Related papers: A local barycentric version of the Bak-Sneppen mod…
Certain types of active systems can be treated as an equilibrium system with excess non-conservative forces driving some of the microscopic degrees of freedom. We derive results for how many particles interacting with each other with both…
A discrete-time totally asymmetric simple exclusion process on a lattice with open boundaries is considered. There are particles of different types. The type of a particle is characterized by the probability that a particle moves to a…
We consider particles on a one-dimensional lattice whose evolution is governed by nearest-neighbor interactions where particles that have reached size zero are removed from the system. Concentrating on configurations with infinitely many…
We present and study lattice and off-lattice microscopic models in which particles interact via a local anisotropic rule. The rule induces preferential hopping along one direction, so that a net current sets in if allowed by boundary…
We present a non-neutral stochastic model for the dynamics taking place in a meta-community ecosystems in presence of migration. The model provides a framework for describing the emergence of multiple ecological scenarios and behaves in two…
We study the limiting degree distribution of the vertex splitting model introduced in \cite{DDJS:2009}. This is a model of randomly growing ordered trees, where in each time step the tree is separated into two components by splitting a…
The conventional Hamming distance measurement captures only the short-time dynamics of the displacement between the uncorrelated random configurations. The minimum difference technique introduced by Tirnakli and Lyra [Int. J. Mod. Phys. C…
The generalization of the the Yang-Baxter relation is proposed. In this generalization the spectral parameters of the particles change after the scattering. The corresponding algebraic structures are discussed. The corresponding action of…
The paper treats an agent-based model with averaging dynamics to which we refer as the K-averaging model. Broadly speaking, our model can be added to the growing list of dynamics exhibiting self-organization such as the well-known…
The spectral properties of the spinless fermion model with nearest-neighbor repulsive interactions on a one-dimensional lattice are investigated using the Bethe ansatz. Although its bulk quantities are exactly the same as those of the…
We consider a class of particle systems which appear in various applications such as approximation theory, plasticity, potential theory and space-filling designs. The positions of the particles on the real line are described as a global…
I propose a model of mutually interacting particles on an M-dimensional unit sphere. I derive the dynamics of the particles by extending the dynamics of the Kuramoto-Sakaguchi model. The dynamics include a natural-frequency matrix, which…
We introduce a model of epidemics among moving particles on any locally finite graph. At any time, each vertex is empty, occupied by a healthy particle, or occupied by an infected particle. Infected particles recover at rate $1$ and…
We implement the damage spreading technique on 2-dimensional isotropic and anisotropic Bak-Sneppen models. Our extensive numerical simulations show that there exists a power-law sensitivity to the initial conditions at the statistically…
The one-dimensional scattering of a two body interacting system by an infinite wall is studied in a quantum-mechanical framework. This problem contains some of the dynamical features present in the collision of atomic, molecular and nuclear…
In a previous work we considered a two-dimensional lattice of particles and calculated its time evolution by using an interaction law based on the spatial position of the particles themselves. The model reproduced the behaviour of…
Motivated by a general principle governing regulation mechanisms in biological cells, we investigate a general interaction scheme between different populations of particles and specific particles, referred to as agents. Assuming that each…
We study the equilibrium phase diagram of a generalized ABC model on an interval of the one-dimensional lattice: each site $i=1,...,N$ is occupied by a particle of type $\a=A,B,C,$ with the average density of each particle species…
Systems of active particles can show a large variety of collective behavior. In theory, two aspects determine the collective behavior: the model at the particle level and the parameter regime. While many studies consider a single model and…
We consider a certain lattice branching random walk with on-site competition and in an environment which is heterogeneous at a macroscopic scale $1/\varepsilon$ in space and time. This can be seen as a model for the spatial dynamics of a…