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

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

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

Identification of novel risk loci for restless legs syndrome in genome-wide association studies in individuals of European ancestry : a meta-analysis

Background Restless legs syndrome is a prevalent chronic neurological disorder with potentially severe mental and physical health consequences. Clearer understanding of the underlying pathophysiology is needed to improve treatment options. We did a meta-analysis of genome-wide association studies (GWASs) to identify potential molecular targets. Methods In the discovery stage, we combined three GWAS datasets (EU-RLS GENE, INTERVAL, and 23andMe) with diagnosis data collected from 2003 to 2017, in face-to-face interviews or via questionnaires, and involving 15126 cases and 95 725 controls of European ancestry. We identified common variants by fixed-effect inverse-variance meta-analysis. Significant genome-wide signals (p Findings We identified and replicated 13 new risk loci for restless legs syndrome and confirmed the previously identified six risk loci. MEIS1 was confirmed as the strongest genetic risk factor for restless legs syndrome (odds ratio 1.92, 95% CI 1 85-1.99). Gene prioritisation, enrichment, and genetic correlation analyses showed that identified pathways were related to neurodevelopment and highlighted genes linked to axon guidance (associated with SEMA6D), synapse formation (NTNG1), and neuronal specification (HOXB cluster family and MYT1). Interpretation Identification of new candidate genes and associated pathways will inform future functional research. Advances in understanding of the molecular mechanisms that underlie restless legs syndrome could lead to new treatment options. We focused on common variants; thus, additional studies are needed to dissect the roles of rare and structural variations.Peer reviewe