370 research outputs found
Towards a variational principle for motivated vehicle motion
We deal with the problem of deriving the microscopic equations governing the
individual car motion based on the assumptions about the strategy of driver
behavior. We suppose the driver behavior to be a result of a certain compromise
between the will to move at a speed that is comfortable for him under the
surrounding external conditions, comprising the physical state of the road, the
weather conditions, etc., and the necessity to keep a safe headway distance
between the cars in front of him. Such a strategy implies that a driver can
compare the possible ways of his further motion and so choose the best one. To
describe the driver preferences we introduce the priority functional whose
extremals specify the driver choice. For simplicity we consider a single-lane
road. In this case solving the corresponding equations for the extremals we
find the relationship between the current acceleration, velocity and position
of the car. As a special case we get a certain generalization of the optimal
velocity model similar to the "intelligent driver model" proposed by Treiber
and Helbing.Comment: 6 pages, RevTeX
Probabilistic cellular automata with conserved quantities
We demonstrate that the concept of a conservation law can be naturally
extended from deterministic to probabilistic cellular automata (PCA) rules. The
local function for conservative PCA must satisfy conditions analogous to
conservation conditions for deterministic cellular automata. Conservation
condition for PCA can also be written in the form of a current conservation
law. For deterministic nearest-neighbour CA the current can be computed
exactly. Local structure approximation can partially predict the equilibrium
current for non-deterministic cases. For linear segments of the fundamental
diagram it actually produces exact results.Comment: 17 pages, 2 figure
Traffic Network Optimum Principle - Minimum Probability of Congestion Occurrence
We introduce an optimum principle for a vehicular traffic network with road
bottlenecks. This network breakdown minimization (BM) principle states that the
network optimum is reached, when link flow rates are assigned in the network in
such a way that the probability for spontaneous occurrence of traffic breakdown
at one of the network bottlenecks during a given observation time reaches the
minimum possible value. Based on numerical simulations with a stochastic
three-phase traffic flow model, we show that in comparison to the well-known
Wardrop's principles the application of the BM principle permits considerably
greater network inflow rates at which no traffic breakdown occurs and,
therefore, free flow remains in the whole network.Comment: 22 pages, 6 figure
Analytical Approach to the One-Dimensional Disordered Exclusion Process with Open Boundaries and Random Sequential Dynamics
A one dimensional disordered particle hopping rate asymmetric exclusion
process (ASEP) with open boundaries and a random sequential dynamics is studied
analytically. Combining the exact results of the steady states in the pure case
with a perturbative mean field-like approach the broken particle-hole symmetry
is highlighted and the phase diagram is studied in the parameter space
, where and represent respectively the
injection rate and the extraction rate of particles. The model displays, as in
the pure case, high-density, low-density and maximum-current phases. All
critical lines are determined analytically showing that the high-density
low-density first order phase transition occurs at . We show
that the maximum-current phase extends its stability region as the disorder is
increased and the usual -decay of the density profile in this
phase is universal. Assuming that some exact results for the disordered model
on a ring hold for a system with open boundaries, we derive some analytical
results for platoon phase transition within the low-density phase and we give
an analytical expression of its corresponding critical injection rate
. As it was observed numerically, we show that the quenched
disorder induces a cusp in the current-density relation at maximum flow in a
certain region of parameter space and determine the analytical expression of
its slope. The results of numerical simulations we develop agree with the
analytical ones.Comment: 23 pages, 7 figures. to appear in J. Stat. Phy
p-species integrable reaction-diffusion processes
We consider a process in which there are p-species of particles, i.e.
A_1,A_2,...,A_p, on an infinite one-dimensional lattice. Each particle
can diffuse to its right neighboring site with rate , if this site is not
already occupied. Also they have the exchange interaction A_j+A_i --> A_i+A_j
with rate We study the range of parameters (interactions) for which
the model is integrable. The wavefunctions of this multi--parameter family of
integrable models are found. We also extend the 2--species model to the case in
which the particles are able to diffuse to their right or left neighboring
sites.Comment: 16 pages, LaTe
Cluster size distributions in particle systems with asymmetric dynamics
We present exact and asymptotic results for clusters in the one-dimensional
totally asymmetric exclusion process (TASEP) with two different dynamics. The
expected length of the largest cluster is shown to diverge logarithmically with
increasing system size for ordinary TASEP dynamics and as a logarithm divided
by a double logarithm for generalized dynamics, where the hopping probability
of a particle depends on the size of the cluster it belongs to. The connection
with the asymptotic theory of extreme order statistics is discussed in detail.
We also consider a related model of interface growth, where the deposited
particles are allowed to relax to the local gravitational minimum.Comment: 12 pages, 3 figures, RevTe
Analytical results for random walks in the presence of disorder and traps
In this paper, we study the dynamics of a random walker diffusing on a
disordered one-dimensional lattice with random trappings. The distribution of
escape probabilities is computed exactly for any strength of the disorder.
These probabilities do not display any multifractal properties contrary to
previous numerical claims. The explanation for this apparent multifractal
behavior is given, and our conclusion are supported by numerical calculations.
These exact results are exploited to compute the large time asymptotics of the
survival probability (or the density) which is found to decay as . An exact lower bound for the density is found to
decay in a similar way.Comment: 21 pages including 3 PS figures. Submitted to Phys. Rev.
Generalized Force Model of Traffic Dynamics
Floating car data of car-following behavior in cities were compared to
existing microsimulation models, after their parameters had been calibrated to
the experimental data. With these parameter values, additional simulations have
been carried out, e.g. of a moving car which approaches a stopped car. It
turned out that, in order to manage such kinds of situations without producing
accidents, improved traffic models are needed. Good results have been obtained
with the proposed generalized force model.Comment: For related work see
http://www.theo2.physik.uni-stuttgart.de/helbing.htm
Intelligent Controlling Simulation of Traffic Flow in a Small City Network
We propose a two dimensional probabilistic cellular automata for the
description of traffic flow in a small city network composed of two
intersections. The traffic in the network is controlled by a set of traffic
lights which can be operated both in fixed-time and a traffic responsive
manner. Vehicular dynamics is simulated and the total delay experienced by the
traffic is evaluated within specified time intervals. We investigate both
decentralized and centralized traffic responsive schemes and in particular
discuss the implementation of the {\it green-wave} strategy. Our investigations
prove that the network delay strongly depends on the signalisation strategy. We
show that in some traffic conditions, the application of the green-wave scheme
may destructively lead to the increment of the global delay.Comment: 8 pages, 10 eps figures, Revte
Multiparticle Biased DLA with surface diffusion: a comprehensive model of electrodeposition
We present a complete study of the Multiparticle Biased Diffusion-Limited
Aggregation (MBDLA) model supplemented with surface difussion (SD), focusing on
the relevance and effects of the latter transport mechanism. By comparing
different algorithms, we show that MBDLA+SD is a very good qualitative model
for electrodeposition in practically all the range of current intensities {\em
provided} one introduces SD in the model in the proper fashion: We have found
that the correct procedure involves simultaneous bulk diffusion and SD,
introducing a time scale arising from the ratio of the rates of both processes.
We discuss in detail the different morphologies obtained and compare them to
the available experimental data with very satisfactory results. We also
characterize the aggregates thus obtained by means of the dynamic scaling
exponents of the interface height, allowing us to distinguish several regimes
in the mentioned interface growth. Our asymptotic scaling exponents are again
in good agreement with recent experiments. We conclude by discussing a global
picture of the influence and consequences of SD in electrodeposition.Comment: 15 pages, 20 figures, accepted for publication in Physical Review
- …