Related papers: N Bugs on a Circle

Consider a growing system of random walks on the 3,2-alternating tree, where generations of nodes alternate between having two and three children. Any time a particle lands on a node which has not been visited previously, a new particle is…

In majority bootstrap percolation on a graph G, an infection spreads according to the following deterministic rule: if at least half of the neighbours of a vertex v are already infected, then v is also infected, and infected vertices remain…

The random walk problem is studied in two and three dimensions in the presence of a random distribution of static traps. An efficient Monte Carlo method, based on a mapping onto a polymer model, is used to measure the survival probability…

Motivated by an analogy with traffic, we simulate two species of particles (`vehicles'), moving stochastically in opposite directions on a two-lane ring road. Each species prefers one lane over the other, controlled by a parameter $0 \leq b…

Peritrichous bacteria such as Escherichia coli swim in viscous fluids by forming a helical bundle of flagellar filaments. The filaments are spatially distributed around the cell body to which they are connected via a flexible hook. To…

In this paper, we study a general Syracuse problem. We give some necessary conditions concerning the existence of eventual non trivial cycles. Some properties based on linear logarithmic forms are established. New general conjectures are…

Single-file systems, in which particles diffuse in narrow channels while not overtaking each other, is a fundamental model for the tracer subdiffusion observed in confined geometries, such as in zeolites or carbon nanotubes. Twenty years…

Computational models of collective behavior in birds has allowed us to infer interaction rules directly from experimental data. Using a generic form of these rules we explore the collective behavior and emergent dynamics of a simulated…

We study gravitational clustering of mass points in three dimensions with random initial positions and periodic boundary conditions (no expansion) by numerical simulations. Correlation properties are well defined in the system and a sort of…

We study theoretically the collective dynamics of particles driven by an optical vortex along a circular path. Phase equations of N particles are derived by taking into account both hydrodynamic and repulsive interactions between them. For…

We study the cyclic dominance of three species in two-dimensional constrained Newman-Watts networks with a four-state variant of the rock-paper-scissors game. By limiting the maximal connection distance $R_{max}$ in Newman-Watts networks…

We provide a polynomial algorithm to find the value and an optimal strategy for a generalization of the Pig game. Modeled as a competitive Markov decision process, the corresponding Bellman equations can be decoupled leading to systems of…

We explore static noise in a discrete quantum random walk over a homogeneous cyclic graph, focusing on spectral and dynamical properties. Using a three-parameter unitary coin, we control the spectral structure of the noiseless step operator…

Using Monte Carlo simulations we have studied the transition from an "active" steady state to an absorbing "inactive" state for two versions of the branching annihilating random walks with parity conservation on a square lattice. In the…

The effect of space inhomogeneities on a diffusing particle is studied in the framework of the 1D random walk. The typical time needed by a particle to cross a one--dimensional finite lane, the so--called residence time, is computed…

We study a variation of the trapping reaction, A+B->A, in which both the traps (A) and the particles (B) undergo diffusion, and the traps upon meeting react according to A+A->0 or A. This two-species reaction-diffusion system is known to…

The theory of learning in games has extensively studied situations where agents respond dynamically to each other by optimizing a fixed utility function. However, in real situations, the strategic environment varies as a result of past…

We investigate the long time behaviour of the one-dimensional ballistic aggregation model that represents a sticky gas of N particles with random initial positions and velocities, moving deterministically, and forming aggregates when they…

We study the problem of clustering sequences of unlabeled point sets taken from a common metric space. Such scenarios arise naturally in applications where a system or process is observed in distinct time intervals, such as biological…

We propose a new model in order to study behaviors of self-organized system such as a group of animals. We assume that the individuals have two degrees of freedom corresponding one to their internal state and the other to their external…