142 research outputs found
Spring-block model for a single-lane highway traffic
A simple one-dimensional spring-block chain with asymmetric interactions is
considered to model an idealized single-lane highway traffic. The main elements
of the system are blocks (modeling cars), springs with unidirectional
interactions (modeling distance keeping interactions between neighbors), static
and kinetic friction (modeling inertia of drivers and cars) and spatiotemporal
disorder in the values of these friction forces (modeling differences in the
driving attitudes). The traveling chain of cars correspond to the dragged
spring-block system. Our statistical analysis for the spring-block chain
predicts a non-trivial and rich complex behavior. As a function of the disorder
level in the system a dynamic phase-transition is observed. For low disorder
levels uncorrelated slidings of blocks are revealed while for high disorder
levels correlated avalanches dominates.Comment: 6 pages, 7 figure
A characteristic particle method for traffic flow simulations on highway networks
A characteristic particle method for the simulation of first order
macroscopic traffic models on road networks is presented. The approach is based
on the method "particleclaw", which solves scalar one dimensional hyperbolic
conservations laws exactly, except for a small error right around shocks. The
method is generalized to nonlinear network flows, where particle approximations
on the edges are suitably coupled together at the network nodes. It is
demonstrated in numerical examples that the resulting particle method can
approximate traffic jams accurately, while only devoting a few degrees of
freedom to each edge of the network.Comment: 15 pages, 5 figures. Accepted to the proceedings of the Sixth
International Workshop Meshfree Methods for PDE 201
Gas-kinetic derivation of Navier-Stokes-like traffic equations
Macroscopic traffic models have recently been severely criticized to base on
lax analogies only and to have a number of deficiencies. Therefore, this paper
shows how to construct a logically consistent fluid-dynamic traffic model from
basic laws for the acceleration and interaction of vehicles. These
considerations lead to the gas-kinetic traffic equation of Paveri-Fontana. Its
stationary and spatially homogeneous solution implies equilibrium relations for
the `fundamental diagram', the variance-density relation, and other quantities
which are partly difficult to determine empirically.
Paveri-Fontana's traffic equation allows the derivation of macroscopic moment
equations which build a system of non-closed equations. This system can be
closed by the well proved method of Chapman and Enskog which leads to
Euler-like traffic equations in zeroth-order approximation and to
Navier-Stokes-like traffic equations in first-order approximation. The latter
are finally corrected for the finite space requirements of vehicles. It is
shown that the resulting model is able to withstand the above mentioned
criticism.Comment: For related work see
http://www.theo2.physik.uni-stuttgart.de/helbing.htm
Critical phenomena and universal dynamics in one-dimensional driven diffusive systems with two species of particles
Recent work on stochastic interacting particle systems with two particle
species (or single-species systems with kinematic constraints) has demonstrated
the existence of spontaneous symmetry breaking, long-range order and phase
coexistence in nonequilibrium steady states, even if translational invariance
is not broken by defects or open boundaries. If both particle species are
conserved, the temporal behaviour is largely unexplored, but first results of
current work on the transition from the microscopic to the macroscopic scale
yield exact coupled nonlinear hydrodynamic equations and indicate the emergence
of novel types of shock waves which are collective excitations stabilized by
the flow of microscopic fluctuations. We review the basic stationary and
dynamic properties of these systems, highlighting the role of conservation laws
and kinetic constraints for the hydrodynamic behaviour, the microscopic origin
of domain wall (shock) stability and the coarsening dynamics of domains during
phase separation.Comment: 72 pages, 6 figures, 201 references (topical review for J. Phys. A:
Math. Gen.
- …