Results 1  10
of
80
Traffic and related selfdriven manyparticle systems
, 2000
"... Since the subject of traffic dynamics has captured the interest of physicists, many surprising effects have been revealed and explained. Some of the questions now understood are the following: Why are vehicles sometimes stopped by ‘‘phantom traffic jams’ ’ even though drivers all like to drive fast? ..."
Abstract

Cited by 146 (23 self)
 Add to MetaCart
Since the subject of traffic dynamics has captured the interest of physicists, many surprising effects have been revealed and explained. Some of the questions now understood are the following: Why are vehicles sometimes stopped by ‘‘phantom traffic jams’ ’ even though drivers all like to drive fast? What are the mechanisms behind stopandgo traffic? Why are there several different kinds of congestion, and how are they related? Why do most traffic jams occur considerably before the road capacity is reached? Can a temporary reduction in the volume of traffic cause a lasting traffic jam? Under which conditions can speed limits speed up traffic? Why do pedestrians moving in opposite directions normally organize into lanes, while similar systems ‘‘freeze by heating’’? All of these questions have been answered by applying and extending methods from statistical physics and nonlinear dynamics to selfdriven manyparticle systems. This article considers the empirical data and then reviews the main approaches to modeling pedestrian and vehicle traffic. These include microscopic (particlebased), mesoscopic (gaskinetic), and macroscopic (fluiddynamic) models. Attention is also paid to the formulation of a micromacro link, to aspects of universality, and to other unifying concepts, such as a general modeling framework for selfdriven manyparticle systems, including spin systems. While the primary focus is upon vehicle and pedestrian traffic, applications to biological or socioeconomic systems such as bacterial colonies, flocks of birds, panics, and stock market dynamics are touched upon as well.
Turbulent Pattern Bases for Cellular Automata
 Physica D
, 1993
"... Unpredictable patterns generated by cellular automata (CA) can be decomposed with respect to a turbulent, positive entropy rate pattern basis. The resulting filtered patterns uncover significant structural organization in a CA's dynamics and information processing capabilities. We illustrate the dec ..."
Abstract

Cited by 46 (14 self)
 Add to MetaCart
Unpredictable patterns generated by cellular automata (CA) can be decomposed with respect to a turbulent, positive entropy rate pattern basis. The resulting filtered patterns uncover significant structural organization in a CA's dynamics and information processing capabilities. We illustrate the decomposition technique by analyzing a binary, range2 cellular automaton having two invariant chaotic domains of different complexities and entropies. Once identified, the domains are seen to organize the CA's state space and to dominate its evolution. Starting from the domains' structures, we show how to construct a finitestate transducer that performs nonlinear spatial filtering such that the resulting spacetime patterns reveal the domains and the intervening walls and dislocations. To show the statistical consequences of domain detection, we compare the entropy and complexity densities of each domain with the globally averaged quantities. A more graphical comparison uses difference patter...
Computational mechanics: Pattern and prediction, structure and simplicity
 Journal of Statistical Physics
, 1999
"... Computational mechanics, an approach to structural complexity, defines a process’s causal states and gives a procedure for finding them. We show that the causalstate representation—an Emachine—is the minimal one consistent with ..."
Abstract

Cited by 43 (8 self)
 Add to MetaCart
Computational mechanics, an approach to structural complexity, defines a process’s causal states and gives a procedure for finding them. We show that the causalstate representation—an Emachine—is the minimal one consistent with
Interdisciplinary application of nonlinear time series methods
 Phys. Reports
, 1998
"... This paper reports on the application to field measurements of time series methods developed on the basis of the theory of deterministic chaos. The major difficulties are pointed out that arise when the data cannot be assumed to be purely deterministic and the potential that remains in this situatio ..."
Abstract

Cited by 42 (5 self)
 Add to MetaCart
This paper reports on the application to field measurements of time series methods developed on the basis of the theory of deterministic chaos. The major difficulties are pointed out that arise when the data cannot be assumed to be purely deterministic and the potential that remains in this situation is discussed. For signals with weakly nonlinear structure, the presence of nonlinearity in a general sense has to be inferred statistically. The paper reviews the relevant methods and discusses the implications for deterministic modeling. Most field measurements yield nonstationary time series, which poses a severe problem for their analysis. Recent progress in the detection and understanding of nonstationarity is reported. If a clear signature of approximate determinism is found, the notions of phase space, attractors, invariant manifolds etc. provide a convenient framework for time series analysis. Although the results have to be interpreted with great care, superior performance can be achieved for typical signal processing tasks. In particular, prediction and filtering of signals are discussed, as well as the classification of system states by means of time series recordings.
A Global Attracting Set for the KuramotoSivashinsky Equation
 Comm. Math. Phys
, 1993
"... this paper, we prove new bounds on the KuramotoSivashinsky equation (KS) by extending the ingenious method of Nicolaenko, Scheurer, and Temam [NST]. We study the KSequation in its "derivative form:" ..."
Abstract

Cited by 28 (1 self)
 Add to MetaCart
this paper, we prove new bounds on the KuramotoSivashinsky equation (KS) by extending the ingenious method of Nicolaenko, Scheurer, and Temam [NST]. We study the KSequation in its "derivative form:"
Origin of crack tip instabilities
 J. Mech. Phys. Solids
, 1995
"... This paper demonstrates that rapid fracture of ideal brittle lattices naturally involves phenomena long seen in experiment, but which have been hard to understand from a continuum point of view. These idealized models do not mimic realistic microstructure, but can be solved exactly and understood co ..."
Abstract

Cited by 20 (6 self)
 Add to MetaCart
This paper demonstrates that rapid fracture of ideal brittle lattices naturally involves phenomena long seen in experiment, but which have been hard to understand from a continuum point of view. These idealized models do not mimic realistic microstructure, but can be solved exactly and understood completely. First it is shown that constant velocity crack solutions do not exist at all for a range of velocities starting at zero and ranging up to about one quarter of the shear wave speed. Next it is shown that above this speed cracks are by and large linearly stable, but that at sufficiently high velocity they become unstable with respect to a nonlinear microcracking instability. The way this instability works itself out is related to the scenario known as intermittency, and the basic time scale which governs it is the inverse of the amount of dissipation in the model. Finally, we compare the theoretical framework with some new experiments in Plexiglas, and show that all qualitative features of the theory are mirrored in our experimental results.
Phase diagram of traffic states in the presence of inhomogeneities
 Physical Review Letters
, 1999
"... We present a phase diagram of the different kinds of congested traffic that are triggered by disturbances when passing ramps or other spatial inhomogeneities of a freeway. The simulation results obtained by the nonlocal, gaskineticbased traffic model are in good agreement with empirical findings. T ..."
Abstract

Cited by 19 (12 self)
 Add to MetaCart
We present a phase diagram of the different kinds of congested traffic that are triggered by disturbances when passing ramps or other spatial inhomogeneities of a freeway. The simulation results obtained by the nonlocal, gaskineticbased traffic model are in good agreement with empirical findings. They allow to understand the observed transitions between free and various kinds of congested traffic, among them localized clusters, stopandgo waves, and different types of “synchronized ” traffic. We also give analytical conditions for the existence of these states which suggest that the phase diagram is universal for a class of different microscopic and macroscopic traffic models.
stochastic dynamics with nonlinear fractal properties
 Supplement U. S. National Report IUGG
, 1987
"... Abstract Stochastic processes with multiplicative noise have been studied independently in several different contexts over the past decades. We focus on the regime, found for a generic set of control parameters, in which stochastic processes with multiplicative noise produce intermittency of a speci ..."
Abstract

Cited by 19 (10 self)
 Add to MetaCart
Abstract Stochastic processes with multiplicative noise have been studied independently in several different contexts over the past decades. We focus on the regime, found for a generic set of control parameters, in which stochastic processes with multiplicative noise produce intermittency of a special kind, characterized by a power law probability density distribution. We present a review of applications, highlight the common physical mechanism and summarize the main known results. The distribution and statistical properties of the duration of intermittent bursts are also characterized in details. 1 1
Axisymmetric surface diffusion: Dynamics and stability of selfsimilar pinchoff
 J. Statist. Phys
, 1998
"... The dynamics of surface diffusion describe the motion of a surface with its normal velocity given by the surface Laplacian of its mean curvature. This flow conserves the volume enclosed inside the surface while minimizing its surface area. We review the axisymmetric equilibria: the cylinder, sphere, ..."
Abstract

Cited by 18 (3 self)
 Add to MetaCart
The dynamics of surface diffusion describe the motion of a surface with its normal velocity given by the surface Laplacian of its mean curvature. This flow conserves the volume enclosed inside the surface while minimizing its surface area. We review the axisymmetric equilibria: the cylinder, sphere, and the Delaunay unduloid. The sphere is stable while the cylinder is longwave unstable. A subcritical bifurcation from the cylinder produces a continuous family of unduloid solutions. We present computations that suggest that the stable manifold of the unduloid forms a separatrix between states that relax to the cylinder in infinite time and those that tend towards finitetime pinchoff. We examine the structure of the pinchoff, showing it has selfsimilar structure, using asymptotic, numerical and analytical methods. In addition to a previously known similarity solution, we find a countable set of similarity solutions, each with a different asymptotic cone angle. We develop a stability ...