It is suggested that the motion of pedestrians can be described as if they would be subject to 'social forces'. These 'forces' are not directly exerted by the pedestrians' personal environment, but they are a measure for the internal motivations of the individuals to perform certain actions (movements). The corresponding force concept is discussed in more detail and can be also applied to the description of other behaviors.

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46 1. Gas-kinetic and macroscopic models 46 2. Microscopic models and cellular automata 47 E. Bi-directional and city traffic 47 F. Effects beyond physics 48 G. Traffic control and optimization 48 V. Pedestrian traffic 49 A. Observations 49 B. Behavioral force model of pedestrian dynamics 50 C. Self-organization phenomena and noise-induced ordering 51 1. Segregation 51 2. Oscillations 52 3. Rotation 52 D. Collective phenomena in panic situations 53 1. "Freezing by heating" 53 2. "Faster-is-slower effect" 53 3. "Phantom panics" 54 4. Herding behavior 54 VI. Flocking and spin systems 54 A.

Humanity has just crossed a major landmark in its history with the majority of people now living in cities. Cities have long been known to be society's predominant engine of innovation and wealth creation, yet they are also its main source of crime, pollution, and disease. The inexorable trend toward urbanization worldwide presents an urgent challenge for developing a predictive, quantitative theory of urban organization and sustainable development. Here we present empirical evidence indicating that the processes relating urbanization to economic development and knowledge creation are very general, being shared by all cities belonging to the same urban system and sustained across different nations and times. Many diverse properties of cities from patent production and personal income to electrical cable length are shown to be power law functions of population size with scaling exponents, ␤, that fall into distinct universality classes. Quantities reflecting wealth creation and innovation have ␤ Ϸ1.2 >1 (increasing returns), whereas those accounting for infrastructure display ␤ Ϸ0.8 <1 (economies of scale). We predict that the pace of social life in the city increases with population size, in quantitative agreement with data, and we discuss how cities are similar to, and differ from, biological organisms, for which ␤<1. Finally, we explore possible consequences of these scaling relations by deriving growth equations, which quantify the dramatic difference between growth fueled by innovation versus that driven by economies of scale. This difference suggests that, as population grows, major innovation cycles must be generated at a continually accelerating rate to sustain growth and avoid stagnation or collapse. population ͉ sustainability ͉ urban studies ͉ increasing returns ͉ economics of scale H umanity has just crossed a major landmark in its history with the majority of people now living in cities (1, 2). The present worldwide trend toward urbanization is intimately related to economic development and to profound changes in social organization, land use, and patterns of human behavior (1, 2). The demographic scale of these changes is unprecedented (2, 3) and will lead to important but as of yet poorly understood impacts on the global environment. In 2000, Ͼ70% of the population in developed countries lived in cities compared with Ϸ40% in developing countries. Cities occupied a mere 0.3% of the total land area but Ϸ3% of arable land. By 2030, the urban population of developing countries is expected to more than double to Ϸ4 billion, with an estimated 3-fold increase in occupancy of land area (3), whereas in developed countries it may still increase by as much as 20%. Paralleling this global urban expansion, there is the necessity for a sustainability transition (4-6) toward a stable total human population, together with a rise in living standards and the establishment of long-term balances between human development needs and the planet's environmental limits (7). Thus, a major challenge worldwide (5, 6) is to un...

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. 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.

The global spread of epidemics, rumors, opinions, and innovations are complex, network-driven dynamic processes. The combined multiscale nature and intrinsic heterogeneity of the underlying networks make it difficult to develop an intuitive understanding of these processes, to distinguish relevant from peripheral factors, to predict their time course, and to locate their origin. However, we show that complex spatiotemporal patterns can be reduced to surprisingly simple, homogeneous wave propagation patterns, if conventional geographic distance is replaced by a probabilistically motivated effective distance. In the context of global, air-traffic-mediated epidemics, we show that effective distance reliably predicts disease arrival times. Even if epidemiological parameters are unknown, the method can still deliver relative arrival times. The approach can also identify the spatial origin of spreading processes and successfully be applied to data of the worldwide 2009 H1N1 influenza pandemic and 2003 SARS epidemic.

Social groups can be remarkably smart and knowledgeable when their averaged judgements are compared with the judgements of individuals. Already Galton [Galton F (1907) Nature 75:7] found evidence that the median estimate of a group can be more accurate than estimates of experts. This wisdom of crowd effect was recently supported by examples from stock markets, political elections, and quiz shows [Surowiecki J (2004) The Wisdom of Crowds]. In contrast, we demonstrate by experimental evidence (N = 144) that even mild social influence can undermine the wisdom of crowd effect in simple estimation tasks. In the experiment, subjects could reconsider their response to factual questions after having received average or full information of the responses of other subjects. We compare subjects' convergence of estimates and improvements in accuracy over five consecutive estimation periods with a control condition, in which no information about others' responses was provided. Although groups are initially "wise," knowledge about estimates of others narrows the diversity of opinions to such an extent that it undermines the wisdom of crowd effect in three different ways. The "social influence effect" diminishes the diversity of the crowd without improvements of its collective error. The "range reduction effect" moves the position of the truth to peripheral regions of the range of estimates so that the crowd becomes less reliable in providing expertise for external observers. The "confidence effect" boosts individuals' confidence after convergence of their estimates despite lack of improved accuracy. Examples of the revealed mechanism range from misled elites to the recent global financial crisis.collective judgment | estimate aggregation | experimental social science | swarm intelligence | overconfidence

T o test simulation models of pedestrian flows, we have performed experiments for corridors, bottleneck areas, and intersections. Our evaluations of video recordings show that the geometric boundary conditions are not only relevant for the capacity of the elements of pedestrian facilities, they also influence the time gap distribution of pedestrians, indicating the existence of self-organization phenomena. After calibration of suitable models, these findings can be used to improve design elements of pedestrian facilities and egress routes. It turns out that "obstacles" can stabilize flow patterns and make them more fluid. Moreover, intersecting flows can be optimized, utilizing the phenomenon of "stripe formation." We also suggest increasing diameters of egress routes in stadia, theaters, and lecture halls to avoid long waiting times for people in the back, and shock waves due to impatience in cases of emergency evacuation. Moreover, zigzag-shaped geometries and columns can reduce the pressure in panicking crowds. The proposed design solutions are expected to increase the efficiency and safety of train stations, airport terminals, stadia, theaters, public buildings, and mass events in the future. As application examples we mention the evacuation of passenger ships and the simulation of pilgrim streams on the Jamarat bridge. Adaptive escape guidance systems, optimal way systems, and simulations of urban pedestrian flows are addressed as well.