Since the subject of traffic dynamics has captured the interest of physicists, many surprising effects have been revealed and explained. Some of the questions now understood are the following: Why are vehicles sometimes stopped by ``phantom traffic jams'' even though drivers all like to drive fast? What are the mechanisms behind stop-and-go traffic? Why are there several different kinds of congestion, and how are they related? Why do most traffic jams occur considerably before the road capacity is reached? Can a temporary reduction in the volume of traffic cause a lasting traffic jam? Under which conditions can speed limits speed up traffic? Why do pedestrians moving in opposite directions normally organize into lanes, while similar systems ``freeze by heating''? All of these questions have been answered by applying and extending methods from statistical physics and nonlinear dynamics to self-driven many-particle systems. This article considers the empirical data and then reviews the main approaches to modeling pedestrian and vehicle traffic. These include microscopic (particle-based), mesoscopic (gas-kinetic), and macroscopic (fluid-dynamic) models. Attention is also paid to the formulation of a micro-macro link, to aspects of universality, and to other unifying concepts, such as a general modeling framework for self-driven many-particle systems, including spin systems. While the primary focus is upon vehicle and pedestrian traffic, applications to biological or socio-economic systems such as bacterial colonies, flocks of birds, panics, and stock market dynamics are touched upon as well.

Traffic and related self-driven many-particle systems

We review the observations and the basic laws describing the essential aspects of collective motion -- being one of the most common and spectacular manifestation of coordinated behavior Our aim is to provide a balanced discussion of the various facets of this highly multidisciplinary field, including experiments, mathematical methods and models for simulations, so that readers with a variety of background could get both the basics and a broader, more detailed picture of the field The observations we report on include systems consisting of units ranging from macromolecules through metallic rods and robots to groups of animals and people Some emphasis is put on models that are simple and realistic enough to reproduce the numerous related observations and are useful for developing concepts for a better understanding of the complexity of systems consisting of many simultaneously moving entities As such, these models allow the establishing of a few fundamental principles of flocking In particular, it is demonstrated, that in spite of considerable differences, a number of deep analogies exist between equilibrium statistical physics systems and those made of self-propelled (in most cases living) units In both cases only a few well defined macroscopic/collective states occur and the transitions between these states follow a similar scenario, involving discontinuity and algebraic divergences

Collective Motion

It has been a decade since multicellularity was proposed as a general bacterial trait. Intercellular communication and multicellular coordination are now known to be widespread among prokaryotes and to affect multiple phenotypes. Many different classes of signaling molecules have been identified in both Gram-positive and Gram-negative species. Bacteria have sophisticated signal transduction networks for integrating intercellular signals with other information to make decisions about gene expression and cellular differentiation. Coordinated multicellular behavior can be observed in a variety of situations, including development of E. coli and B. subtilis colonies, swarming by Proteus and Serratia, and spatially organized interspecific metabolic cooperation in anaerobic bioreactor granules. Bacteria benefit from multicellular cooperation by using cellular division of labor, accessing resources that cannot effectively be utilized by single cells, collectively defending against antagonists, and optimizing population survival by differentiating into distinct cell types.

Thinking about bacterial populations as multicellular organisms

Microscopic view of epitaxial metal growth: nucleation and aggregation

Publisher Summary The chapter discusses an emerging area of study: that of applying self-organization theory to mobile vertebrate groups composed of many interacting individuals such as bird flocks, ungulate herds, fish schools, and human crowds in an attempt to improve our understanding of underlying organizational principles. Mathematical modeling is becoming increasingly recognized as an important research tool when studying collective behavior. The chapter presents the interaction dynamics among individuals result in the formation, internal structuring, and collective behaviors of vertebrate groups. The chapter explores the distribution of grouping individuals over larger spatial and temporal scales, and discusses how individual behaviors lead to population-level dynamics. Behavioral differences among individuals within a group may have an important internal structuring influence. By using simulation models, it can be shown how individuals can modify their positions relative to other group members without necessitating information about their current position within the group. In considering self-organization within vertebrate groups it is evident that the organization at one level, for example, that of the group relates to that at higher levels. For example, self-sorting processes that lead to internal structuring within groups also result in population-level patterns when such groups fragment, thus affecting the probability that an individual will be in a group of a given size and composition at any moment in time. These population properties then feed back to the individual interactions by changing the probability of encounters among different members of a population. The chapter concludes that to understand collective behaviors fully, these properties cannot necessarily be considered in isolation.

Self-Organization and Collective Behavior in Vertebrates

Bacterial colonies must often cope with unfavourable environmental conditions. To do so, they have developed sophisticated modes of cooperative behaviour. It has been found that such behaviour can cause bacterial colonies to exhibit complex growth patterns similar to those observed during non-equilibrium growth processes in non-living systems; some of the qualitative features of the latter may be invoked to account for the complex patterns of bacterial growth. Here we show that a simple model of bacterial growth can reproduce the salient features of the observed growth patterns. The model incorporates random walkers, representing aggregates of bacteria, which move in response to gradients in nutrient concentration and communicate with each other by means of chemotactic 'feedback'. These simple features allow the colony to respond efficiently to adverse growth conditions, and generate self-organization over a wide range of length scales.

Ofer Schochet

Papers

Generic modelling of cooperative growth patterns in bacterial colonies