Showing papers by "Andreas Schadschneider published in 2004"
TL;DR: It is shown that walking speeds vmax>1 lead to results which are in very good agreement with empirical data, and the variation of vmax has a strong influence on the shape of the flow–density relation.
Abstract: We study discretization effects in cellular automata models for pedestrian dynamics by reducing the cell size. Then a particle occupies more than one cell which leads to subtle effects in the dynamics, e.g. non-local conflict situations. Results from computer simulations of the floor field model are compared with empirical findings. Furthermore, the influence of increasing the maximal walking speed vmax is investigated by increasing the interaction range beyond nearest neighbour interactions. The extension of the model to vmax>1 turns out to be a severe challenge which can be solved in different ways. Four major variants are discussed that take into account different dynamical aspects. The variation of vmax has a strong influence on the shape of the flow–density relation. We show that walking speeds vmax>1 lead to results which are in very good agreement with empirical data.
210 citations
Journal Article•
TL;DR: The floor field model, which is a cellular automaton model for studying evacuation dynamics, is investigated and extended and a method for calculating the static floor field, which describes the shortest distance to an exit door, in an arbitrary geometry of rooms is presented.
Abstract: The floor field model, which is a cellular automaton model for studying evacuation dynamics, is investigated and extended. A method for calculating the static floor field, which describes the shortest distance to an exit door, in an arbitrary geometry of rooms is presented. The wall potential and contraction effect at a wide exit are also proposed in order to obtain realistic behavior near corners and bottlenecks. These extensions are important for evacuation simulations, especially in the case of panics.
207 citations
TL;DR: In this paper, discretisation effects in cellular automata models for pedestrian dynamics by reducing the cell size are investigated. And the influence of increasing the maximal walking speed is investigated by increasing the interaction range beyond nearest neighbor interactions.
Abstract: We study discretisation effects in cellular automata models for pedestrian dynamics by reducing the cell size. Then a particle occupies more than one cell which leads to subtle effects in the dynamics, e.g. non-local conflict situations. Results from computer simulations of the floor field model are compared with empirical findings. Furthermore the influence of increasing the maximal walking speed $v_{{\rm max}}$ is investigated by increasing the interaction range beyond nearest neighbour interactions. The extension of the model to $v_{{\rm max}}>1$ turns out to be a severe challenge which can be solved in different ways. Four major variants are discussed that take into account different dynamical aspects. The variation of $v_{{\rm max}}$ has strong influence on the shape of the flow-density relation. We show that walking speeds $v_{{\rm max}}>1$ lead to results which are in very good agreement with empirical data.
123 citations
TL;DR: Based on a detailed microscopic test scenario motivated by recent empirical studies of single-vehicle data, several cellular automaton models for traffic flow are compared and find three levels of agreement with the empirical data.
Abstract: Based on a detailed microscopic test scenario motivated by recent empirical studies of single-vehicle data, several cellular automaton models for traffic flow are compared. We find three levels of agreement with the empirical data: (1) models that do not reproduce even qualitatively the most important empirical observations, (2) models that are on a macroscopic level in reasonable agreement with the empirics, and (3) models that reproduce the empirical data on a microscopic level as well. Our results are not only relevant for applications, but also shed light on the relevant interactions in traffic flow.
119 citations
TL;DR: A model of bi-directional ant traffic on pre-existing ant trails captures in a simple way some of the generic collective features of movements of real ants on a trail and demonstrates that there are crucial qualitative differences between vehicular- and ant-traffics.
80 citations
Posted Content•
TL;DR: In this paper, a model of bi-directional ant traffic on pre-existing ant-trails is proposed to capture generic collective features of movements of real ants on a trail.
Abstract: Motivated by recent experimental work of Burd et al., we propose a model of bi-directional ant-traffic on pre-existing ant-trails. It captures in a simple way some of the generic collective features of movements of real ants on a trail. Analyzing this model, we demonstrate that there are crucial qualitative differences between vehicular- and ant-traffics. In particular, we predict some unusual features of the flow rate that can be tested experimentally. As in the uni-directional model a non-monotonic density-dependence of the average velocity can be observed in certain parameter regimes. As a consequence of the interaction between oppositely moving ants the flow rate can become approximately constant over some density interval.
77 citations
TL;DR: A new stochastic cellular automaton 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.
Abstract: 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.
71 citations
TL;DR: In this paper, the authors present an overview emphasizing the common trends that rely on theoretical modeling of the spatial patterns of living organisms and their evolution over different timescales, such as the patterns on the skins of zebras and giraffes.
Abstract: Flocks of birds and schools of fish are familiar examples of spatial patterns formed by living organisms. In contrast to the patterns on the skins of, say, zebras and giraffes, the patterns of our interest are transient although different patterns change over different timescales. The aesthetic beauty of these patterns has attracted the attention of poets and philosophers for centuries. Scientists from various disciplines, however, are in search of common underlying principles that give rise to the transient patterns in colonies of organisms. Such patterns are observed not only in colonies of organisms as simple as single-cell bacteria, but also in social insects like ants and termites. They are also observed in colonies of vertebrates as complex as birds and fish, and in human societies. In recent years, physicists have utilized the framework of statistical physics to understand these patterns. In this article, we present an overview emphasizing the common trends that rely on theoretical modeling of thes...
59 citations
Posted Content•
TL;DR: An overview of the common trends that rely on theoretical modeling of these systems using the so-called agent-based Lagrangian approach is presented.
Abstract: Flocks of birds and schools of fish are familiar examples of spatial patterns formed by living organisms. In contrast to the patterns on the skins of, say, zebra and giraffe, the patterns of our interest are {\it transient} although different patterns change over different time scales. The aesthetic beauty of these patterns have attracted the attentions of poets and philosophers for centuries. Scientists from various disciplines, however, are in search of common underlying principles that give rise to the transient patterns in colonies of organisms. Such patterns are observed not only in colonies of organisms as simple as single-cell bacteria, as interesting as social insects like ants and termites as well as in colonies of vertebrates as complex as birds and fish but also in human societies. In recent years, particularly over the last one decade, physicists have utilized the conceptual framework as well as the methodological toolbox of statistical mechanics to unravel the mystery of these patterns. In this article we present an overview emphasizing the common trends that rely on theoretical modelling of these systems using the so-called agent-based Lagrangian approach.
48 citations
TL;DR: In this article, a stochastic cellular automaton model for the collective movement of ants on a trail is proposed. But the model exhibits a continuous phase transition at the critial density only in a limiting case, and the phase diagram of the model is investigated by replacing the periodic boundary conditions by open boundary conditions.
Abstract: The traffic-like collective movement of ants on a trail can be described by a stochastic cellular automaton model. We have earlier investigated its unusual flow-density relation by using various mean field approximations and computer simulations. In this paper, we study the model following an alternative approach based on the analogy with the zero range process, which is one of the few known exactly solvable stochastic dynamical models. We show that our theory can quantitatively account for the unusual non-monotonic dependence of the average speed of the ants on their density for finite lattices with periodic boundary conditions. Moreover, we argue that the model exhibits a continuous phase transition at the critial density only in a limiting case. Furthermore, we investigate the phase diagram of the model by replacing the periodic boundary conditions by open boundary conditions.
48 citations
TL;DR: A cellular automaton model of traffic flow taking into account velocity anticipation is introduced that exhibits phase separation with a condensed phase in which particles move coherently with finite velocity coexisting with either a non-condensed (free-flow) phase or another condensed phase that is non-moving.
Abstract: A cellular automaton model of traffic flow taking into account velocity anticipation is introduced. The strength of anticipation can be varied to describe different driving schemes. We find a new phase separation into a free-flow regime and a so-called v-platoon in an intermediate density regime. In a v-platoon all cars move with velocity v and have vanishing headway. The velocity v of a platoon only depends on the strength of anticipation. At high densities, a congested state characterized by the coexistence of a 0-platoon with several v-platoons is reached. The results are not only relevant for automated highway systems, but also help to elucidate the effects of anticipation that play an essential role in realistic traffic models. From a physics point of view the model is interesting because it exhibits phase separation with a condensed phase in which particles move coherently with finite velocity coexisting with either a non-condensed (free-flow) phase or another condensed phase that is non-moving.
TL;DR: In this paper, the ground state phase diagram of a one-dimensional t-U-J model, at half-filling, was studied and a phase with gapless charge and massive spin excitations, characterized by the coexistence of triplet superconducting and spin density wave instabilities was realized.
Abstract: In this paper we study the ground state phase diagram of a one-dimensional t-U-J model, at half-filling. In the large-bandwidth limit and for ferromagnetic exchange with easy-plane anisotropy, a phase with gapless charge and massive spin excitations, characterized by the coexistence of triplet superconducting and spin density wave instabilities is realized in the ground state. With reduction of the bandwidth, a transition into an insulating phase showing properties of the spin-
$\frac{1}{2}$
XY model takes place.
25 Oct 2004
TL;DR: It is argued that the flow-density diagram exhibits a second order phase transition at the critial density only in a limiting case and can quantitatively account for the unusual non-monotonic dependence of the average speed of the ants on their density for finite lattices with periodic boundary conditions.
Abstract: Recently we have proposed a stochastic cellular automaton model of ants on a trail and investigated its unusual flow-density relation by using a mean field theory and computer simulations. In this paper, we study the model in detail by utilizing the analogy with the zero range process, which is known as one of the exactly solvable stochastic models. We show that our theory can quantitatively account for the unusual non-monotonic dependence of the average speed of the ants on their density for finite lattices with periodic boundary conditions. Moreover, we argue that the flow-density diagram exhibits a second order phase transition at the critial density only in a limiting case.
TL;DR: In this paper, the ground state phase diagram of a one-dimensional $t-U-J$ model, at half-filling, was studied and a phase with gapless charge and massive spin excitations, characterized by the coexistence of triplet superconducting and spin density wave instabilities was realized.
Abstract: In this paper we study the ground state phase diagram of a one-dimensional $t-U-J$ model, at half-filling. In the large-bandwidth limit and for ferromagnetic exchange with easy-plane anisotropy, a phase with gapless charge and massive spin excitations, characterized by the coexistence of triplet superconducting and spin density wave instabilities is realized in the ground state. With reduction of the bandwidth, a transition into an insulating phase showing properties of the spin-1/2 XY model takes place.