties of such a walk by studying the phase diagram…
We present an exact mapping between two simple spin models: the Fredrickson-Andersen (FA) model and a model of annihilating random walks with spontaneous creation from the vacuum, A+A <-> 0. We discuss the geometric structure of the mapping…
We investigated the phase transition behavior of a binary spreading process in two dimensions for different particle diffusion strengths ($D$). We found that $N>2$ cluster mean-field approximations must be considered to get consistent…
We determine the phase diagrams of conservative diffusive contact processes by means of numerical simulations. These models are versions of the ordinary diffusive single-creation, pair-creation and triplet-creation contact processes in…
We examine a model in which a nonequilibrium phase transition from an active to an extinct state is observed. The order of this phase transition has been shown to be either continuous or first-order, depending on the parameter values and…
We study the density of clustered immobile reactants in the diffusion-controlled single species annihilation. An initial state in which these impurities occupy a subspace of codimension d' leads to a substantial enhancement of their…
A diffusion-limited aggregation process, in which clusters coalesce by means of 3-particle reaction, A+A+A->A, is investigated. In one dimension we give a heuristic argument that predicts logarithmic corrections to the mean-field asymptotic…
Discontinuous percolation transitions and the associated tricritical points are manifest in a wide range of both equilibrium and non-equilibrium cooperative phenomena. To demonstrate this, we present and relate the continuous and first…
We introduce a model for a population on a lattice with diffusion and birth/death according to 2A->3A and A->0 for a particle A. We find that the model displays a phase transition from an active to an absorbing state which is continuous in…
In biological materials, strong binding despite an applied load force is often based on clusters of dynamic bonds that share the load. Different macroscopic behaviors have been described depending on whether the load is shared locally or…
Extensive simulations are performed of the diffusion-limited reaction A$+$B$\to 0$ in one dimension, with initially separated reagents. The reaction rate profile, and the probability distributions of the separation and midpoint of the…
This chapter provides a pedagogical introduction and overview of spatial and temporal correlation and fluctuation effects resulting from the fundamentally stochastic kinetics underlying chemical reactions and the dynamics of populations or…
We study the decay process for the reaction-diffusion process of three species on the small-world network. The decay process is manipulated from the deterministic rate equation of three species in the reaction-diffusion system. The particle…
The microscopic structure and movement of reaction fronts in reaction diffusion systems far from equilibrium are investigated. We show that some three-site interaction models exhibit exact diffusive shock measures, i.e. domains of different…
Reaction-diffusion processes are the foundational model for a diverse range of complex systems, ranging from biochemical reactions to social agent-based phenomena. The underlying dynamics of these systems occur at the individual…
The pair-contact process 2A->3A, 2A->0 with diffusion of individual particles is a simple branching-annihilation processes which exhibits a phase transition from an active into an absorbing phase with an unusual type of critical behaviour…