50,163 research outputs found
A fully-discrete-state kinetic theory approach to modeling vehicular traffic
This paper presents a new mathematical model of vehicular traffic, based on
the methods of the generalized kinetic theory, in which the space of
microscopic states (position and velocity) of the vehicles is genuinely
discrete. While in the recent literature discrete-velocity kinetic models of
car traffic have already been successfully proposed, this is, to our knowledge,
the first attempt to account for all aspects of the physical granularity of car
flow within the formalism of the aforesaid mathematical theory. Thanks to a
rich but handy structure, the resulting model allows one to easily implement
and simulate various realistic scenarios giving rise to characteristic traffic
phenomena of practical interest (e.g., queue formation due to roadworks or to a
traffic light). Moreover, it is analytically tractable under quite general
assumptions, whereby fundamental properties of the solutions can be rigorously
proved.Comment: 22 pages, 3 figure
Generic principles of active transport
Nonequilibrium collective motion is ubiquitous in nature and often results in
a rich collection of intringuing phenomena, such as the formation of shocks or
patterns, subdiffusive kinetics, traffic jams, and nonequilibrium phase
transitions. These stochastic many-body features characterize transport
processes in biology, soft condensed matter and, possibly, also in nanoscience.
Inspired by these applications, a wide class of lattice-gas models has recently
been considered. Building on the celebrated {\it totally asymmetric simple
exclusion process} (TASEP) and a generalization accounting for the exchanges
with a reservoir, we discuss the qualitative and quantitative nonequilibrium
properties of these model systems. We specifically analyze the case of a
dimeric lattice gas, the transport in the presence of pointwise disorder and
along coupled tracks.Comment: 21 pages, 10 figures. Pedagogical paper based on a lecture delivered
at the conference on "Stochastic models in biological sciences" (May 29 -
June 2, 2006 in Warsaw). For the Banach Center Publication
Nonequilibrium Steady States of Matrix Product Form: A Solver's Guide
We consider the general problem of determining the steady state of stochastic
nonequilibrium systems such as those that have been used to model (among other
things) biological transport and traffic flow. We begin with a broad overview
of this class of driven diffusive systems - which includes exclusion processes
- focusing on interesting physical properties, such as shocks and phase
transitions. We then turn our attention specifically to those models for which
the exact distribution of microstates in the steady state can be expressed in a
matrix product form. In addition to a gentle introduction to this matrix
product approach, how it works and how it relates to similar constructions that
arise in other physical contexts, we present a unified, pedagogical account of
the various means by which the statistical mechanical calculations of
macroscopic physical quantities are actually performed. We also review a number
of more advanced topics, including nonequilibrium free energy functionals, the
classification of exclusion processes involving multiple particle species,
existence proofs of a matrix product state for a given model and more
complicated variants of the matrix product state that allow various types of
parallel dynamics to be handled. We conclude with a brief discussion of open
problems for future research.Comment: 127 pages, 31 figures, invited topical review for J. Phys. A (uses
IOP class file
Steady state solutions of hydrodynamic traffic models
We investigate steady state solutions of hydrodynamic traffic models in the
absence of any intrinsic inhomogeneity on roads such as on-ramps. It is shown
that typical hydrodynamic models possess seven different types of inhomogeneous
steady state solutions. The seven solutions include those that have been
reported previously only for microscopic models. The characteristic properties
of wide jam such as moving velocity of its spatiotemporal pattern and/or
out-flux from wide jam are shown to be uniquely determined and thus independent
of initial conditions of dynamic evolution. Topological considerations suggest
that all of the solutions should be common to a wide class of traffic models.
The results are discussed in connection with the universality conjecture for
traffic models. Also the prevalence of the limit-cycle solution in a recent
study of a microscopic model is explained in this approach.Comment: 9 pages, 6 figure
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