731 research outputs found
How to solve Fokker-Planck equation treating mixed eigenvalue spectrum?
An analogy of the Fokker-Planck equation (FPE) with the Schr\"odinger
equation allows us to use quantum mechanics technique to find the analytical
solution of the FPE in a number of cases. However, previous studies have been
limited to the Schr\"odinger potential with a discrete eigenvalue spectrum.
Here, we will show how this approach can be also applied to a mixed eigenvalue
spectrum with bounded and free states. We solve the FPE with boundaries located
at x=\pm L/2 and take the limit L\rightarrow\infty, considering the examples
with constant Schr\"{o}dinger potential and with P\"{o}schl-Teller potential.
An oversimplified approach was proposed earlier by M.T. Araujo and E. Drigo
Filho. A detailed investigation of the two examples shows that the correct
solution, obtained in this paper, is consistent with the expected Fokker-Planck
dynamics.Comment: 13 pages, 5 figure
Solid-State Excitation Laser for Laser-Ultrasonics
The inspection speed of laser-ultrasonics compared with conventional ultrasonic testing is limited by the pulse repetition rate of the excitation laser. The maximum pulse repetition rate reported up to now for CO2-lasers, which are presently used for nearly all systems, is in the range of 400 Hz. In this paper a new approach based on a diode-pumped solid-state laser is discussed, which is currently being developed. This new excitation laser is designed for a repetition rate of 1 kHz and will operate at a mid-IR wavelength of 3.3 m. The higher repeti-tion rate enables a higher inspection speed, whereas the mid-IR wavelength anticipates a better coupling efficiency. The total power for pumping the laser crystals is transported via flexible optical fibres to the compact laser head, thus allowing operation on a robot arm. The laser head consists of a master oscillator feeding several lines of power amplifiers and in-cludes nonlinear optical wavelength conversion by an optical parametric process. It is char-acterized by a modular construction which provides optimal conditions for operation at high average power as well as for easy maintenance. These features will enable building reliable, long-lived, rugged, smart laser ultrasonic systems in futur
Probabilistic Description of Traffic Breakdowns
We analyze the characteristic features of traffic breakdown. To describe this
phenomenon we apply to the probabilistic model regarding the jam emergence as
the formation of a large car cluster on highway. In these terms the breakdown
occurs through the formation of a certain critical nucleus in the metastable
vehicle flow, which enables us to confine ourselves to one cluster model. We
assume that, first, the growth of the car cluster is governed by attachment of
cars to the cluster whose rate is mainly determined by the mean headway
distance between the car in the vehicle flow and, may be, also by the headway
distance in the cluster. Second, the cluster dissolution is determined by the
car escape from the cluster whose rate depends on the cluster size directly.
The latter is justified using the available experimental data for the
correlation properties of the synchronized mode. We write the appropriate
master equation converted then into the Fokker-Plank equation for the cluster
distribution function and analyze the formation of the critical car cluster due
to the climb over a certain potential barrier. The further cluster growth
irreversibly gives rise to the jam formation. Numerical estimates of the
obtained characteristics and the experimental data of the traffic breakdown are
compared. In particular, we draw a conclusion that the characteristic intrinsic
time scale of the breakdown phenomenon should be about one minute and explain
the case why the traffic volume interval inside which traffic breakdown is
observed is sufficiently wide.Comment: RevTeX 4, 14 pages, 10 figure
Zero range model of traffic flow
A multi--cluster model of traffic flow is studied, in which the motion of
cars is described by a stochastic master equation. Assuming that the escape
rate from a cluster depends only on the cluster size, the dynamics of the model
is directly mapped to the mathematically well-studied zero-range process.
Knowledge of the asymptotic behaviour of the transition rates for large
clusters allows us to apply an established criterion for phase separation in
one-dimensional driven systems. The distribution over cluster sizes in our
zero-range model is given by a one--step master equation in one dimension. It
provides an approximate mean--field dynamics, which, however, leads to the
exact stationary state. Based on this equation, we have calculated the critical
density at which phase separation takes place. We have shown that within a
certain range of densities above the critical value a metastable homogeneous
state exists before coarsening sets in. Within this approach we have estimated
the critical cluster size and the mean nucleation time for a condensate in a
large system. The metastablity in the zero-range process is reflected in a
metastable branch of the fundamental flux--density diagram of traffic flow. Our
work thus provides a possible analytical description of traffic jam formation
as well as important insight into condensation in the zero-range process.Comment: 10 pages, 13 figures, small changes are made according to finally
accepted version for publication in Phys. Rev.
Equilibrium distributions in thermodynamical traffic gas
We derive the exact formula for thermal-equilibrium spacing distribution of
one-dimensional particle gas with repulsive potential V(r)=r^(-a) (a>0)
depending on the distance r between the neighboring particles. The calculated
distribution (for a=1) is successfully compared with the highway-traffic
clearance distributions, which provides a detailed view of changes in
microscopical structure of traffic sample depending on traffic density. In
addition to that, the observed correspondence is a strong support of studies
applying the equilibrium statistical physics to traffic modelling.Comment: 5 pages, 6 figures, changed content, added reference
Long-lived states of oscillator chain with dynamical traps
A simple model of oscillator chain with dynamical traps and additive white
noise is considered. Its dynamics was studied numerically. As demonstrated,
when the trap effect is pronounced nonequilibrium phase transitions of a new
type arise. Locally they manifest themselves via distortion of the particle
arrangement symmetry. Depending on the system parameters the particle
arrangement is characterized by the corresponding distributions taking either a
bimodal form, or twoscale one, or unimodal onescale form which, however,
deviates substantially from the Gaussian distribution. The individual particle
velocities exhibit also a number of anomalies, in particular, their
distribution can be extremely wide or take a quasi-cusp form. A large number of
different cooperative structures and superstructures made of these formations
are found in the visualized time patterns. Their evolution is, in some sense,
independent of the individual particle dynamics, enabling us to regard them as
dynamical phases.Comment: 8 pages, 5 figurs, TeX style of European Physical Journa
Cluster formation and anomalous fundamental diagram in an ant trail model
A recently proposed stochastic cellular automaton model ({\it J. Phys. A 35,
L573 (2002)}), motivated by the motions of ants in a trail, is investigated in
detail in this paper. The flux of ants in this model is sensitive to the
probability of evaporation of pheromone, and the average speed of the ants
varies non-monotonically with their density. This remarkable property is
analyzed here using phenomenological and microscopic approximations thereby
elucidating the nature of the spatio-temporal organization of the ants. We find
that the observations can be understood by the formation of loose clusters,
i.e. space regions of enhanced, but not maximal, density.Comment: 11 pages, REVTEX, with 11 embedded EPS file
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