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The presence of global conserved quantities in interacting systems generically leads to diffusive transport at late times. Here, we show that systems conserving the dipole moment of an associated global charge, or even higher moment…
The bounded rationality plays a vital role in the collective behavior of the evacuation process. Also investigating human behavior in such an extreme situation is a continuing concern within social psychology. In this paper, we construct a…
The growth of a tissue, which depends on cell-cell interactions and biologically relevant process such as cell division and apoptosis, is regulated by a mechanical feedback mechanism. We account for these effects in a minimal…
We study a two-dimensional cellular automaton (CA), called Diffusion Rule (DR), which exhibits diffusion-like dynamics of propagating patterns. In computational experiments we discover a wide range of mobile and stationary localizations…
We study locally interacting processes in discrete time, often called probabilistic cellular automata, indexed by locally finite graphs. For infinite regular trees and certain generalized Galton-Watson trees, we show that the marginal…
Spontaneous directed motion, a hallmark of cell biology, is unusual in classical statistical physics. Here we study, using both numerical and analytical methods, organized motion in models of the cytoskeleton in which constituents are…
We propose a calibrated two-dimensional cellular automaton model to simulate pedestrian motion behavior. It is a v=4 (3) model with exclusion statistics and random shuffled dynamics. The underlying regular grid structure results in a…
The problem of a random walk in a disordered media is mapped into a model of a random walk with memory. The latter model, as opposed to the former one, does not make reference to a particular realization of the disorder. The equivalence of…
The motion of a eukaryotic cell presents a variety of interesting and challenging problems from both a modeling and a computational perspective. The processes span many spatial scales (from molecular to tissue) as well as disparate time…
Processive molecular motors which drive the traffic of organelles in cells move in a directed way along cytoskeletal filaments. On large time scales, they perform motor walks, i.e., peculiar random walks which arise from the repeated…
In this paper we study the statistical properties of a reversible cellular automaton in two out-of-equilibrium settings. In the first part we consider two instances of the initial value problem, corresponding to the inhomogeneous quench and…
A wide array of biological systems can navigate in shallow gradients of chemoattractant with remarkable precision. Whilst previous approaches model such systems using coarse-grained chemical density profiles, we construct a dynamical model…
The main purpose of this work is the mathematical modelling of large populations of cells under different deterministic interactions among themselves, in balance with naturally random diffusion. We focus on cell-cell adhesion mechanisms for…
Highly evolved animals continuously update their knowledge of social factors, refining movement decisions based on both historical and real-time observations. Despite its significance, research on the underlying mechanisms remains limited.…
In the quasi-stationary states of the Hamiltonian Mean-Field model, we numerically compute correlation functions of momenta and diffusion of angles with homogeneous initial conditions. This is an example, in a N-body Hamiltonian system, of…
In this paper I present a first attempt for a possible description of fluids dynamics by mean of a cellular automata technique. With the use of simple and elementary rules, based on random behaviour either, the model permits to obtain the…
We study time series concerning rare events. The occurrence of a rare event is depicted as a jump of constant intensity always occurring in the same direction, thereby generating an asymmetric diffusion process. We consider the case where…
A two-dimensional cellular automaton model of traffic flow with open boundaries are investigated by computer simulations. The outflow of cars from the system and the average velocity are investigated. The time sequences of the outflow and…
In this article we review classical and recent results in anomalous diffusion and provide mechanisms useful for the study of the fundamentals of certain processes, mainly in condensed matter physics, chemistry and biology. Emphasis will be…
Lattice-based random walk models are widely used to study populations of migrating cells with motility bias and proliferation. Crowding is typically represented by volume exclusion, where each lattice site can be occupied by at most one…