460 research outputs found
Dynamical Phase Transition in One Dimensional Traffic Flow Model with Blockage
Effects of a bottleneck in a linear trafficway is investigated using a simple
cellular automaton model. Introducing a blockage site which transmit cars at
some transmission probability into the rule-184 cellular automaton, we observe
three different phases with increasing car concentration: Besides the free
phase and the jam phase, which exist already in the pure rule-184 model, the
mixed phase of these two appears at intermediate concentration with
well-defined phase boundaries. This mixed phase, where cars pile up behind the
blockage to form a jam region, is characterized by a constant flow. In the
thermodynamic limit, we obtain the exact expressions for several characteristic
quantities in terms of the car density and the transmission rate. These
quantities depend strongly on the system size at the phase boundaries; We
analyse these finite size effects based on the finite-size scaling.Comment: 14 pages, LaTeX 13 postscript figures available upon
request,OUCMT-94-
Solvable Optimal Velocity Models and Asymptotic Trajectory
In the Optimal Velocity Model proposed as a new version of Car Following
Model, it has been found that a congested flow is generated spontaneously from
a homogeneous flow for a certain range of the traffic density. A
well-established congested flow obtained in a numerical simulation shows a
remarkable repetitive property such that the velocity of a vehicle evolves
exactly in the same way as that of its preceding one except a time delay .
This leads to a global pattern formation in time development of vehicles'
motion, and gives rise to a closed trajectory on -
(headway-velocity) plane connecting congested and free flow points. To obtain
the closed trajectory analytically, we propose a new approach to the pattern
formation, which makes it possible to reduce the coupled car following
equations to a single difference-differential equation (Rondo equation). To
demonstrate our approach, we employ a class of linear models which are exactly
solvable. We also introduce the concept of ``asymptotic trajectory'' to
determine and (the backward velocity of the pattern), the global
parameters associated with vehicles' collective motion in a congested flow, in
terms of parameters such as the sensitivity , which appeared in the original
coupled equations.Comment: 25 pages, 15 eps figures, LaTe
Kinetics of Clustering in Traffic Flows
We study a simple aggregation model that mimics the clustering of traffic on
a one-lane roadway. In this model, each ``car'' moves ballistically at its
initial velocity until it overtakes the preceding car or cluster. After this
encounter, the incident car assumes the velocity of the cluster which it has
just joined. The properties of the initial distribution of velocities in the
small velocity limit control the long-time properties of the aggregation
process. For an initial velocity distribution with a power-law tail at small
velocities, \pvim as , a simple scaling argument shows that the
average cluster size grows as n \sim t^{\va} and that the average velocity
decays as v \sim t^{-\vb} as . We derive an analytical solution
for the survival probability of a single car and an asymptotically exact
expression for the joint mass-velocity distribution function. We also consider
the properties of spatially heterogeneous traffic and the kinetics of traffic
clustering in the presence of an input of cars.Comment: 18 pages, Plain TeX, 2 postscript figure
Two-lane traffic rules for cellular automata: A systematic approach
Microscopic modeling of multi-lane traffic is usually done by applying
heuristic lane changing rules, and often with unsatisfying results. Recently, a
cellular automaton model for two-lane traffic was able to overcome some of
these problems and to produce a correct density inversion at densities somewhat
below the maximum flow density. In this paper, we summarize different
approaches to lane changing and their results, and propose a general scheme,
according to which realistic lane changing rules can be developed. We test this
scheme by applying it to several different lane changing rules, which, in spite
of their differences, generate similar and realistic results. We thus conclude
that, for producing realistic results, the logical structure of the lane
changing rules, as proposed here, is at least as important as the microscopic
details of the rules
Steady-state selection in driven diffusive systems with open boundaries
We investigate the stationary states of one-dimensional driven diffusive
systems, coupled to boundary reservoirs with fixed particle densities. We argue
that the generic phase diagram is governed by an extremal principle for the
macroscopic current irrespective of the local dynamics. In particular, we
predict a minimal current phase for systems with local minimum in the
current--density relation. This phase is explained by a dynamical phenomenon,
the branching and coalescence of shocks, Monte-Carlo simulations confirm the
theoretical scenario.Comment: 6 pages, 5 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
Maxwell Model of Traffic Flows
We investigate traffic flows using the kinetic Boltzmann equations with a
Maxwell collision integral. This approach allows analytical determination of
the transient behavior and the size distributions. The relaxation of the car
and cluster velocity distributions towards steady state is characterized by a
wide range of velocity dependent relaxation scales, , with
the ratio of the passing and the collision rates. Furthermore, these
relaxation time scales decrease with the velocity, with the smallest scale
corresponding to the decay of the overall density. The steady state cluster
size distribution follows an unusual scaling form . This distribution is primarily algebraic, , for , and is exponential otherwise.Comment: revtex, 10 page
The radiative lepton flavor violating decays in the split fermion scenario in the two Higgs doublet model
We study the branching ratios of the lepton flavor violating processes \mu ->
e \gamma, \tau -> e \gamma and \tau -> \mu\gamma in the split fermion scenario,
in the framework of the two Higgs doublet model. We observe that the branching
ratios are relatively more sensitive to the compactification scale and the
Gaussian widths of the leptons in the extra dimensions, for two extra
dimensions and especially for the \tau -> \mu \gamma decay.Comment: 19 pages, 7 Figure
Theoretical approach to two-dimensional traffic flow models
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 is a transition between a freely moving phase with high
velocity to a jammed state with low velocity. We study the dynamics of such a
model starting with the microscopic evolution equation, which will serve as a
basis for further analysis. It is shown that a kinetic approach, based on the
Boltzmann assumption, is able to provide a reasonably good description of the
jamming transition. We further introduce a space-time continuous
phenomenological model leading to a couple of partial differential equations
whose preliminary results agree rather well with the numerical simulations.Comment: 15 pages, REVTeX 3.0, 7 uuencoded figures upon request to
[email protected]
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