312 research outputs found
Mean Field Theory for Pedestrian Outflow through an Exit
An average pedestrian flow through an exit is one of the most important index
in evaluating pedestrian dynamics. In order to study the flow in detail, the
floor field model, which is a crowd model by using cellular automaton, is
extended by taking into account a realistic behavior of pedestrians around the
exit. The model is studied by both numerical simulations and cluster analysis
to obtain a theoretical expression of an average pedestrian flow through the
exit. It is found quantitatively that the effect of exit door width, a wall,
and pedestrian's mood of competition or cooperation significantly influence the
average flow. The results show that there is suitable width of the exit and
position according to pedestrian's mood.Comment: 9 pages, 16 figure
A New Expression of Soliton Solution to the Ultradiscrete Toda Equation
A new type of multi-soliton solution to the ultradiscrete Toda equation is
proposed. The solution can be transformed into another expression of solution
in a perturbation form. A direct proof of the solution is also given.Comment: 13 page
A stochastic cellular automaton model for traffic flow with multiple metastable states
A new stochastic cellular automaton (CA) model of traffic flow, which
includes slow-to-start effects and a driver's perspective, is proposed by
extending the Burgers CA and the Nagel-Schreckenberg CA model. The flow-density
relation of this model shows multiple metastable branches near the transition
density from free to congested traffic, which form a wide scattering area in
the fundamental diagram. The stability of these branches and their velocity
distributions are explicitly studied by numerical simulations.Comment: 11 pages, 20 figures, submitted for publicatio
Two-dimensional Burgers Cellular Automaton
A two-dimensional cellular automaton(CA) associated with a two-dimensional
Burgers equation is presented. The 2D Burgers equation is an integrable
generalization of the well-known Burgers equation, and is transformed into a 2D
diffusion equation by the Cole-Hopf transformation. The CA is derived from the
2D Burgers equation by using the ultradiscrete method, which can transform
dependent variables into discrete ones. Some exact solutions of the CA, such as
shock wave solutions, are studied in detail.Comment: Latex2.09, 17 pages including 7 figure
Max-Plus Algebra for Complex Variables and Its Application to Discrete Fourier Transformation
A generalization of the max-plus transformation, which is known as a method
to derive cellular automata from integrable equations, is proposed for complex
numbers. Operation rules for this transformation is also studied for general
number of complex variables. As an application, the max-plus transformation is
applied to the discrete Fourier transformation. Stretched coordinates are
introduced to obtain the max-plus transformation whose imaginary part coinsides
with a phase of the discrete Fourier transformation
Hysteresis phenomenon in deterministic traffic flows
We study phase transitions of a system of particles on the one-dimensional
integer lattice moving with constant acceleration, with a collision law
respecting slower particles. This simple deterministic ``particle-hopping''
traffic flow model being a straightforward generalization to the well known
Nagel-Schreckenberg model covers also a more recent slow-to-start model as a
special case. The model has two distinct ergodic (unmixed) phases with two
critical values. When traffic density is below the lowest critical value, the
steady state of the model corresponds to the ``free-flowing'' (or ``gaseous'')
phase. When the density exceeds the second critical value the model produces
large, persistent, well-defined traffic jams, which correspond to the
``jammed'' (or ``liquid'') phase. Between the two critical values each of these
phases may take place, which can be interpreted as an ``overcooled gas'' phase
when a small perturbation can change drastically gas into liquid. Mathematical
analysis is accomplished in part by the exact derivation of the life-time of
individual traffic jams for a given configuration of particles.Comment: 22 pages, 6 figures, corrected and improved version, to appear in the
Journal of Statistical Physic
Introduction of Frictional and Turning Function for Pedestrian Outflow with an Obstacle
In this paper, two important factors which affect the pedestrian outflow at a
bottleneck significantly are studied in detail to analyze the effect of an
obstacle set up in front of an exit. One is a conflict at an exit when
pedestrians evacuate from a room. We use floor field model for simulating such
behavior, which is a well-studied pedestrian model using cellular automata. The
conflicts have been taken into account by the friction parameter. However, the
friction parameter so far is a constant and does not depend on the number of
the pedestrians conflicting at the same time. Thus, we have improved the
friction parameter by the frictional function, which is a function of the
number of the pedestrians involved in the conflict. Second, we have newly
introduced the cost of turning of pedestrians at the exit. Since pedestrians
have inertia, their walking speeds decrease when they turn, and the pedestrian
outflow decreases.
The validity of the extended model, which includes the frictional function
and the turning function, is verified by both a mean field theory and
experiments. In our experiments, the pedestrian flow increases when we put an
obstacle in front of an exit. The analytical results clearly explains the
mechanism of the effect of the obstacle, i.e., the obstacle blocks pedestrians
moving to the exit and decreases the average number of pedestrians involved in
the conflict. We have also found that an obstacle works more effectively when
we shift it from the center since pedestrians go through the exit with less
turning
Bubble burst as jamming phase transition
Recently research on bubble and its burst attract much interest of
researchers in various field such as economics and physics. Economists have
been regarding bubble as a disorder in prices. However, this research strategy
has overlooked an importance of the volume of transactions. In this paper, we
have proposed a bubble burst model by focusing the transactions incorporating a
traffic model that represents spontaneous traffic jam. We find that the
phenomenon of bubble burst shares many similar properties with traffic jam
formation by comparing data taken from US housing market. Our result suggests
that the transaction could be a driving force of bursting phenomenon.Comment: 9 pages,12 figure
Modeling the desired direction in a force-based model for pedestrian dynamics
We introduce an enhanced model based on the generalized centrifugal force
model. Furthermore, the desired direction of pedestrians is investigated. A new
approach leaning on the well-known concept of static and dynamic floor-fields
in cellular automata is presented. Numerical results of the model are presented
and compared with empirical data.Comment: 14 pages 11 figures, submitted to TGF'1
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