Related papers: Equilibrium-like statistical mechanics in space-ti…
We present a novel approach to understand vehicular traffic jams by studying a simple model, Elementary Cellular Automaton Rule 184 (ECA 184). Using key traffic observables, such as the total delay and relaxation time, as well as…
We present a rigorous derivation of the flow at arbitrary time in a deterministic cellular automaton model of traffic flow. The derivation employs regularities in preimages of blocks of zeros, reducing the problem of preimage enumeration to…
We present a rigorous derivation of the flow at arbitrary time in a deterministic cellular automaton model of traffic flow. The derivation employs regularities in preimages of blocks of zeros, reducing the problem of preimage enumeration to…
We present a rigorous derivation of the flow at arbitrary time in a deterministic cellular automaton model of traffic flow. The derivation employs regularities in preimages of blocks of zeros, reducing the problem of preimage enumeration to…
Unlike equilibrium statistical mechanics, with its well-established foundations, a similar widely-accepted framework for non-equilibrium statistical mechanics (NESM) remains elusive. Here, we review some of the many recent activities on…
In this paper we study the space evolution in the Rule 54 reversible cellular automaton, which is a paradigmatic example of a deterministic interacting lattice gas. We show that the spatial translation of time configurations of the…
Various lattice gas automata have been proposed in the past decades to simulate physics and address a host of problems on collective dynamics arising in diverse fields. In this work, we employ the lattice gas model defined on the sphere to…
We study the statistical properties of a cellular automata model of traffic flow with the look-ahead potential. The model defines stochastic rules for the movement of cars on a lattice. We analyze the underlying statistical assumptions…
An overview is given of recent advances in nonequilibrium statistical mechanics about the statistics of random paths and current fluctuations. Although statistics is carried out in space for equilibrium statistical mechanics, statistics is…
In this paper we present a theoretical analysis of a recently proposed two-dimensional Cellular Automata model for traffic flow in cities with the novel ingredient of turning capability. Numerical simulations of this model show that there…
We study equilibrium statistical mechanics of Fermion lattice systems which require a different treatment compared with spin lattice systems due to the non-commutativity of local algebras for disjoint regions. Our major result is the…
Understanding the mechanisms leading to the formation and the propagation of traffic jams in large cities is of crucial importance for urban planning and traffic management. Many studies have already considered the emergence of traffic jams…
The statistical modeling of space-time extremes in environmental applications is key to understanding complex dependence structures in original event data and to generating realistic scenarios for impact models. In this context of…
We study the microscopic time fluctuations of traffic-load and the global statistical properties of a dense traffic of particles on scale-free cyclic graphs. For a wide range of driving rates $R$ the traffic is stationary and the load…
In the so-called "microscopic" models of vehicular traffic, attention is paid explicitly to each individual vehicle each of which is represented by a "particle"; the nature of the "interactions" among these particles is determined by the…
I give a highly selective overview of the way statistical mechanics explains the microscopic origins of the time asymmetric evolution of macroscopic systems towards equilibrium and of first order phase transitions in equilibrium. These…
We study several deterministic one-dimensional traffic models. For integer positions and velocities we find the typical high and low density phases separated by a simple transition. If positions and velocities are continuous variables the…
We introduce and analyze a model for the transport of particles or energy in extended lattice systems. The dynamics of the model acts on a discrete phase space at discrete times but has nonetheless some of the characteristic properties of…
We introduce a general formulation for an implicit equation-free method in the setting of slow-fast systems. First, we give a rigorous convergence result for equation-free analysis showing that the implicitly defined coarse-level time…
This paper proposes an improved cellular automaton traffic flow model based on the brake light model, which takes into account that the desired time gap of vehicles is remarkably larger than one second. Although the hypothetical steady…