相关论文: How fast does Langton's ant move?

In this paper we consider the discrete Allen-Cahn equation posed on a two-dimensional rectangular lattice. We analyze the large-time behaviour of solutions that start as bounded perturbations to the well-known planar front solution that…

We develop a general technique to calculate the probability of transitions over the barriers in spin-glasses in the framework of the dynamical theory. We use Lagrangian formulation of the instanton dynamics in which the transitions are…

Active walker models have recently proved their great value for describing the formation of clusters, periodic patterns, and spiral waves as well as the development of rivers, dielectric breakdown patterns, and many other structures. It is…

We consider the simplest identical-fermion system that exhibits the phenomenon of entanglement (beyond exchange correlations) to analyze its speed of evolution towards an orthogonal state, and revisit the relation between this latter and…

We study a branching Brownian motion $Z$ in $\mathbb{R}^d$, among obstacles scattered according to a Poisson random measure with a radially decaying intensity. Obstacles are balls with constant radius and each one works as a trap for the…

A simple algorithm for constructing an effective traffic model is presented. The algorithm uses statistically well-defined quantities extracted from the flow-density plot, and the resulting effective model naturally captures and predicts…

We study the properties of least time trajectories for particles moving on a two dimensional surface which consists of piecewise homogeneous regions. The particles are assumed to move with different constant speeds on different regions and…

A cellular automaton model of traffic flow taking into account velocity anticipation is introduced. The strength of anticipation can be varied which allows to describe different driving schemes. We find phase separation into a free-flow…

Jamming transition in traffic flow (between free and jammed traffic) for homogeneous car following model has been investigated taking into account fluctuations of characteristic acceleration/braking time. These fluctuations are defined by…

Simple random walks on various types of partially horizontally oriented regular lattices are considered. The horizontal orientations of the lattices can be of various types (deterministic or random) and depending on the nature of the…

The escape of the randomly accelerated undamped particle from the finite interval under action of stochastic resetting is studied. The motion of such a particle is described by the full Langevin equation and the particle is characterized by…

We analyze the structure and dynamics in the low-density phase of the deterministic two-dimensional cellular automaton model of traffic flow introduced in [O. Biham, A.A. Middleton and D. Levine, Phys. Rev. A 46, R6124 (1992)]. The model…

We propose an active walker model for the motion of individual ants communicating via chemical signals. It is assumed that communication takes the form of a time-dependent pheromone field that feedbacks into the motion ants through…

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…

The fast-superfast transition is a particular movement of eigenvalues found by Lewis et al. when studying the family of sleeping equilibria in the Lagrange top. Although this behaviour of eigenvalues typically suggests a change in stability…

We develop an instanton approach to the non-equilibrium dynamics in one-dimensional random environments. The long time behavior is controlled by rare fluctuations of the disorder potential and, accordingly, by the tail of the distribution…

Evolution of coherent states is considered for a particle confined to a cylinder moving in a harmonic oscillator potential. Because of the discontinuous changes as time goes by of the phase representing the position of a particle on a…

We report the emergence of Log-normal Superstatistics in the collective motion of ants confined in a quasi-2D arena and exposed to a panic-inducing stimulus. A data-driven superstatistical Langevin model accurately reproduces the transition…

We investigate a driven diffusive lattice gas model with two oppositely moving species of particles. The model is motivated by bi-directional traffic of ants on a pre-existing trail. A third species, corresponding to pheromones used by the…

Adiabatic passage employs a slowly varying time-dependent Hamiltonian to control the evolution of a quantum system along the Hamiltonian eigenstates. For processes of finite duration, the exact time evolving state may deviate from the…