247 research outputs found
Density fluctuations and phase separation in a traffic flow model
Within the Nagel-Schreckenberg traffic flow model we consider the transition
from the free flow regime to the jammed regime. We introduce a method of
analyzing the data which is based on the local density distribution. This
analyzes allows us to determine the phase diagram and to examine the separation
of the system into a coexisting free flow phase and a jammed phase above the
transition. The investigation of the steady state structure factor yields that
the decomposition in this phase coexistence regime is driven by density
fluctuations, provided they exceed a critical wavelength.Comment: in 'Traffic and Granular Flow 97', edited by D.E. Wolf and M.
Schreckenberg, Springer, Singapore (1998
A simple Monte Carlo model for crowd dynamics
In this paper we introduce a simple Monte Carlo method for simulating the
dynamics of a crowd. Within our model a collection of hard-disk agents is
subjected to a series of two-stage steps, implying (i) the displacement of one
specific agent followed by (ii) a rearrangement of the rest of the group
through a Monte Carlo dynamics. The rules for the combined steps are determined
by the specific setting of the granular flow, so that our scheme should be
easily adapted to describe crowd dynamics issues of many sorts, from stampedes
in panic scenarios to organized flow around obstacles or through bottlenecks.
We validate our scheme by computing the serving times statistics of a group of
agents crowding to be served around a desk. In the case of a size homogeneous
crowd, we recover intuitive results prompted by physical sense. However, as a
further illustration of our theoretical framework, we show that heterogeneous
systems display a less obvious behavior, as smaller agents feature shorter
serving times. Finally, we analyze our results in the light of known properties
of non-equilibrium hard-disk fluids and discuss general implications of our
model.Comment: to be published in Physical Review
Quantum Fields in Nonstatic background: A Histories Perspective
For a quantum field living on a non - static spacetime no instantaneous
Hamiltonian is definable, for this generically necessitates a choice of
inequivalent representation of the canonical commutation relations at each
instant of time. This fact suggests a description in terms of time - dependent
Hilbert spaces, a concept that fits naturally in a (consistent) histories
framework. Our primary tool for the construction of the quantum theory in a
continuous -time histories format is the recently developed formalism based on
the notion of the history group . This we employ to study a model system
involving a 1+1 scalar field in a cavity with moving boundaries.
The instantaneous (smeared) Hamiltonian and a decoherence functional are then
rigorously defined so that finite values for the time - averaged particle
creation rate are obtainable through the study of energy histories. We also
construct the Schwinger - Keldysh closed- time - path generating functional as
a ``Fourier transform'' of the decoherence functional and evaluate the
corresponding n - point functions.Comment: 27 pages, LATEX; minor changes and corrections; version to appear in
JM
The Effect Of Delay Times On The Optimal Velocity Traffic Flow Behavior
We have numerically investigated the effect of the delay times and
of a mixture of fast and slow vehicles on the fundamental diagram of
the optimal velocity model. The optimal velocity function of the fast cars
depends not only on the headway of each car but also on the headway of the
immediately preceding one. It is found that the small delay times have almost
no effects, while, for sufficiently large delay time the current
profile displays qualitatively five different forms depending on ,
and the fractions and of the fast and slow cars
respectively. The velocity (current) exhibits first order transitions at low
and/or high densities, from freely moving phase to the congested state, and
from congested state to the jamming one respectively accompanied by the
existence of a local minimal current. Furthermore, there exist a critical value
of above which the metastability and hysteresis appear. The
spatial-temporal traffic patterns present more complex structur
Economics-Based Optimization of Unstable Flows
As an example for the optimization of unstable flows, we present an
economics-based method for deciding the optimal rates at which vehicles are
allowed to enter a highway. It exploits the naturally occuring fluctuations of
traffic flow and is flexible enough to adapt in real time to the transient flow
characteristics of road traffic. Simulations based on realistic parameter
values show that this strategy is feasible for naturally occurring traffic, and
that even far from optimality, injection policies can improve traffic flow.
Moreover, the same method can be applied to the optimization of flows of gases
and granular media.Comment: Revised version of ``Optimizing Traffic Flow'' (cond-mat/9809397).
For related work see http://www.parc.xerox.com/dynamics/ and
http://www.theo2.physik.uni-stuttgart.de/helbing.htm
Off-Equilibrium Dynamics of a 4D Spin Glass with Asymmetric Couplings
We study the off-equilibrium dynamics of the Edwards-Anderson spin glass in
four dimensions under the influence of a non-hamiltonian perturbation. We find
that for small asymmetry the model behaves as the hamiltonian one, while for
large asymmetry the behaviour of the model can be well described by an
interrupted aging scenario. The autocorrelation function C(t_w+\tau,t_w) scales
as \tau/t_w^\beta, with \beta a function of the asymmetry. For very long
waiting times the previous regime crosses over to a time translational
invariant regime (TTI) with stretched exponential relaxation. The model does
not show signs of reaching a TTI regime for weak asymmetry, but in the aging
regime the exponent \beta is always different from one, showing a non trivial
aging scenario.Comment: Latex, 12 pages, 9 figure
Deterministic approach to microscopic three-phase traffic theory
Two different deterministic microscopic traffic flow models, which are in the
context of the Kerner's there-phase traffic theory, are introduced. In an
acceleration time delay model (ATD-model), different time delays in driver
acceleration associated with driver behaviour in various local driving
situations are explicitly incorporated into the model. Vehicle acceleration
depends on local traffic situation, i.e., whether a driver is within the free
flow, or synchronized flow, or else wide moving jam traffic phase. In a speed
adaptation model (SA-model), vehicle speed adaptation occurs in synchronized
flow depending on driving conditions. It is found that the ATD- and SA-models
show spatiotemporal congested traffic patterns that are adequate with empirical
results. In the ATD- and SA-models, the onset of congestion in free flow at a
freeway bottleneck is associated with a first-order phase transition from free
flow to synchronized flow; moving jams emerge spontaneously in synchronized
flow only. Differences between the ATD- and SA-models are studied. A comparison
of the ATD- and SA-models with stochastic models in the context of three phase
traffic theory is made. A critical discussion of earlier traffic flow theories
and models based on the fundamental diagram approach is presented.Comment: 40 pages, 14 figure
Volatile Decision Dynamics: Experiments, Stochastic Description, Intermittency Control, and Traffic Optimization
The coordinated and efficient distribution of limited resources by individual
decisions is a fundamental, unsolved problem. When individuals compete for road
capacities, time, space, money, goods, etc., they normally make decisions based
on aggregate rather than complete information, such as TV news or stock market
indices. In related experiments, we have observed a volatile decision dynamics
and far-from-optimal payoff distributions. We have also identified ways of
information presentation that can considerably improve the overall performance
of the system. In order to determine optimal strategies of decision guidance by
means of user-specific recommendations, a stochastic behavioural description is
developed. These strategies manage to increase the adaptibility to changing
conditions and to reduce the deviation from the time-dependent user
equilibrium, thereby enhancing the average and individual payoffs. Hence, our
guidance strategies can increase the performance of all users by reducing
overreaction and stabilizing the decision dynamics. These results are highly
significant for predicting decision behaviour, for reaching optimal behavioural
distributions by decision support systems, and for information service
providers. One of the promising fields of application is traffic optimization.Comment: For related work see http://www.helbing.or
Car-oriented mean-field theory for traffic flow models
We present a new analytical description of the cellular automaton model for
single-lane traffic. In contrast to previous approaches we do not use the
occupation number of sites as dynamical variable but rather the distance
between consecutive cars. Therefore certain longer-ranged correlations are
taken into account and even a mean-field approach yields non-trivial results.
In fact for the model with the exact solution is reproduced. For
the fundamental diagram shows a good agreement with results from
simulations.Comment: LaTex, 10 pages, 2 postscript figure
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