Showing papers by "Andreas Schadschneider published in 2008"

Evacuation Dynamics: Empirical Results, Modeling and Applications

Abstract: 1 Institut fur Theoretische Physik, Universitat zu Koln, 50937 Koln, Germany as@thp.uni-koeln.de 2 Interdisziplinares Zentrum fur komplexe Systeme, 53117 Bonn, Germany 3 Institute for Building Material Technology and Fire Safety Science, University of Wuppertal, 42285 Wuppertal, Germany 4 TraffGo HT GmbH, Bismarckstr. 142 , 47057 Duisburg, Germany 5 PTV AG, Stumpfstr. 1, 76131 Karlsruhe, Germany 6 Julich Supercomputing Centre, Research Centre Julich, 52425 Julich, Germany

Phase diagram and edge effects in the ASEP with bottlenecks

Abstract: We investigate the totally asymmetrical simple exclusion process (TASEP) in the presence of a bottleneck, i.e. a sequence of consecutive defect sites with reduced hopping rate. The influence of such a bottleneck on the phase diagram is studied by computer simulations and a novel analytical approach. We find a clear dependence of the current and the properties of the phase diagram not only on the length of the bottleneck, but also on its position. For bottlenecks near the boundaries, this motivates the concept of effective boundary rates. Furthermore the inclusion of a second, smaller bottleneck far from the first one has no influence on the transport capacity. These results will form the basis of an effective description of the disordered TASEP and are relevant for the modelling of protein synthesis or intracellular transport systems where the motion of molecular motors is hindered by immobile blocking molecules.

Single-bottleneck approximation for driven lattice gases with disorder and open boundary conditions

Abstract: We investigate the effects of disorder on driven lattice gases with open boundaries using the totally asymmetric simple exclusion process as a paradigmatic example. Disorder is realized by randomly distributed defect sites with reduced hopping rate. In contrast to equilibrium, even macroscopic quantities in disordered non-equilibrium systems depend sensitively on the defect sample. We study the current as a function of the entry and exit rates and the realization of disorder and find that it is, in leading order, determined by the longest stretch of consecutive defect sites (single-bottleneck approximation, SBA). Using results from extreme value statistics the SBA allows us to study ensembles with fixed defect density which gives accurate results, e.g. for the expectation value of the current. Corrections to SBA come from effective interactions of bottlenecks close to the longest one. Defects close to the boundaries can be described by effective boundary rates and lead to shifts of the phase transitions. Finally it is shown that the SBA also works for more complex models. As an example we discuss a model with internal states that has been proposed to describe transport of the kinesin KIF1A.

Fundamental Diagram and Validation of Crowd Models

Abstract: In recent years, several approaches for crowd modeling have been proposed. However, so far not much attention has been paid to their quantitativevalidation. The fundamental diagram , i.e. the density-dependence of the flow or velocity, is probably the most important relation as it connects the basic parameter to describe the dynamic of crowds. But specifications in different handbooks as well as experimental measurements for the fundamental diagram differ considerably. We give a review of the experimental data base and the causes for the discrepancies discussed in the literature. Up to now it was neglected that the way of measurement can cause variations between the results of different studies. To shed some light on this problem we studied by means of experimental trajectories of the single file movement how different measurement methods influence the resulting fundamental diagram.

Characteristics of ant-inspired traffic flow

Abstract: We investigate the organization of traffic flow on preexisting uni- and bidirectional ant trails. Our investigations comprise a theoretical as well as an empirical part. We propose minimal models of uni- and bi-directional traffic flow implemented as cellular automata. Using these models, the spatio-temporal organization of ants on the trail is studied. Based on this, some unusual flow characteristics which differ from those known from other traffic systems, like vehicular traffic or pedestrians dynamics, are found. The theoretical investigations are supplemented by an empirical study of bidirectional traffic on a trail of Leptogenys processionalis. Finally, we discuss some plausible implications of our observations from the perspective of flow optimization.

Modelling of Transport and Traffic Problems

Abstract: The Asymmetric Simple Exclusion Process (ASEP) is the simplest cellular automaton which captures the essential aspects of most transport and traffic phenomena. It describes the directed motion of particles obeying an exclusion principle. For specific applications, however, various generalizations of the ASEP are necessary. These are discussed for the case of highway traffic, ant trails, pedestrian dynamics and intracellular transport.

Intra-cellular traffic: bio-molecular motors on filamentary tracks

Abstract: Molecular motors are macromolecular complexes which use some form of input energy to perform mechanical work The filamentary tracks, on which these motors move, are made of either proteins (eg, microtubules) or nucleic acids (DNA or RNA) Often, many such motors move simultaneously on the same track and their collective properties have superficial similarities with vehicular traffic on highways The models we have developed provide ``unified'' description: in the low-density limit, a model captures the transport properties of a single motor while, at higher densities the same model accounts for the collective spatio-temporal organization of interacting motors By drawing analogy with vehicular traffic, we have introduced novel quantities for characterizing the nature of the spatio-temporal organization of molecular motors on their tracks We show how the traffic-like intracellular collective phenomena depend on the mechano-chemistry of the corresponding individual motors

Intra-cellular traffic: bio-molecular motors on filamentary tracks

Abstract: Molecular motors are macromolecular complexes which use some form of input energy to perform mechanical work. The filamentary tracks, on which these motors move, are made of either proteins (e.g., microtubules) or nucleic acids (DNA or RNA). Often, many such motors move simultaneously on the same track and their collective properties have superficial similarities with vehicular traffic on highways. The models we have developed provide "unified" description: in the low-density limit, a model captures the transport properties of a single motor while, at higher densities the same model accounts for the collective spatio-temporal organization of interacting motors. By drawing analogy with vehicular traffic, we have introduced novel quantities for characterizing the nature of the spatio-temporal organization of molecular motors on their tracks. We show how the traffic-like intracellular collective phenomena depend on the mechano-chemistry of the corresponding individual motors.

Conflicts and Friction in Pedestrian Dynamics

Abstract: "Conflicts" occur generically in particle-hopping models with parallel dynamics when multiple occupation of sites is forbidden. For cellular automata models of pedestrian dynamics we argue that such conflicts represent an important aspect of the real dynamics. Clogging at bottlenecks is described more realistically if one introduces "friction", i.e. conflicts in which none of the involved agents is allowed to move.

Quantum corner — transfer matrix dmrg

Abstract: We propose a new method for the calculation of thermodynamic properties of one-dimensional quantum systems by combining the TMRG approach with the corner transfer-matrix method. The corner transfer-matrix DMRG method brings reasonable advantage over TMRG for classical systems. We have modified the concept for the calculation of thermal properties of one-dimensional quantum systems. The novel QCTMRG algorithm is implemented and used to study two simple test cases, the classical Ising chain and the isotropic Heisenberg model. In a discussion, the advantages and challenges are illuminated.

From CA to Gene Expression: Machines and Mechanisms

Abstract: Molecular motors are proteins or macromolecular complexes which use input energy to perform mechanical work. Some of these motors move on filamentous proteins whereas other move on DNA or RNA strands. Often, many such motors move simultaneously on the same track and their collective movement is similar to vehicular traffic on highways. We have developed theoretical models of different types of molecular motor traffic by appropriately extending the totally asymmetric simple exclusion process (TASEP). Thus, our models of molecular motor traffic belong to the broad class of driven-diffusive lattice gas models which have close relations with cellular automata. By drawing analogy with vehicular traffic, we have introduced novel quantities for characterizing the nature of the spatio-temporal organization of molecular motors on their tracks. We show how the mechano-chemistry of the individual motors influence the traffic-like intracellular collective phenomena.

Quantum Corner-Transfer Matrix DMRG

Abstract: We propose a new method for the calculation of thermodynamic properties of one-dimensional quantum systems by combining the TMRG approach with the corner transfer-matrix method. The corner transfer-matrix DMRG method brings reasonable advantage over TMRG for classical systems. We have modified the concept for the calculation of thermal properties of one-dimensional quantum systems. The novel QCTMRG algorithm is implemented and used to study two simple test cases, the classical Ising chain and the isotropic Heisenberg model. In a discussion, the advantages and challenges are illuminated.