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56
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? ..."
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Cited by 146 (23 self)
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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.
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 ..."
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Cited by 43 (8 self)
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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
Interrelations between Stochastic Equations for Systems with Pair Interactions
 Physica A
, 1992
"... Several types of stochastic equations are important in thermodynamics, chemistry, evolutionary biology, population dynamics and quantitative social science. For systems with pair interactions four different types of equations are derived, starting from a master equation for the state space: First, g ..."
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Cited by 12 (7 self)
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Several types of stochastic equations are important in thermodynamics, chemistry, evolutionary biology, population dynamics and quantitative social science. For systems with pair interactions four different types of equations are derived, starting from a master equation for the state space: First, general mean value and (co)variance equations. Second, Boltzmannlike equations. Third, a master equation for the configuration space allowing transition rates which depend on the occupation numbers of the states. Fourth, a FokkerPlanck equation and a “BoltzmannFokkerPlanck equation”. The interrelations of these equations and the conditions for their validity are worked out clearly. A procedure for a selfconsistent solution of the nonlinear equations is proposed. Generalizations to interactions between an arbitrary number of systems are discussed. 1
Boltzmannlike and BoltzmannFokkerPlanck equations as a foundation of behavioral models
 PHYSICA A
, 1993
"... It is shown, that the Boltzmannlike equations allow the formulation of a very general model for behavioral changes. This model takes into account spontaneous (or externally induced) behavioral changes and behavioral changes by pair interactions. As most important social pair interactions imitative ..."
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Cited by 11 (4 self)
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It is shown, that the Boltzmannlike equations allow the formulation of a very general model for behavioral changes. This model takes into account spontaneous (or externally induced) behavioral changes and behavioral changes by pair interactions. As most important social pair interactions imitative and avoidance processes are distinguished. The resulting model turns out to include as special cases many theoretical concepts of the social sciences. A KramersMoyal expansion of the Boltzmannlike equations leads to the BoltzmannFokkerPlanck equations, which allows the introduction of “social forces ” and “social fields”. A social field reflects the influence of the public opinion, social norms and trends on behaviorial changes. It is not only given by external factors (the environment) but also by the interactions of the individuals. Variations of the individual behavior are taken into account by diffusion coefficients.
Renormalizationgroup method for reduction of evolution equations; invariant manifolds and envelopes
, 2000
"... The renormalization group (RG) method as a powerful tool for reduction of evolution equations is formulated in terms of the notion of invariant manifolds. We start with derivation of an exact RG equation which is analogous to the Wilsonian RG equations in statistical physics and quantum field theory ..."
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Cited by 9 (3 self)
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The renormalization group (RG) method as a powerful tool for reduction of evolution equations is formulated in terms of the notion of invariant manifolds. We start with derivation of an exact RG equation which is analogous to the Wilsonian RG equations in statistical physics and quantum field theory. It is clarified that the perturbative RG method constructs invariant manifolds successively as the initial value of evolution equations, thereby the meaning to set t0 = t is naturally understood where t0 is the arbitrary initial time. We show that the integral constants in the unperturbative solution constitutes natural coordinates of the invariant manifold when the linear operator A in the evolution equation has no Jordan cell; when A has a Jordan cell, a slight modification is necessary because the dimension of the invariant manifold is increased by the perturbation. The RG equation determines the slow motion of the wouldbe integral constants in the unperturbative solution on the invariant manifold. We present the mechanical procedure to construct the perturbative solutions hence the initial values with which the RG equation gives meaningful results. The underlying structure of the reduction by the RG method as formulated in the present work turns out to completely fit to the universal one elucidated by Kuramoto some years ago. We indicate that the reduction procedure of evolution equations has a good correspondence with the renormalization procedure in quantum field theory; the counter part of the universal structure of reduction elucidated by Kuramoto may be the Polchinski’s theorem for renormalizable field theories. We apply the method to interface dynamics such as kinkantikink and solitonsoliton interactions in the latter of which a linear operator having a Jordancell structure appears.
Stochastic and Boltzmannlike models for behavioral changes, and their relation to game theory
 Physica A
, 1993
"... In the last decade, stochastic models have shown to be very useful for quantitative modelling of social processes. Here, a configurational master equation for the description of behavioral changes by pair interactions of individuals is developed. Three kinds of social pair interactions are distingui ..."
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Cited by 9 (5 self)
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In the last decade, stochastic models have shown to be very useful for quantitative modelling of social processes. Here, a configurational master equation for the description of behavioral changes by pair interactions of individuals is developed. Three kinds of social pair interactions are distinguished: Avoidance processes, compromising processes, and imitative processes. Computational results are presented for a special case of imitative processes: the competition of two equivalent strategies. They show a phase transition that describes the selforganization of a behavioral convention. This phase transition is further analyzed by examining the equations for the most probable behavioral distribution, which are Boltzmannlike equations. Special cases of Boltzmannlike equations do not obey the Htheorem and have oscillatory or even chaotic solutions. A suitable Taylor approximation leads to the socalled game dynamical equations (also known as selectionmutation equations in the theory of evolution). 1
A mathematical model for attitude formation by pair interactions
 Physica A
, 1992
"... Two complementary mathematical models for attitude formation are considered: Starting from the model of Weidlich and Haag (1983), which assumes indirect interactions that are mediated by a mean field, a new model is proposed, which is characterized by direct pair interactions. Three types of pair in ..."
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Cited by 8 (5 self)
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Two complementary mathematical models for attitude formation are considered: Starting from the model of Weidlich and Haag (1983), which assumes indirect interactions that are mediated by a mean field, a new model is proposed, which is characterized by direct pair interactions. Three types of pair interactions leading to attitude changes can be found: First, changes by some kind of avoidance behavior. Second, changes by a readiness for compromises. Third, changes by persuasion. Different types of behavior are distinguished by introducing several subpopulations. Representative solutions of the model are illustrated by computational results.
Extended detailed balance for systems with irreversible reactions
"... The principle of detailed balance states that in equilibrium each elementary process is equilibrated by its reverse process. For many real physicochemical complex systems (e.g. homogeneous combustion, heterogeneous catalytic oxidation, most enzyme reactions etc), detailed mechanisms include both re ..."
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Cited by 6 (3 self)
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The principle of detailed balance states that in equilibrium each elementary process is equilibrated by its reverse process. For many real physicochemical complex systems (e.g. homogeneous combustion, heterogeneous catalytic oxidation, most enzyme reactions etc), detailed mechanisms include both reversible and irreversible reactions. In this case, the principle of detailed balance cannot be applied directly. We represent irreversible reactions as limits of reversible steps and obtain the principle of detailed balance for complex mechanisms with some irreversible elementary processes. We proved two consequences of the detailed balance for these mechanisms: the structural condition and the algebraic condition that form together the extended form of detailed balance. The algebraic condition is the principle of detailed balance for the reversible part. The structural condition is: the convex hull of the stoichiometric vectors of the irreversible reactions has empty intersection with the linear span of the stoichiometric vectors of the reversible reaction. Physically, this means that the irreversible reactions cannot be included in oriented pathways. The systems with the extended form of detailed balance are also the limits of the reversible systems with detailed balance when some of the equilibrium concentrations (or activities) tend to zero. Surprisingly, the structure of the limit reaction mechanism crucially depends on the relative speeds of this tendency to zero.