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A new stochastic cellular automaton (CA) model of traffic flow, which includes slow-to-start effects and a driver's perspective, is proposed by extending the Burgers CA and the Nagel-Schreckenberg CA model. The flow-density relation of this…
The numerical simulation of multiphase flows presents several challenges, namely the transport of different phases within de domain and the inclusion of capillary effects. Here, these are approached by enforcing a discrete…
Defining the density flow of perturbations moving at a given speed for cellular automata, we establish equalities and inequalities between the measurable entropy of a cellular automaton and the measurable entropy of its associated shift.
A method for studying the qualitative dynamical properties of abstract computing machines based on the approximation of their program-size complexity using a general lossless compression algorithm is presented. It is shown that the…
Computational fluid dynamics is a direct modeling of physical laws in a discretized space. The basic physical laws include the mass, momentum and energy conservations, physically consistent transport process, and similar domain of…
In this paper, we give an elaborate and understandable review of traffic cellular automata (TCA) models, which are a class of computationally efficient microscopic traffic flow models. TCA models arise from the physics discipline of…
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…
We present a 2-dimensional cellular automaton model for the simulation of pedestrian dynamics. The model is extremely efficient and allows simulations of large crowds faster than real time since it includes only nearest-neighbour…
The Active Flux method can be seen as an extended finite volume method. The degrees of freedom of this method are cell averages, as in finite volume methods, and in addition shared point values at the cell interfaces, giving rise to a…
We rigorously prove a form of disorder-resistance for a class of one-dimensional cellular automaton rules, including some that arise as boundary dynamics of two-dimensional solidification rules. Specifically, when started from a random…
We study the dynamics of (synchronous) one-dimensional cellular automata with cyclical boundary conditions that evolve according to the majority rule with radius $ r $. We introduce a notion that we term cell stability with which we express…
This paper studies directional dynamics in cellular automata, a formalism previously introduced by the third author. The central idea is to study the dynamical behaviour of a cellular automaton through the conjoint action of its global rule…
We say that a Cellular Automata (CA) is coalescing when its execution on two distinct (random) initial configurations in the same asynchronous mode (the same cells are updated in each configuration at each time step) makes both…
We propose an arbitrarily high-order accurate numerical method for conservation laws that is based on a continuous approximation of the solution. The degrees of freedom are point values at cell interfaces and moments of the solution inside…
Incompressibility is a fundamental condition in most fluid models. Accumulation of simulation errors violates it and causes volume loss. Past work suggested correction methods to battle it. These methods, however, are imperfect and in some…
Many fundamental biological processes are dependent on cellular migration. Although the mechanical mechanisms of single-cell migration are relatively well understood, those underlying migration of multiple cells adhered to each other in a…
We discuss the interpolation of the electric and magnetic fields within a charge-conserving Particle-In-Cell scheme. The choice of the interpolation procedure for the fields acting on a particle can be constrained by analyzing conservation…
In this paper, we explore the two-dimensional behavior of cellular automata with shuffle updates. As a test case, we consider the evacuation of a square room by pedestrians modeled by a cellular automaton model with a static floor field.…
We introduce a methodology for seeking conservation laws within a Hamiltonian dynamical system, which we term ``neural deflation''. Inspired by deflation methods for steady states of dynamical systems, we propose to {iteratively} train a…
It is shown that a variety of deterministic cellular automaton models of highway traffic flow obey a variational principle which states that, for a given car density, the average car flow is a non-decreasing function of time. This result is…