arXiv subjects

Katsuhiro Nishinari

Publications and source records attributed to Katsuhiro Nishinari.

At least 91 records · Page 5Linked to original sources

arXiv2009

Exact solution and asymptotic behaviour of the asymmetric simple exclusion process on a ring

In this paper, we study an exact solution of the asymmetric simple exclusion process on a periodic lattice of finite sites with two typical updates, i.e., random and parallel. Then, we find that the explicit formulas for the partition function and the average velocity are expressed by the Gauss hypergeometric function. In order to obtain these results, we effectively exploit the recursion formula for the partition function for the zero-range process. The zero-range process corresponds to the asymmetric simple exclusion process if one chooses the relevant hop rates of particles, and the recursion gives the partition function, in principle, for any finite system size. Moreover, we reveal the asymptotic behaviour of the average velocity in the thermodynamic limit, expanding the formula as a series in system size.

cond-mat.stat-mech↗

arXiv2009

Trafficlike collective movement of ants on trails: absence of jammed phase

We report experimental results on unidirectional traffic-like collective movement of ants on trails. Our work is primarily motivated by fundamental questions on the collective spatio-temporal organization in systems of interacting motile constituents driven far from equilibrium. Making use of the analogies with vehicular traffic, we analyze our experimental data for the spatio-temporal organisation of the ants on the trail. From this analysis, we extract the flow-density relation as well as the distributions of velocities of the ants and distance-headways. Some of our observations are consistent with our earlier models of ant-traffic, which are appropriate extensions of the asymmetric simple exclusion process (ASEP). In sharp contrast to highway traffic and most other transport processes, the average velocity of the ants is almost independent of their density on the trail. Consequently, no jammed phase is observed.

physics.bio-ph↗

arXiv2009

Characteristics of ant-inspired traffic flow: Applying the social insect metaphor to traffic models

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.

stat.AP↗

arXiv2009

Ultra-discrete Optimal Velocity Model: a Cellular-Automaton Model for Traffic Flow and Linear Instability of High-Flux Traffic

In this paper, we propose the ultra-discrete optimal velocity model, a cellular-automaton model for traffic flow, by applying the ultra-discrete method for the optimal velocity model. The optimal velocity model, defined by a differential equation, is one of the most important models; in particular, it successfully reproduces the instability of high-flux traffic. It is often pointed out that there is a close relation between the optimal velocity model and the mKdV equation, a soliton equation. Meanwhile, the ultra-discrete method enables one to reduce soliton equations to cellular automata which inherit the solitonic nature, such as an infinite number of conservation laws, and soliton solutions. We find that the theory of soliton equations is available for generic differential equations, and the simulation results reveal that the model obtained reproduces both absolutely unstable and convectively unstable flows as well as the optimal velocity model.

nlin.CG↗

arXiv2008

Achievement of Alternative Configurations of Vehicles on Multiple Lanes

Heavy traffic congestion daily occurs at merging sections on highway. For releasing this congestion, possibility of alternative configuration of vehicles on multiple-lane road is discussed in this paper. This is the configuration where no vehicles move aside on the other lane. It has a merit in making smooth merging at an intersection or a junction due to so-called the "zipper effect". We show, by developing a cellular automaton model for multiple lanes, that this configuration is achieved by simple local interactions between vehicles neighboring each other. The degree of the alternative configuration in terms of the spatial increase of parallel driving length is studied by using both numerical simulations and mean field theory. We successfully construct a theoretical method for calculating this degree of the alternative configuration by using cluster approximation. It is shown that the theoretical results coincide with those of the simulations very well.

physics.soc-ph↗

arXiv2008

Traffic phenomena in biology: from molecular motors to organisms

Traffic-like collective movements are observed at almost all levels of biological systems. Molecular motor proteins like, for example, kinesin and dynein, which are the vehicles of almost all intra-cellular transport in eukayotic cells, sometimes encounter traffic jam that manifests as a disease of the organism. Similarly, traffic jam of collagenase MMP-1, which moves on the collagen fibrils of the extracellular matrix of vertebrates, has also been observed in recent experiments. Traffic-like movements of social insects like ants and termites on trails are, perhaps, more familiar in our everyday life. Experimental, theoretical and computational investigations in the last few years have led to a deeper understanding of the generic or common physical principles involved in these phenomena. In particular, some of the methods of non-equilibrium statistical mechanics, pioneered almost a hundred years ago by Einstein, Langevin and others, turned out to be powerful theoretical tools for quantitative analysis of models of these traffic-like collective phenomena as these systems are intrinsically far from equilibrium. In this review we critically examine the current status of our understanding, expose the limitations of the existing methods, mention open challenging questions and speculate on the possible future directions of research in this interdisciplinary area where physics meets not only chemistry and biology but also (nano-)technology.

physics.bio-ph↗

arXiv2008

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

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.

physics.bio-ph↗

arXiv2007

Mean Field Theory for Pedestrian Outflow through an Exit

An average pedestrian flow through an exit is one of the most important index in evaluating pedestrian dynamics. In order to study the flow in detail, the floor field model, which is a crowd model by using cellular automaton, is extended by taking into account a realistic behavior of pedestrians around the exit. The model is studied by both numerical simulations and cluster analysis to obtain a theoretical expression of an average pedestrian flow through the exit. It is found quantitatively that the effect of exit door width, a wall, and pedestrian's mood of competition or cooperation significantly influence the average flow. The results show that there is suitable width of the exit and position according to pedestrian's mood.

cond-mat.stat-mech↗

arXiv2007

Modelling of self-driven particles: foraging ants and pedestrians

Models for the behavior of ants and pedestrians are studied in an unified way in this paper. Each ant follows pheromone put by preceding ants, hence creating a trail on the ground, while pedestrians also try to follow others in a crowd for efficient and safe walking. These following behaviors are incorporated in our stochastic models by using only local update rules for computational efficiency. It is demonstrated that the ant trail model shows an unusual non-monotonic dependence of the average speed of the ants on their density, which can be well analyzed by the zero-range process. We also show that this anomalous behavior is clearly observed in an experiment of multiple robots. Next, the relation between the ant trail model and the floor field model for studying evacuation dynamics of pedestrians is discussed. The latter is regarded as a two-dimensional generalization of the ant trail model, where the pheromone is replaced by footprints.

cond-mat.stat-mech↗

arXiv2007

Physics of Transport and Traffic Phenomena in Biology: from molecular motors and cells to organisms

Traffic-like collective movements are observed at almost all levels of biological systems. Molecular motor proteins like, for example, kinesin and dynein, which are the vehicles of almost all intra-cellular transport in eukayotic cells, sometimes encounter traffic jam that manifests as a disease of the organism. Similarly, traffic jam of collagenase MMP-1, which moves on the collagen fibrils of the extracellular matrix of vertebrates, has also been observed in recent experiments. Traffic-like movements of social insects like ants and termites on trails are, perhaps, more familiar in our everyday life. Experimental, theoretical and computational investigations in the last few years have led to a deeper understanding of the generic or common physical principles involved in these phenomena. In particular, some of the methods of non-equilibrium statistical mechanics, pioneered almost a hundred years ago by Einstein, Langevin and others, turned out to be powerful theoretical tools for quantitaive analysis of models of these traffic-like collective phenomena as these systems are intrinsically far from equilibrium. In this review we critically examine the current status of our understanding, expose the limitations of the existing methods, mention open challenging questions and speculate on the possible future directions of research in this interdisciplinary area where physics meets not only chemistry and biology but also (nano-)technology.

physics.bio-ph↗

arXiv2007

Intra-cellular transport by single-headed kinesin KIF1A: effects of single-motor mechano-chemistry and steric interactions

In eukaryotic cells, many motor proteins can move simultaneously on a single microtubule track. This leads to interesting collective phenomena like jamming. Recently we reported ({\it Phys. Rev. Lett. {\bf 95}, 118101 (2005)}) a lattice-gas model which describes traffic of unconventional (single-headed) kinesins KIF1A. Here we generalize this model, introducing a novel interaction parameter $c$, to account for an interesting mechano-chemical process which has not been considered in any earlier model. We have been able to extract all the parameters of the model, except $c$, from experimentally measured quantities. In contrast to earlier models of intra-cellular molecular motor traffic, our model assigns distinct ``chemical'' (or, conformational) states to each kinesin to account for the hydrolysis of ATP, the chemical fuel of the motor. Our model makes experimentally testable theoretical predictions. We determine the phase diagram of the model in planes spanned by experimentally controllable parameters, namely, the concentrations of kinesins and ATP. Furthermore, the phase-separated regime is studied in some detail using analytical methods and simulations to determine e.g. the position of shocks. Comparison of our theoretical predictions with experimental results is expected to elucidate the nature of the mechano-chemical process captured by the parameter $c$.

physics.bio-ph↗

arXiv2006

A new stochastic cellular automaton model on traffic flow and its jamming phase transition

A general stochastic traffic cellular automaton (CA) model, which includes slow-to-start effect and driver's perspective, is proposed in this paper. It is shown that this model includes well known traffic CA models such as Nagel-Schreckenberg model, Quick-Start model, and Slow-to-Start model as specific cases. Fundamental diagrams of this new model clearly show metastable states around the critical density even when stochastic effect is present. We also obtain analytic expressions of the phase transition curve in phase diagrams by using approximate flow-density relations at boundaries. These phase transition curves are in excellent agreement with numerical results.

cond-mat.stat-mech↗

arXiv2006

Competition of coarsening and shredding of clusters in a driven diffusive lattice gas

We investigate a driven diffusive lattice gas model with two oppositely moving species of particles. The model is motivated by bi-directional traffic of ants on a pre-existing trail. A third species, corresponding to pheromones used by the ants for communication, is not conserved and mediates interactions between the particles. Here we study the spatio-temporal organization of the particles. In the uni-directional variant of this model it is known to be determined by the formation and coarsening of ``loose clusters''. For our bi-directional model, we show that the interaction of oppositely moving clusters is essential. In the late stages of evolution the cluster size oscillates because of a competition between their `shredding' during encounters with oppositely moving counterparts and subsequent "coarsening" during collision-free evolution. We also establish a nontrivial dependence of the spatio-temporal organization on the system size.

physics.bio-ph↗

arXiv2005

Intra-cellular transport of single-headed molecular motors KIF1A

Motivated by experiments on single-headed kinesin KIF1A, we develop a model of intra-cellular transport by interacting molecular motors. It captures explicitly not only the effects of ATP hydrolysis, but also the ratchet mechanism which drives individual motors. Our model accounts for the experimentally observed single molecule properties in the low density limit and also predicts a phase diagram that shows the influence of hydrolysis and Langmuir kinetics on the collective spatio-temporal organization of the motors. Finally, we provide experimental evidence for the existence of domain walls in our {\it in-vitro} experiment with fluorescently labeled KIF1A.

physics.bio-ph↗

arXiv2004

Discretisation effects and the influence of walking speed in cellular automata models for pedestrian dynamics

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.

cond-mat.stat-mech↗

arXiv2004

Collective effects in traffic on bi-directional ant-trails

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.

cond-mat.stat-mech↗

arXiv2004

Self-organized patterns and traffic flow in colonies of organisms: from bacteria and social insects to vertebrates

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.

q-bio.PE↗

arXiv2004

Interpreting the Wide Scattering of Synchronized Traffic Data by Time Gap Statistics

Based on the statistical evaluation of experimental single-vehicle data, we propose a quantitative interpretation of the erratic scattering of flow-density data in synchronized traffic flows. A correlation analysis suggests that the dynamical flow-density data are well compatible with the so-called jam line characterizing fully developed traffic jams, if one takes into account the variation of their propagation speed due to the large variation of the netto time gaps (the inhomogeneity of traffic flow). The form of the time gap distribution depends not only on the density, but also on the measurement cross section: The most probable netto time gap in congested traffic flow upstream of a bottleneck is significantly increased compared to uncongested freeway sections. Moreover, we identify different power-law scaling laws for the relative variance of netto time gaps as a function of the sampling size. While the exponent is -1 in free traffic corresponding to statistically independent time gaps, the exponent is about -2/3 in congested traffic flow because of correlations between queued vehicles.

cond-mat.stat-mech↗