相关论文: An Exactly Solvable Model for Single-Lane Unidirec…

We perform intensive computations of Generalised Langton's Ants, discovering rules with a big number of highways. We depict the structure of some of them, formally proving that the number of highways which are possible for a given rule does…

Ants are known to be able to find paths of minimal length between the nest and food sources. The deposit of pheromones while they search for food and their chemotactical response to them has been proposed as a crucial element in the…

Tolls are collected on many highways as a means of traffic control and revenue generation. However, the presence of tollbooths on highway surely slows down traffic flow. Here, we investigate how the presence of tollbooths affect the average…

We present an exactly solvable model for queue dynamics. Our model is very simple but provides the essential property for such dynamics. As an example, the model has the traveling cluster solution as well as the homogeneous flow solution.…

We consider a continuous mathematical description of a population of ants and simulate numerically their foraging behavior using a system of partial differential equations of chemotaxis type. We show that this system accurately reproduces…

We develop and analyse a finite volume scheme for a nonlocal active matter system known to exhibit a rich array of complex behaviours. The model under investigation was derived from a stochastic system of interacting particles describing a…

Collective behavior of active elements inspired by mass of biological organisms is addressed. Especially, two topics are focused on among amazing behaviors performed by colony of ants. First, task allocation phenomena are treated from the…

The thermal ratchets model toggles a spatially periodic asymmetric potential to rectify random walks and achieve transport of diffusing particles. We numerically solve the governing equation for the full dynamics of an infinite 1D ratchet…

Using a simple model for the trail formation of ants, the relation between i)the schedule of feeding which represents the unsteady natural environment, ii)emerging patterns of trails connecting a nest with food resources, and iii)the…

In one-dimensional, heterogeneous systems, the whole traffic dynamics depend strongly on the behavior of the leading vehicle. This result holds for a class of vehicular traffic models satisfying the following properties. The interactions…

The present paper proposes a novel interpretation of the widely scattered states (called synchronized traffic) stimulated by Kerner's hypotheses about the existence of a multitude of metastable states in the fundamental diagram. Using…

We study analytically the tracer particle mobility in single-file systems with distributed friction constants. Our system serves as a prototype for non-equilibrium, heterogeneous, strongly interacting Brownian systems. The long time…

We extend the Aw-Rascle macroscopic model of car traffic into a two-way multi-lane model of pedestrian traffic. Within this model, we propose a technique for the handling of the congestion constraint, i.e. the fact that the pedestrian…

We present an exactly solvable nonlinear model for the directed motion of an object due to zero-mean fluctuations on a uniform featureless surface. Directed motion results from the effect of dry (Coulombic) friction coupled to asymmetric…

We study the asymptotic stability of periodic solutions for sweeping processes defined by a polyhedron with translationally moving faces. Previous results are improved by obtaining a stronger $W^{1,2}$ convergence. Then we present an…

Interacting particles diffusing in single-file is a fundamental model of transport in narrow channels where particles cannot bypass each other. An important result has been obtained by Kollmann [Phys. Rev. Lett. 90, 180602 (2003)] for the…

We investigate the dynamics of a single tracer exploring a course of fixed obstacles in the vicinity of the percolation transition for particles confined to the infinite cluster. The mean-square displacement displays anomalous transport,…

Switching interacting particle systems studied in probability theory are the stochastic processes of hopping particles on a lattice made up of slow and fast particles, where the switching between these types of particles occurs randomly at…

Collective motion by animal groups is affected by internal interactions, external constraints and the influx of information. A quantitative understanding of how these different factors give rise to different modes of collective motion is,…

We study the asymptotic behavior of a nonlinear PDE model for ant trail formation, which was introduced in [3]. We establish the existence of a compact global attractor and prove the nonlinear instability of the homogeneous steady state…