A power law for the duration of high-flow states and its interpretation from a heterogeneous traffic flow perspective

We study the duration of "high-flow states” in freeway traffic, defined as the time periods for which traffic flows exceed a given flow threshold. Our empirical data are surprisingly well represented by a power law. Moreover, the power law exponent for a two-lane freeway seems to be independent of the chosen flow threshold. In order to interpret this discovery, we investigate a simple theoretical model of heterogeneous traffic with overtaking maneuvers, which is able to reproduce both, the empirical power law and its exponen

Analysis of the runoff response of an Alpine catchment at different scales

International audienceTo understand how hydrological processes are related across different spatial scales, 201 rainfall runoff events were examined in three nested catchments of the upper river Saalach in the Austrian Alps. The Saalach basin is a nested catchment covering different spatial scales, from the micro-scale (Limberg, 0.07 km2), to the small-catchment scale (Rammern, 15.5 km2), and the meso-scale (Viehhofen, 150 km2). At these three scales two different event types could clearly be identified, depending on rainfall characteristics and initial baseflow level: (1) a unimodal event type with a quick rising and falling hydrograph, responding to short duration rainfall, and (2) a bimodal event type with a double peak hydrograph at the micro-scale and substantially increased flow values at the larger basins Rammern and Viehhofen, responding to long duration rainfall events. In all cases where a bimodal event was identified at the microscale, the hydrographs at the larger scales exhibited significantly attenuated recession behavior, quantified by recession constants. At all scales, the bimodal events are associated with considerably higher runoff volumes than the unimodal events. From the investigations at the headwater Limberg we came to the conclusion that the higher amount of runoff of bimodal events is due to the mobilization of subsurface flow processes. The analysis shows that the occurrence of the two event types is consistent over three orders of magnitude in area. This link between the scales means that the runoff behavior of the headwater may be used as an indicator of the runoff behavior of much larger areas

Analysis of the runoff response of an alpine catchment at different scales

International audienceTo understand how hydrological processes are related across different spatial scales, 201 rainfall runoff events were examined in three nested catchments of the upper river Saalach in the Austrian Alps. The Saalach basin is a nested catchment covering different spatial scales, from the micro-scale (Limberg, 0.07 km²), to the small-catchment scale (Rammern, 15.5 km²), and the meso-scale (Viehhofen, 150 km²). At these three scales two different event types could clearly be identified, depending on rainfall characteristics and initial baseflow level: (1) a unimodal event type with a quick rising and falling hydrograph, responding to short duration rainfall, and (2) a bimodal event type with a double peak hydrograph at the micro-scale and substantially increased flow values at the larger basins Rammern and Viehhofen, responding to long duration rainfall events. In all cases where a bimodal event was identified at the microscale, the hydrographs at the larger scales exhibited significantly attenuated recession behavior, quantified by recession constants. At all scales, the bimodal events are associated with considerably higher runoff volumes than the unimodal events. From the investigations at the headwater Limberg we came to the conclusion that the higher amount of runoff of bimodal events is due to the mobilization of subsurface flow processes. The analysis shows that the occurrence of the two event types is consistent over three orders of magnitude in area. This link between the scales means that the runoff behavior of the headwater may be used as an indicator of the runoff behavior of much larger areas

An empirical test for cellular automaton models of traffic flow

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 new light on the relevant interactions in traffic flow.Comment: 28 pages, 36 figures, accepted for publication in PR

Statistical Mechanics of Canonical-Dissipative Systems and Applications to Swarm Dynamics

We develop the theory of canonical-dissipative systems, based on the assumption that both the conservative and the dissipative elements of the dynamics are determined by invariants of motion. In this case, known solutions for conservative systems can be used for an extension of the dynamics, which also includes elements such as the take-up/dissipation of energy. This way, a rather complex dynamics can be mapped to an analytically tractable model, while still covering important features of non-equilibrium systems. In our paper, this approach is used to derive a rather general swarm model that considers (a) the energetic conditions of swarming, i.e. for active motion, (b) interactions between the particles based on global couplings. We derive analytical expressions for the non-equilibrium velocity distribution and the mean squared displacement of the swarm. Further, we investigate the influence of different global couplings on the overall behavior of the swarm by means of particle-based computer simulations and compare them with the analytical estimations.Comment: 14 pages incl. 13 figures. v2: misprints in Eq. (40) corrected, ref. updated. For related work see also: http://summa.physik.hu-berlin.de/~frank/active.htm

Generalized Force Model of Traffic Dynamics

Floating car data of car-following behavior in cities were compared to existing microsimulation models, after their parameters had been calibrated to the experimental data. With these parameter values, additional simulations have been carried out, e.g. of a moving car which approaches a stopped car. It turned out that, in order to manage such kinds of situations without producing accidents, improved traffic models are needed. Good results have been obtained with the proposed generalized force model.Comment: For related work see http://www.theo2.physik.uni-stuttgart.de/helbing.htm

Criterion for traffic phases in single vehicle data and empirical test of a microscopic three-phase traffic theory

A microscopic criterion for distinguishing synchronized flow and wide moving jam phases in single vehicle data measured at a single freeway location is presented. Empirical local congested traffic states in single vehicle data measured on different days are classified into synchronized flow states and states consisting of synchronized flow and wide moving jam(s). Then empirical microscopic characteristics for these different local congested traffic states are studied. Using these characteristics and empirical spatiotemporal macroscopic traffic phenomena, an empirical test of a microscopic three-phase traffic flow theory is performed. Simulations show that the microscopic criterion and macroscopic spatiotemporal objective criteria lead to the same identification of the synchronized flow and wide moving jam phases in congested traffic. It is found that microscopic three-phase traffic models can explain both microscopic and macroscopic empirical congested pattern features. It is obtained that microscopic distributions for vehicle speed difference as well as fundamental diagrams and speed correlation functions can depend on the spatial co-ordinate considerably. It turns out that microscopic optimal velocity (OV) functions and time headway distributions are not necessarily qualitatively different, even if local congested traffic states are qualitatively different. The reason for this is that important spatiotemporal features of congested traffic patterns are it lost in these as well as in many other macroscopic and microscopic traffic characteristics, which are widely used as the empirical basis for a test of traffic flow models, specifically, cellular automata traffic flow models.Comment: 27 pages, 16 figure

Congested Traffic States in Empirical Observations and Microscopic Simulations

We present data from several German freeways showing different kinds of congested traffic forming near road inhomogeneities, specifically lane closings, intersections, or uphill gradients. The states are localized or extended, homogeneous or oscillating. Combined states are observed as well, like the coexistence of moving localized clusters and clusters pinned at road inhomogeneities, or regions of oscillating congested traffic upstream of nearly homogeneous congested traffic. The experimental findings are consistent with a recently proposed theoretical phase diagram for traffic near on-ramps [D. Helbing, A. Hennecke, and M. Treiber, Phys. Rev. Lett. {\bf 82}, 4360 (1999)]. We simulate these situations with a novel continuous microscopic single-lane model, the ``intelligent driver model'' (IDM), using the empirical boundary conditions. All observations, including the coexistence of states, are qualitatively reproduced by describing inhomogeneities with local variations of one model parameter. We show that the results of the microscopic model can be understood by formulating the theoretical phase diagram for bottlenecks in a more general way. In particular, a local drop of the road capacity induced by parameter variations has practically the same effect as an on-ramp.Comment: Now published in Phys. Rev. E. Minor changes suggested by a referee are incorporated; full bibliographic info added. For related work see http://www.mtreiber.de/ and http://www.helbing.org

Active Brownian Motion Models and Applications to Ratchets

We give an overview over recent studies on the model of Active Brownian Motion (ABM) coupled to reservoirs providing free energy which may be converted into kinetic energy of motion. First, we present an introduction to a general concept of active Brownian particles which are capable to take up energy from the source and transform part of it in order to perform various activities. In the second part of our presentation we consider applications of ABM to ratchet systems with different forms of differentiable potentials. Both analytical and numerical evaluations are discussed for three cases of sinusoidal, staircase-like and Mateos ratchet potentials, also with the additional loads modeled by tilted potential structure. In addition, stochastic character of the kinetics is investigated by considering perturbation by Gaussian white noise which is shown to be responsible for driving the directionality of the asymptotic flux in the ratchet. This \textit{stochastically driven directionality} effect is visualized as a strong nonmonotonic dependence of the statistics of the right versus left trajectories of motion leading to a net current of particles. Possible applications of the ratchet systems to molecular motors are also briefly discussedComment: 12 pages, 17 figure

Modeling Vortex Swarming In Daphnia

Based on experimental observations in \textit{Daphnia}, we introduce an agent-based model for the motion of single and swarms of animals. Each agent is described by a stochastic equation that also considers the conditions for active biological motion. An environmental potential further reflects local conditions for \textit{Daphnia}, such as attraction to light sources. This model is sufficient to describe the observed cycling behavior of single \textit{Daphnia}. To simulate vortex swarming of many \textit{Daphnia}, i.e. the collective rotation of the swarm in one direction, we extend the model by considering avoidance of collisions. Two different ansatzes to model such a behavior are developed and compared. By means of computer simulations of a multi-agent system we show that local avoidance - as a special form of asymmetric repulsion between animals - leads to the emergence of a vortex swarm. The transition from uncorrelated rotation of single agents to the vortex swarming as a function of the swarm size is investigated. Eventually, some evidence of avoidance behavior in \textit{Daphnia} is provided by comparing experimental and simulation results for two animals.Comment: 24 pages including 11 multi-part figs. Major revisions compared to version 1, new results on transition from uncorrelated rotation to vortex swarming. Extended discussion. For related publications see http://www.sg.ethz.ch/people/scfrank/Publication