Related papers: Stochastic dynamics on evolving geometric graphs
To identify emerging microscopic structures in low temperature spin glasses, we study self-sustained clusters (SSC) in spin models defined on sparse random graphs. A message-passing algorithm is developed to determine the probability of…
Stochastic models play an essential role in accounting for the variability and unpredictability seen in real-world. This paper focuses on the application of the gamma distribution to analysis of the stationary distributions of populations…
A stochastic differential equation that describes the dynamics of single-domain magnetic particles at any temperature is derived using a classical formalism. The deterministic terms recover existing theory and the stochastic process takes…
Population structure can have a significant effect on evolution. For some systems with sufficient symmetry, analytic results can be derived within the mathematical framework of evolutionary graph theory which relate to the outcome of the…
The spatial logistic model is a system of point entities (particles) in $\mathbb{R}^d$ which reproduce themselves at distant points (dispersal) and die, also due to competition. The states of such systems are probability measures on the…
The self-gravitating systems are formed by particles interacting through gravity. They describe structure formation in the universe. As a consequence of the long range interaction of gravity, they are inhomogeneous even at thermal…
In this paper, we construct under general assumptions the stochastic dynamics of an interacting particle system in a bounded domain $\Omega$ with sticky boundary. Under appropriate conditions on the interaction the constructed process…
Let $\Gamma$ denote the space of all locally finite subsets (configurations) in $\mathbb R^d$. A stochastic dynamics of binary jumps in continuum is a Markov process on $\Gamma$ in which pairs of particles simultaneously hop over $\mathbb…
Various lattice gas automata have been proposed in the past decades to simulate physics and address a host of problems on collective dynamics arising in diverse fields. In this work, we employ the lattice gas model defined on the sphere to…
We study a system of $N$ interacting particles on $\bf{Z}$. The stochastic dynamics consists of two components: a free motion of each particle (independent random walks) and a pair-wise interaction between particles. The interaction belongs…
In the stochastic sandpile model on a graph, particles interact pairwise as follows: if two particles occupy the same vertex, they must each take an independent random walk step with some probability $0<p<1$ of not moving. These…
The evolution of galaxies is governed by equations with chaotic solutions: gravity and compressible hydrodynamics. While this micro-scale chaos and stochasticity has been well studied, it is poorly understood how it couples to macro-scale…
We investigate regular configurations of a small number of particles settling under gravity in a viscous fluid. The particles do not touch each other and can move relative to each other. The dynamics is analyzed in the point-particle…
In this paper we propose a model for open Markov chains that can be interpreted as a system of non-interacting particles evolving according to the rules of a Markov chain. The number of particles in the system is not constant, because we…
We will construct a theory which can explain the dynamics toward the steady state self-gravitating systems (SGSs) where many particles interact via the gravitational force. Real examples of SGS in the universe are globular clusters and…
We present local distributed, stochastic algorithms for \emph{alignment} in self-organizing particle systems (SOPS) on two-dimensional lattices, where particles occupy unique sites on the lattice, and particles can make spatial moves to…
We study by Molecular Dynamics simulation a dense one-component system of particles confined on a spherical substrate. We more specifically investigate the evolution of the structural and dynamical properties of the system when changing the…
We consider birth and death stochastic dynamics of particle systems with attractive interaction. The heuristic generator of the dynamics has a constant birth rate and density dependent decreasing death rate. The corresponding statistical…
Jamming is a phenomenon shared by a wide variety of systems, such as granular materials, foams, and glasses in their high density regime. This has motivated the development of a theoretical framework capable of explaining many of their…
In this paper, we proposed a stochastic model which describes two species of particles moving in counterflow. The model generalizes the theoretical framework describing the transport in random systems since particles can work as mobile…