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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.

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., Comment: LATEX, 37 pages, 8 EPS figures, Titles of cited papers added

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.

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., 11 pages with 15 figures

A new stochastic Lagrange model of traffic flow, which includes slow-to-start effects and a driver's perspective, is proposed by extending the Burgers cellular automaton (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. The stability of these branches is explicitly studied by numerical simulations.

We report new results obtained using cellular automata for pedestrian dynamics with friction. Monte-Carlo simulations of evacuation processes are compared with experimental results on competitive behavior in emergency egress from an aircraft. In the model, the recently introduced

The Krauss-model is a stochastic model for traffic flow which is continuous in space. For periodic boundary conditions it is well understood and known to display a non-unique flow-density relation (fundamental diagram) for certain densities. In many applications, however, the behaviour under open boundary conditions plays a crucial role.In contrast to all models investigated so far, the high flow states of the Krauss-model are not metastable, but also stable. Nevertheless we find that the current in open systems obeys an extremal principle introduced for the case of simpler discrete models. The phase diagram of the open system will be completely determined by the fundamental diagram of the periodic system through this principle. In order to allow the investigation of the whole state space of the Krauss-model, appropriate strategies for the injection of cars into the system are needed.Two methods solving this problem are discussed and the boundary-induced phase transitions for both methods are studied.We also suggest a supplementary rule for the extremal principle to account for cases where not all the possible bulk states are generated by the chosen boundary conditions., Comment: 12 Pages, 14 figures

Generically, in models of driven interacting particles, the average speed of the particles decreases monotonically with increasing density. We propose a counterexample, motivated by the motion of ants in a trail, where the average speed of the particles varies non-monotonically with their density because of the coupling of their dynamics with another dynamical variable. These results, in principle, can be tested experimentally.

The investigation of traffic flow problems has a long tradition and various methods and approaches have been applied. In this review we focus on statistical mechanics and nonequilibrium aspects. It is shown that many properties of traffic flow can be modelled successfully by using rather simple cellular automaton models. Analytical methods for the investigation of discrete models are presented in some detail. Apart from highway traffic, also the modelling of city traffic and pedestrian dynamics will be discussed.

We determine the N-particle stationary states of a staggered stochastic hopping model with reflective boundaries. It is shown that the stationary states are in fact so-called optimum ground states. Recursion relations in the particle number for any l-point density correlation function will be derived. Furthermore, the connection between reflective boundaries and the occurrence of optimum ground states is examined. An explicit counterexample shows that reflective boundaries do not enforce the stationary state to be an optimum ground state.

We consider the asymmetric random average process (ARAP) with continuous mass variables and parallel discrete time dynamics studied recently by Krug/Garcia and Rajesh/Majumdar [both J. Statist. Phys.99 (2000)]. The model is defined by an arbitrary state-independent fraction density function φ(r) with support on the unit interval. We examine the exactness of mean-field steady-state mass distributions in dependence of φ and identify as a conjecture based on high order calculations the class ℳ of density functions yielding product measure solutions. Additionally the exact form of the associated mass distributions P(m) is derived. Using these results we show examplary the exactness of the mean-field ansatz for monomial fraction densities φ(r)=(n−1) rn−2 with n≥2. For verification we calculate the mass distributions P(m) explicitly and prove directly that product measure holds. Furthermore we show that even in cases where the steady state is not given by a product measure very accurate approximants can be found in the class ℳ.

We study merging pedestrian streams at T-junctions using the Floor Field Cellular Automata Model. The discreteness of the underlying lattice of the cellular automaton model limits the resolution of the predicted densities. We therefore compare different methods for the determination of the density. In particular we consider a discrete version of the Voronoi method which allows to define individual densities for each pedestrian.

The occurrence of phase separation into a jammed phase and a free-flow phase with non-interacting agents is a common feature observed in vehicular traffic. Experiments have shown a similar behavior for pedestrians, though the situation in pedestrian dynamics is more complicated. The two separate phases in one-dimensional “single-file” pedestrian movement are a jammed high-density phase and a phase of medium to high density with slowly moving pedestrians. Both phases consist of interacting agents. In order to understand this phenomenon we develop the one-dimensional Stochastic Headway Dependent Velocity Model which is continuous in space but discrete in time. The velocity of each agent depends on its headway and on its velocity: standing agents are subjected to a slow-to-start rule. The model can reproduce the experimentally observed phase separation at high densities.

The dynamics of pedestrian crowds has been studied intensively in recent years, both theoretically and empirically. However, in many situations pedestrian crowds are rather static, e.g. due to jamming near bottlenecks or queueing at ticket counters or supermarket checkouts. Classically such queues are often described by a M/M/1 queue which neglects the internal structure (density profile) of the queue by focussing on the queue length as the only dynamical variable. This is different in the exclusive queueing process (EQP) in which we consider the queue on a microscopic level. It is equivalent to a totally asymmetric exclusion process (TASEP) of varying length. The EQP has a surprisingly rich phase diagram with respect to the arrival probability α and the service probability β. The behavior on the phase transition line is much more complex than for the TASEP with a fixed system length. It is nonuniversal and depends strongly on the update procedure used.

The dynamics of pedestrian crowds has been studied intensively in recent years, both theoretically and empirically. However, in many situations pedestrian crowds are rather static, e.g. due to jamming near bottlenecks or queueing at ticket counters or supermarket checkouts. Classically such queues are often described by the M/M/1 queue that neglects the internal structure (density profile) of the queue by focussing on the system length as the only dynamical variable. This is different in the Exclusive Queueing Process (EQP) in which the queue is considered on a microscopic level. It is equivalent to a Totally Asymmetric Exclusion Process (TASEP) of varying length. The EQP has a surprisingly rich phase diagram with respect to the arrival probability alpha and the service probability beta. The behavior on the phase transition line is much more complex than for the TASEP with a fixed system length. It is nonuniversal and depends strongly on the update procedure used. In this article, we review the main properties of the EQP. We also mention extensions and applications of the EQP and some related models., 20 pages, 11 figures, to appear in Mathematical Models and Methods in Applied Sciences, Special Issue "Traffic, Crowds and Swarms 2015"; contains a review of results from arXiv:1012.4525, arXiv:1109.0425, arXiv:1210.1482, arXiv:1308.2417, arXiv:1409.0329 and some new results

We propose a simple microscopic model for arching phenomena at bottlenecks. The dynamics of particles in front of a bottleneck is described by a one-dimensional stochastic cellular automaton on a semicircular geometry. The model reproduces oscillation phenomena due to the formation and collapsing of arches. It predicts the existence of a critical bottleneck size for continuous particle flows. The dependence of the jamming probability on the system size is approximated by the Gompertz function. The analytical results are in good agreement with simulations.

Clogging of granular materials and jamming of pedestrian crowds occur because of the formation of arches at bottlenecks. We propose a simple microscopic model that is able to reproduce oscillation phenomena due to formation and destabilization of arches in 2-dimensional flows. The dynamics of particles in front of a bottleneck is described by a one-dimensional stochastic cellular automaton on a semicircular geometry. The model predicts the existence of a critical bottleneck size for jamless particle flows and allows to determine the dependence of the jamming probability on the system size. The model can also be studied analytically and the results are in good agreement with simulations.

We propose a 2-dimensional cellular automaton model to simulate pedestrian traffic. It is a vmax=1 model with exclusion statistics and parallel dynamics. Long-range interactions between the pedestrians are mediated by a so called floor field which modifies the transition rates to neighbouring cells. This field, which can be discrete or continuous, is subject to diffusion and decay. Furthermore it can be modified by the motion of the pedestrians. Therefore the model uses an idea similar to chemotaxis, but with pedestrians following a virtual rather than a chemical trace. Our main goal is to show that the introduction of such a floor field is sufficient to model collective effects and self-organization encountered in pedestrian dynamics, e.g. lane formation in counterflow through a large corridor. As an application we also present simulations of the evacuation of a large room with reduced visibility, e.g. due to failure of lights or smoke.

We apply the transfer-matrix DMRG (TMRG) to a stochastic model, the Domany-Kinzel cellular automaton, which exhibits a non-equilibrium phase transition in the directed percolation universality class. Estimates for the stochastic time evolution, phase boundaries and critical exponents can be obtained with high precision. This is possible using only modest numerical effort since the thermodynamic limit can be taken analytically in our approach. We also point out further advantages of the TMRG over other numerical approaches, such as classical DMRG or Monte-Carlo simulations.

A microscopic description of packet transport in the Internet by using a simple cellular automaton model is presented. A generalised exclusion process is introduced which allows to study travel times of the particles ('data packets') along a fixed path in the network. Computer simulations reveal the appearance of a free flow and a jammed phase separated by a (critical) transition regime. The power spectra are compared to empirical data for the RTT (Round Trip Time) obtained from measurements in the Internet. We find that the model is able to reproduce the characteristic statistical behaviour in agreement with the empirical data for both phases (free flow and congested). The phases are therefore jamming properties and not related to the structure of the network. Moreover the model shows, as observed in reality, critical behaviour (1/f-noise) for paths with critical load., 9 pages, 7 figures

The jamming behavior of a single lane traffic model based on a cellular automaton approach is studied. Our investigations concentrate on the so-called VDR model which is a simple generalization of the well-known Nagel-Schreckenberg model. In the VDR model one finds a separation between a free flow phase and jammed vehicles. This phase separation allows to use random walk like arguments to predict the resolving probabilities and lifetimes of jam clusters or disturbances. These predictions are in good agreement with the results of computer simulations and even become exact for a special case of the model. Our findings allow a deeper insight into the dynamics of wide jams occuring in the model., 16 pages, 7 figures

A recently developed theory for boundary-induced phenomena in nonequilibrium systems predicts the existence of various steady-state phase transitions induced by the motion of a shock wave. We provide direct empirical evidence that a phase transition between a free flow and a congested phase occurring in traffic flow on highways in the vicinity of on- and off-ramps can be interpreted as an example of such a boundary-induced phase transition of first order. We analyse the empirical traffic data and give a theoretical interpretation of the transition in terms of the macroscopic current. Additionally we support the theory with computer simulations of the Nagel-Schreckenberg model of vehicular traffic on a road segment which also exhibits the expected second-order transition. Our results suggest ways to predict and to some extent to optimize the capacity of a general traffic network.

We present results on the modeling of on- and off-ramps in cellular automata for traffic flow, especially the Nagel-Schreckenberg model. We study two different types of on-ramps that cause qualitatively the same effects. In a certain density regime one observes plateau formation in the fundamental diagram. The plateau value depends on the input-rate of cars at the on-ramp. The on-ramp acts as a local perturbation that separates the system into two regimes: A regime of free flow and another one where only jammed states exist. This phase separation is the reason for the plateau formation and implies a behaviour analogous to that of stationary defects. This analogy allows to perform very fast simulations of complex traffic networks with a large number of on- and off-ramps because one can parametrise on-ramps in an exceedingly easy way., Comment: 11 pages, 9 figures, accepted for publication in Int. J. Mod. Phys. C

Computer simulation of vehicular traffic can give us insight into a wide variety of phenomena observed in real traffic flow, thereby leading to a greater qualitative understanding of its basic principles. These simulations also help us explore the effects of implementing new traffic rules and control systems without doing potentially hazardous experiments with real traffic. For the sake of computational efficiency, many of the microscopic traffic models developed in recent years have been formulated using the language of cellular automata. These models of vehicular traffic belong to a class of nonequilibrium systems called driven-diffusive lattice gases (B. Schmittmann and R.K.P. Zia, 1995; G. Schutz, 2000). Over the last few years, several groups have been doing extensive computer simulations to understand the nature of the steady states and fluctuations, as well as the kinetics of evolution toward these steady states. The starting points of our discussion are the Nagel-Schreckenberg model (K. Nagel and M. Schreckenberg, 1992) and the Biham-Middleton-Levine model (O. Biham et al., 1992).

Recently it has been shown that the zero-energy eigenstate -- corresponding to the stationary state -- of a stochastic Hamiltonian with nearest-neighbour interaction in the bulk and single-site boundary terms, can always be written in the form of a so-called matrix-product state. We generalize this result to stochastic Hamiltonians with arbitrary, but finite, interaction range. As an application two different particle-hopping models with three-site bulk interaction are studied. For these models which can be interpreted as cellular automata for traffic flow, we present exact solutions for periodic boundary conditions and some suitably chosen boundary interactions., LaTeX(2e), 12 pages, 2 figures

For single-lane traffic models it is well known that particle disorder leads to platoon formation at low densities. Here we discuss the effect of slow cars in two-lane systems. Surprisingly, even a small number of slow cars can initiate the formation of platoons at low densities. The robustness of this phenomenon is investigated for different variants of the lane-changing rules as well as for different variants on the single-lane dynamics. It is shown that anticipation of drivers reduces the influence of slow cars drastically., RevTeX, 22 eps-figures included, 10 pages

The asymmetric exclusion process (ASEP) has attracted a lot of interest not only because of its many applications, e.g., in the context of the kinetics of biopolymerization and traffic flow theory, but also because it is a paradigmatic model for nonequilibrium systems. Here we study the ASEP for different types of updates, namely random-sequential, sequential, sublattice-parallel, and parallel. In order to compare the effects of the different update procedures on the properties of the stationary state, we use large-scale Monte Carlo simulations and analytical methods, especially the so-called matrix-product Ansatz (MPA). We present in detail the exact solution for the model with sublattice-parallel and sequential updates using the MPA. For the case of parallel update, which is important for applications like traffic flow theory, we determine the phase diagram, the current, and density profiles based on Monte Carlo simulations. We furthermore suggest an MPA for that case and derive the corresponding matrix algebra.

We extend the Bethe Ansatz solution of a onedimensional integrable fermionic model with correlated hopping to the parameter regime Δt > 1. It is found that the model is equivalent to one with interaction 2 − Δt, but with twisted boundary conditions. Apart from the ground state energy we investigate the low-lying excitations and the asymptotic behaviour of the correlation functions. As in the ease of Δt < 1 we find dominating superconducting correlations for small doping. The behaviour in this regime therefore differs from that of the non-integrable model with symmetric bond-charge interaction (Hirsch model).

Using Bogoliubov's inequality we rigorously show that the one- and two-dimensional Hubbard model with narrow bands does not exhibit long-range order for different kinds of pairing, e.g. s -wave Cooper pairing and generalized η pairing. This result holds at any finite temperature for both repulsive and attractive Coulomb interactions. At zero temperature there will be no on-site electron pairing long-range order if a gap in the charge excitation spectrum exists. The present results do not cover the case of d x 2 − y 2 pairing of electrons.

We present a new analytical description of the cellular automaton model for single-lane traffic. In contrast to previous approaches we do not use the occupation number of sites as dynamical variable but rather the distance between consecutive cars. Therefore certain longer-ranged correlations are taken into account and even a mean-field approach yields non-trivial results. In fact for the model with $v_{max}=1$ the exact solution is reproduced. For $v_{max}=2$ the fundamental diagram shows a good agreement with results from simulations., Comment: LaTex, 10 pages, 2 postscript figures

The relation between flow and density is an essential quantitative characteristic to describe the efficiency of traffic systems. We have performed experiments with single-file motion of bicycles and compare the results with previous studies for car and pedestrian motion in similar setups. In the space-time diagrams we observe three different states of motion (free flow state, jammed state and stop-and-go waves) in all these systems. Despite of their obvious differences they are described by a universal fundamental diagram after proper rescaling of space and time which takes into account the size and free velocity of the three kinds of agents. This indicates that the similarities between the systems go deeper than expected., 5 pages, 5 figures

As part of the German Government’s high-tech strategy, the Federal Ministry of Education and Research (BMBF) has launched a programme on “Research for Civil Security”. The field of “Protecting and Saving Human Life” in this programme includes funding for the Hermes Project. The project with a three year duration was completed in December 2011. The aim of the collaborative project was to improve safety for people in large multifunctional buildings and also at big events by exploring the effectiveness of an evacuation assistant. In this project, we realized a real-time simulation for the reliable prediction of evacuation process.

There exists a wide range of simulation software for the pedestrian dynamics area. Most of these software are commercial, or do not give an insight in their functionality. While this might be of little importance for some end user, it is very important for researchers to know exactly what the models are performing. This constitutes a significant advantage in the interpretation of the results. In this paper we introduce OpenPedSim (Open Pedestrian Simulation), an open source framework for performing pedestrian simulations. This framework should support researchers by the development of new models by providing a suitable environment with appropriate interfaces.

Mathematical models for pedestrian dynamics contribute increasingly to the process of understanding the dynamics of crowds, which has a positive impact in designing building and enhancing their level of safety. In order to improve their validity and maximize the significance of their predictions, several experiments were conducted and evaluated. The results of these experiments give authentic insights into the dynamics of pedestrians and serve as a benchmark for the models. Therefore, the quantitative validation of mathematical models is an important step in their development and eases their application in real-world scenarios. In this article we briefly introduce the generalized centrifugal force model (GCFM). Computer simulations with the GCFM are compared with different empirical data obtained in controlled experiments. In order to test the quality of the model, several scenarios are simulated without changing the parameters of the underlying model.

In this study, series of experiments under laboratory conditions were carried out to study uni- and bidirectional pedestrian streams in a straight corridor. The software PeTrack is used to extract pedestrian trajectories from video recordings automatically. From these trajectories the characteristics of bidirectional flow are analyzed using the Voronoi method. The fundamental diagram for various types of bidirectional streams agree well and no large differences are found in observed density range ρ < 2.5 m−2. By comparing the diagram between uni- and bidirectional stream, it is shown that the density-flow relationships agree well for the free flow state. However, the maximum specific flow in unidirectional streams is significantly larger than that in bidirectional streams.

The exclusive queueing process (EQP) is a generalization of the classical M/M/1 queue. It is equivalent to a totally asymmetric exclusion process (TASEP) of varying length. Here we consider two discrete-time versions of the EQP with parallel and backward-sequential update rules. The phase diagram (with respect to the arrival probability \alpha\ and the service probability \beta) is divided into two phases corresponding to divergence and convergence of the system length. We investigate the behavior on the critical line separating these phases. For both update rules, we find diffusive behavior for small output probability (\beta\beta_c it becomes sub-diffusive and nonuniversal: the exponents characterizing the divergence of the system length and the number of customers are found to depend on the update rule. For the backward-update case, they also depend on the hopping parameter p, and remain finite when p is large, indicating a first order transition., Comment: v2: published version

In this study, we provide results of controlled experiments of single file bicycle movement on a circuit. We compare the fundamental characteristics of bicycle traffic with that of car and pedestrian traffic, which have been studied extensively in previous research under similar condition. From the comparison of the time-space diagrams of these three one-dimensional traffic flows, different states of motion (free flow state, the jammed state and stop-and-go waves) can be observed in all these systems. The fundamental diagrams are compared in two different ways. Without considering the size and free velocity of these three kinds of objects, the data points occupy different density ranges in the diagram. However, when we use the concept of scaling by considering the free velocity and size of the moving objects, the fundamental diagrams show the same structure and values. This implies that the transport properties in these three different types of single file traffic flow could be unified in a certain range by simple scaling. These results provide insights into the dynamics but also may be relevant for the improvement of mixed traffic systems.

The improvement of safety at mass events has become an important issue not only due to several disasters involving large crowds. To support security services in case of emergencies we have developed an evacuation assistant which allows forecasting the emergency egress of large crowds in complex buildings. Such a forecast requires pedestrian models which produce realistic crowd dynamics and, at the same time, can be simulated faster than real-time. Here we give an overview of the project and present first results.

The formation of lanes is a well known emergent behavior in pedestrian counterflow as well as in some other physical systems. Nevertheless, not much is known quantitatively which is related to the fact that the empirical situation is quite poor. Here we analyze lane formation in a two-dimensional cellular automaton for pedestrian dynamics. To quantify the lane structure, we make use of a laning order parameter which has been used previously to detect lanes in colloidal systems. The main purpose of our work is to determine a phase diagram in dependence on the coupling constants and the particle density. Furthermore, we compare the results of our simulation with experimental data.

We study the stationary properties of a microscopic traffic flow model related to a continuous time mass transport process. It is a stochastic collision-free mapping of a classical deterministic first order car-following model calibrated by the targeted speed function and the driver reaction time. The stationary states of the model are analytically treated for vanishing reaction time. Some approximations are calculated, assuming a product form of the invariant measure. When the reaction time is strictly positive, the process is studied by simulation. A relation between the parameters and the propagation of kinematic stop-and-go waves is identified as identical to the well-known stability condition of the car-following model. The results underline a negative impact of the driver reaction time parameter on the homogeneity of the flow in stationary state.

A brief overview of mathematical modeling of pedestrian dynamics is presented. Hereby, we focus on space-continuous models which include interactions between the pedestrian by forces. Conceptual problems of such models are addressed. Side-effects of spatially continuous force-based models, especially oscillations and overlapping which occur for erroneous choices of the forces, are analyzed in a quantitative manner. As a representative example of force-based models the Generalized Centrifugal Force Model (GCFM) is introduced. Key components of the model are presented and discussed. Finally, simulations with the GCFM in corridors and bottlenecks are shown and compared with experimental data.

The occurrence of phase separation is a common feature observed in vehicular traffic. Experiments have shown a similar behavior for pedestrians, though the situation in pedestrian dynamics is more complicated. The two separate phases in one-dimensional “single-file” pedestrian movement are a jammed high-density phase and a phase of medium to high density with slowly moving pedestrians. Both phases consist of interacting particles (pedestrians). To understand the emergence of this kind of phase separation, we develop a simple cellular automaton model. The transition probabilities of the modeled pedestrians in general depend on their current velocities and on the occupancy of the next two cells in front of them. For inhomogeneous initial conditions the simulated pedestrian trajectories clearly feature two distinct phases analogous to the experiment. The lifetime of the decaying jammed phase is consistent with experimental results.

In this study, series of experiments under laboratory conditions were carried out to investigate pedestrian flow through a T-junction, i.e., two branches merging into the main stream. The whole duration of the experiments was recorded by video cameras and the trajectories of each pedestrian were extracted using the software Petrack from these videos. The Voronoi method is used to resolve the fine structure of the fundamental diagram and spatial dependence of the measured quantities from trajectories. In our study, only the data in the stationary state are used by analyzing the time series of density and velocity. The density, velocity and specific flow profiles are obtained by refining the size of the measurement area (here 10 × 10 cm are adopted). With such a high resolution, the spatial distribution of density, velocity and specific flow can be obtained separately and the regions with higher value can be observed intuitively. Finally, the fundamental diagrams of T-junction flow is compared in three different locations. It is shown that the fundamental diagrams of the two branches match well. However, the velocities in front of the merging are significantly lower than that in the main stream at the same densities. After the merging, the specific flow increases with the density ρ till 2. 5 m−2. While in the branches, the specific flow is almost independent of the density between ρ = 1. 5 and 3. 5 m−2.

We introduce an enhanced model based on the generalized centrifugal force model. Furthermore, the desired direction of pedestrians is investigated. A new approach leaning on the well-known concept of static and dynamic floor-fields in cellular automata is presented. Numerical results of the model are presented and compared with empirical data.

We consider generalized Hubbard models in arbitrary dimensions which have additional nearest-neighbour interactions. It is shown that in a large region of the parameter space these models have ground states of the η-pairing type. These ground states exhibit off-diagonal long-range order and are thus superconducting. In special cases the complete (T=0) phase diagram can be obtained.

We investigate ground-state properties of two correlated-hopping electron models, the Hirsch and the Bariev model. Both models are of recent interest in the context of hole superconductivity. Applying the Lanczos technique to small clusters, we numerically determine the binding energy, the spin gaps, correlation functions, and other properties for various values of the bond-charge interaction parameter. Our results for small systems indicate that pairing is favoured in a certain parameter range. However, in contrast to the Bariev model, superconducting correlations are suppressed in the Hirsch model, for a bond-charge repulsion larger than a critical value., Comment: 7 pages (LaTeX) + 6 postcript figures in a separate uuencoded file

A recently presented anisotropic generalization of the multicomponent supersymmetric $t-J$ model in one dimension is investigated. This model of fermions with general spin-$S$ is solved by Bethe ansatz for the ground state and the low-lying excitations. Due to the anisotropy of the interaction the model possesses $2S$ massive modes and one single gapless excitation. The physical properties indicate the existence of Cooper-type multiplets of $2S+1$ fermions with finite binding energy. The critical behaviour is described by a $c=1$ conformal field theory with continuously varying exponents depending on the particle density. There are two distinct regimes of the phase diagram with dominating density-density and multiplet-multiplet correlations, respectively. The effective mass of the charge carriers is calculated. In comparison to the limit of isotropic interactions the mass is strongly enhanced in general., 10 pages, 3 Postscript figures appended as uuencoded compressed tar-file to appear in Z. Phys. B, preprint Cologne-94-4744