Simulating dynamical features of escape panic

Limits of predictability in human mobility

A range of applications, from predicting the spread of human and electronic viruses to city planning and resource management in mobile communications, depend on our ability to foresee the whereabouts and mobility of individuals, raising a fundamental question: To what degree is human behavior predictable? Here we explore the limits of predictability in human dynamics by studying the mobility patterns of anonymized mobile phone users. By measuring the entropy of each individual's trajectory, we find a 93% potential predictability in user mobility across the whole user base. Despite the significant differences in the travel patterns, we find a remarkable lack of variability in predictability, which is largely independent of the distance users cover on a regular basis.

Epidemiological characteristics of human stampedes

OBJECTIVE

The potential for deadly human stampedes to occur at any mass gathering event highlights this unique form of crowd disaster as deserving of special attention from both scientific and planning perspectives. Improved understanding of human stampedes is indispensable in the mitigation of this type of mass casualty. With relatively few peer-reviewed reports on deadly human stampedes, information from news reports and the Internet is essential to increased collective understanding. Without incorporating nontraditional sources, no other way to reasonably acquire sufficient data is available. This study analyzed human stampede events from 1980 to 2007 to identify epidemiological characteristics associated with increased mortality.

METHODS

A LexisNexis search was followed by sequential searches of multiple Internet-based English-language news agencies. Date, country, geographical region, time of occurrence, type of event, location, mechanism, number of participants, number injured, and number of deaths were recorded. Bivariate analyses of number of deaths or injuries were conducted using a nonparametric Wilcoxon rank test. Multivariate regression was performed to determine the factors associated with increased number of fatalities during stampede events.

RESULTS

A total of 215 human stampede events were reported from 1980 to 2007, resulting in 7069 deaths and at least 14,078 injuries from 213 events with available fatality information and 179 events with injury information. In bivariate analysis, stampedes occurring in the Middle East, in developing countries, outdoors, or associated with religious events had the highest median number of deaths. In multivariate analysis, events that occurred in developing countries and outdoors were associated with increased number of fatalities. Stampedes that occurred in the context of sports, religious, music, and political events, or that had a unidirectional mechanism, also increased the relative number of deaths.

CONCLUSIONS

Several epidemiological features of human stampedes associated with increased mortality are identified. Standardized collection of epidemiological data pertaining to human stampedes is strongly recommended, and further study of this recurrent, distinctive disaster is warranted.

Introduction of frictional and turning function for pedestrian outflow with an obstacle

In this paper, two important factors which affect the pedestrian outflow at a bottleneck significantly are studied in detail to analyze the effect of an obstacle setup in front of an exit. One is a conflict at an exit when pedestrians evacuate from a room. We use floor field model for simulating such behavior, which is a well-studied pedestrian model using cellular automata. The conflicts have been taken into account by the friction parameter. However, the friction parameter so far is a constant and does not depend on the number of the pedestrians conflicting at the same time. Thus, we have improved the friction parameter by the frictional function, which is a function of the number of the pedestrians involved in the conflict. Second, we have presented the cost of turning of pedestrians at the exit. Since pedestrians have inertia, their walking speeds decrease when they turn and the pedestrian outflow decreases. The validity of the extended model, which includes the frictional function and the turning function, is supported by the comparison of a mean-field theory and real experiments. We have observed that the pedestrian flow increases when we put an obstacle in front of an exit in our real experiments. The analytical results clearly explains the mechanism of the effect of the obstacle, i.e., the obstacle blocks pedestrians moving to the exit and decreases the average number of pedestrians involved in the conflict. We have also found that an obstacle works more effectively when we shift it from the center since pedestrians go through the exit with less turning.

A particle dynamic model of red blood cell aggregation kinetics

To elucidate the relationship between microscopic red blood cell (RBC) interactions and macroscopic rheological behavior, we propose a two-dimensional particle model capable of mimicking the main characteristics of RBC aggregation kinetics. The mechanical model of RBCs sheared in Couette flow is based on Newton law. We assumed a hydrodynamic force to move particles, a force to describe aggregation and an elasticity force. The role of molecular mass and concentration of neutral polymers on aggregation [Neu, B., and H. J. Meiselman. Biophys. J. 83:2482-2490, 2002] could be mimicked. Specifically, it was shown that for any shear rate (SR), the mean aggregate size (MAS) grew with time until it reached a constant value, which is consistent with in vitro experiments. It was also demonstrated that we could mimic the modal relationship between MAS and SR and the occurrence of maximum aggregation at about 0.1 s(-1). As anticipated, simulations indicated that an increase in aggregation force augmented MAS. Further, augmentation of the depletion layer thickness influenced MAS only for SR close to zero, which is a new finding. To conclude, our contribution reveals that the aggregation force intensity and SR influence the steady state MAS, and that the depletion and layer thickness affect the aggregation speed.

Experimental study of the behavioural mechanisms underlying self-organization in human crowds

In animal societies as well as in human crowds, many observed collective behaviours result from self-organized processes based on local interactions among individuals. However, models of crowd dynamics are still lacking a systematic individual-level experimental verification, and the local mechanisms underlying the formation of collective patterns are not yet known in detail. We have conducted a set of well-controlled experiments with pedestrians performing simple avoidance tasks in order to determine the laws ruling their behaviour during interactions. The analysis of the large trajectory dataset was used to compute a behavioural map that describes the average change of the direction and speed of a pedestrian for various interaction distances and angles. The experimental results reveal features of the decision process when pedestrians choose the side on which they evade, and show a side preference that is amplified by mutual interactions. The predictions of a binary interaction model based on the above findings were then compared with bidirectional flows of people recorded in a crowded street. Simulations generate two asymmetric lanes with opposite directions of motion, in quantitative agreement with our empirical observations. The knowledge of pedestrian behavioural laws is an important step ahead in the understanding of the underlying dynamics of crowd behaviour and allows for reliable predictions of collective pedestrian movements under natural conditions.

Constant-net-time headway as a key mechanism behind pedestrian flow dynamics

We show that keeping a constant lower limit on the net-time headway is the key mechanism behind the dynamics of pedestrian streams. There is a large variety in flow and speed as functions of density for empirical data of pedestrian streams obtained from studies in different countries. The net-time headway, however, stays approximately constant over all these different data sets. By using this fact, we demonstrate how the underlying dynamics of pedestrian crowds, naturally follows from local interactions. This means that there is no need to come up with an arbitrary fit function (with arbitrary fit parameters) as has traditionally been done. Further, by using not only the average density values but the variance as well, we show how the recently reported stop-and-go waves [Helbing, Phys. Rev. E 75, 046109 (2007)] emerge when local density variations take values exceeding a certain maximum global (average) density, which makes pedestrians stop.

Dynamic continuum pedestrian flow model with memory effect

In this paper, we develop a macroscopic model for pedestrian flow using the dynamic continuum modeling approach. We consider a two-dimensional walking facility that is represented as a continuum within which pedestrians can move freely in any direction. A pedestrian chooses a route based on his or her memory of the shortest path to the desired destination when the facility is empty and, at the same time, tries to avoid high densities. In this model, pedestrian flow is governed by a two-dimensional conservation law, and a general speed-flow-density relationship is considered. The model equation is solved numerically using the discontinuous Galerkin method, and a numerical example is employed to demonstrate both the model and the effectiveness of the numerical method.

Group decisions in humans and animals: a survey

Humans routinely make many decisions collectively, whether they choose a restaurant with friends, elect political leaders or decide actions to tackle international problems, such as climate change, that affect the future of the whole planet. We might be less aware of it, but group decisions are just as important to social animals as they are for us. Animal groups have to collectively decide about communal movements, activities, nesting sites and enterprises, such as cooperative breeding or hunting, that crucially affect their survival and reproduction. While human group decisions have been studied for millennia, the study of animal group decisions is relatively young, but is now expanding rapidly. It emerges that group decisions in animals pose many similar questions to those in humans. The purpose of the present issue is to integrate and combine approaches in the social and natural sciences in an area in which theoretical challenges and research questions are often similar, and to introduce each discipline to the other's key ideas, findings and successful methods. In order to make such an introduction as effective as possible, here, we briefly review conceptual similarities and differences between the sciences, and provide a guide to the present issue.

Getting to Know Your Neighbors: Unsupervised Learning of Topography from Real-World, Event-Based Input

Biological neural systems must grow their own connections and maintain topological relations between elements that are related to the sensory input surface. Artificial systems have traditionally prewired such maps, but the sensor arrangement is not always known and can be expensive to specify before run time. Here we present a method for learning and updating topographic maps in systems comprising modular, event-based elements. Using an unsupervised neural spike-timing-based learning rule combined with Hebbian learning, our algorithm uses the spatiotemporal coherence of the external world to train its network. It improves on existing algorithms by not assuming a known topography of the target map and includes a novel method for automatically detecting edge elements. We show how, for stimuli that are small relative to the sensor resolution, the temporal learning window parameters can be determined without using any user-specified constants. For stimuli that are larger relative to the sensor resolution, we provide a parameter extraction method that generally outperforms the small-stimulus method but requires one user-specified constant. The algorithm was tested on real data from a 64 × 64-pixel section of an event-based temporal contrast silicon retina and a 360-tile tactile luminous floor. It learned 95.8% of the correct neighborhood relations for the silicon retina within about 400 seconds of real-world input from a driving scene and 98.1% correct for the sensory floor after about 160 minutes of human pedestrian traffic. Residual errors occurred in regions receiving little or ambiguous input, and the learned topological representations were able to update automatically in response to simulated damage. Our algorithm has applications in the design of modular autonomous systems in which the interfaces between components are learned during operation rather than at design time.

Predictive protocol of flocks with small-world connection pattern

By introducing a predictive mechanism with small-world connections, we propose a new motion protocol for self-driven flocks. The small-world connections are implemented by randomly adding long-range interactions from the leader to a few distant agents, namely, pseudoleaders. The leader can directly affect the pseudoleaders, thereby influencing all the other agents through them efficiently. Moreover, these pseudoleaders are able to predict the leader's motion several steps ahead and use this information in decision making towards coherent flocking with more stable formation. It is shown that drastic improvement can be achieved in terms of both the consensus performance and the communication cost. From the engineering point of view, the current protocol allows for a significant improvement in the cohesion and rigidity of the formation at a fairly low cost of adding a few long-range links embedded with predictive capabilities. Significantly, this work uncovers an important feature of flocks that predictive capability and long-range links can compensate for the insufficiency of each other. These conclusions are valid for both the attractive and repulsive swarm model and the Vicsek model.

FRACTAL, A MICROSCOPIC CROWD MODEL

The core of this research is related to the human crowd problem. Some major problems are congestion, emergency evacuation, and fatal catastrophe. In fact, it has been realized that many crowd related problems can be resolved by influencing (controlling) human flow with providing various control measures. Thus, the problem itself becomes the motivation for this research and the solution is approached through model and simulation within the virtual environment.

The relationship between fractal pattern and crowd behavior is produced with respect to the crowd behavior model. It exposes a comparison between the crowd paths resulting from the model developed and the fractal formation created to imitate the crowd paths. A new approach for crowd behavior modeling is proposed based on fractal features and, thus, gives new understanding about a relationship between fractal pattern and crowd behavior. Several innovations of fractal patterns that can be used in crowd behavior model applications adds to the novelty of the research contribution. Ultimately, the new method of modeling the crowd can be obtained and at the same time the new direction of crowd modeling research can be directed.

Analysis of pedestrian dynamics in counter flow via an extended lattice gas model

The modeling of human behavior is an important approach to reproduce realistic phenomena for pedestrian flow. In this paper, an extended lattice gas model is proposed to simulate pedestrian counter flow under the open boundary conditions by considering the human subconscious behavior and different maximum velocities. The simulation results show that the presented model can capture some essential features of pedestrian counter flows, such as lane formation, segregation effect, and phase separation at higher densities. In particular, an interesting feature that the faster walkers overtake the slower ones and then form a narrow-sparse walkway near the central partition line is discovered. The phase diagram comparison and analysis show that the subconscious behavior plays a key role in reducing the occurrence of jam cluster. The effects of the symmetrical and asymmetrical injection rate, different partition lines, and different combinations of maximum velocities on pedestrian flow are investigated. An important conclusion is that it is needless to separate faster and slower pedestrians in the same direction by a partition line. Furthermore, the increase of the number of faster walkers does not always benefit the counter flow in all situations. It depends on the magnitude and asymmetry of injection rate. And at larger maximum velocity, the obtained critical transition point corresponding to the maximum flow rate of the fundamental diagram is in good agreement with the empirical results.

Collective behavior in animal groups: theoretical models and empirical studies

Collective phenomena in animal groups have attracted much attention in the last years, becoming one of the hottest topics in ethology. There are various reasons for this. On the one hand, animal grouping provides a paradigmatic example of self-organization, where collective behavior emerges in absence of centralized control. The mechanism of group formation, where local rules for the individuals lead to a coherent global state, is very general and transcends the detailed nature of its components. In this respect, collective animal behavior is a subject of great interdisciplinary interest. On the other hand, there are several important issues related to the biological function of grouping and its evolutionary success. Research in this field boasts a number of theoretical models, but much less empirical results to compare with. For this reason, even if the general mechanisms through which self-organization is achieved are qualitatively well understood, a quantitative test of the models assumptions is still lacking. New analysis on large groups, which require sophisticated technological procedures, can provide the necessary empirical data.

Static floor field and exit choice for pedestrian evacuation in rooms with internal obstacles and multiple exits

A modified floor field model is proposed to simulate pedestrian evacuation in rooms with internal obstacles and multiple exits. The modifications lie in developing a method to calculate the static floor field for every lattice site, which is determined by the most feasible distance to an exit, and employing a logit-based discrete choice principle to govern the exit selection. Simulation results show that the evacuation time is sensitive to the exit position and some model parameters. For pedestrians unfamiliar with the exit location, additional doors may not be necessary and can cause a negative effect on evacuation time. It is also found that unfamiliarity with the room's inner configuration and blindly following others will lead to an increase of the evacuation time.

Decelerating microdynamics can accelerate macrodynamics in the voter model

For the voter model, we study the effect of a memory-dependent transition rate. We assume that the transition of a spin into the opposite state decreases with the time it has been in its current state. Counterintuitively, we find that the time to reach a macroscopically ordered state can be accelerated by slowing down the microscopic dynamics in this way. This holds for different network topologies, including fully connected ones. We find that the ordering dynamics is governed by two competing processes which either stabilize the majority or the minority state. If the first one dominates, it accelerates the ordering of the system. The conclusions of this Letter are not restricted to the voter model, but remain valid to many other spin systems as well.

Irreversible aggregation of flexible chainlike walkers without adherence

The flexible chainlike walker (FCW) model is proposed as a minimal model of a deformable moving object and as an extension of the regular random-walk model. The many-body system of FCWs is studied by numerical simulations on a square lattice. It is shown that FCWs aggregate spontaneously and irreversibly where no adherence is assumed, in contrast to the established aggregation models, where adherence is indispensable for their occurrence and irreversibility. This type of aggregation is enabled by and demonstrates the significance of the deformability of moving objects.

Information transfer in moving animal groups

Moving animal groups provide some of the most intriguing and difficult to characterise examples of collective behaviour. We review some recent (and not so recent) empirical research on the motion of animal groups, including fish, locusts and homing pigeons. An important concept which unifies our understanding of these groups is that of transfer of directional information. Individuals which change their direction of travel in response to the direction taken by their near neighbours can quickly transfer information about the presence of a predatory threat or food source. We show that such information transfer is optimised when the density of individuals in a group is close to that at which a phase transition occurs between random and ordered motion. Similarly, we show that even relatively small differences in information possessed by group members can lead to strong collective-level decisions for one of two options. By combining the use of self-propelled particle and social force models of collective motion with thinking about the evolution of flocking we aim to better understand how complexity arises within these groups.

Social learning of novel route preferences in adult humans

Non-human animals can acquire novel route preferences by following knowledgeable individuals. Such socially learned route preferences can be stably maintained over multiple transmission episodes, sometimes forming long-lived traditions. In humans, preferences for familiar routes or heavily used worn trails over unfamiliar ones have been described in various contexts. However, social learning of route preferences has not been experimentally demonstrated in humans. Here, we demonstrate that social learning and tradition influence route choice. We led adult male and female participants into a room by one of two routes. Participants followed the demonstrated route choices, and later remembered and preferred this choice even when determinably suboptimal (i.e. longer and not preferred by control participants) or when the choice was indicated as arbitrary (the demonstrator took one route to retrieve a poster that had ostensibly fallen). Moreover, route preferences were stably maintained over multiple transmission episodes. We suggest that simple social learning processes, often neglected in human and primate research, can result in long-lived route preferences that may influence a range of additional behaviour patterns.

Singularities and symmetry breaking in swarms

A large-scale system consisting of self-propelled particles, moving under the directional alignment rule (DAR), can often self-organize to an ordered state that emerges from an initially rotationally symmetric configuration. It is commonly accepted that the DAR, which leads to effective long-range interactions, is the underlying mechanism contributing to the collective motion. However, in this paper, we demonstrate that a swarm under the DAR has unperceived and inherent singularities. Furthermore, we show that the compelled symmetry-breaking effects at or near the singularities, as well as the topological connectivity of the swarm in the evolution process, contribute fundamentally to the emergence of the collective behavior; and the elimination or weakening of singularities in the DAR will induce an unexpected sharp transition from coherent movement to isotropic dispersion. These results provide some insights into the fundamental issue of collective dynamics: What is the underlying mechanism causing the spontaneous symmetry breaking and leading to eventual coherent motion?

Interaction ruling animal collective behavior depends on topological rather than metric distance: evidence from a field study

Numerical models indicate that collective animal behavior may emerge from simple local rules of interaction among the individuals. However, very little is known about the nature of such interaction, so that models and theories mostly rely on aprioristic assumptions. By reconstructing the three-dimensional positions of individual birds in airborne flocks of a few thousand members, we show that the interaction does not depend on the metric distance, as most current models and theories assume, but rather on the topological distance. In fact, we discovered that each bird interacts on average with a fixed number of neighbors (six to seven), rather than with all neighbors within a fixed metric distance. We argue that a topological interaction is indispensable to maintain a flock's cohesion against the large density changes caused by external perturbations, typically predation. We support this hypothesis by numerical simulations, showing that a topological interaction grants significantly higher cohesion of the aggregation compared with a standard metric one.

Self-organization in high-density bacterial colonies: efficient crowd control

Colonies of bacterial cells can display complex collective dynamics, frequently culminating in the formation of biofilms and other ordered super-structures. Recent studies suggest that to cope with local environmental challenges, bacterial cells can actively seek out small chambers or cavities and assemble there, engaging in quorum sensing behavior. By using a novel microfluidic device, we showed that within chambers of distinct shapes and sizes allowing continuous cell escape, bacterial colonies can gradually self-organize. The directions of orientation of cells, their growth, and collective motion are mutually correlated and dictated by the chamber walls and locations of chamber exits. The ultimate highly organized steady state is conducive to a more-organized escape of cells from the chambers and increased access of nutrients into and evacuation of waste out of the colonies. Using a computational model, we suggest that the lengths of the cells might be optimized to maximize self-organization while minimizing the potential for stampede-like exit blockage. The self-organization described here may be crucial for the early stage of the organization of high-density bacterial colonies populating small, physically confined growth niches. It suggests that this phenomenon can play a critical role in bacterial biofilm initiation and development of other complex multicellular bacterial super-structures, including those implicated in infectious diseases.

Getting to grips with the plant metabolic network

Research into plant metabolism has a long history, and analytical approaches of ever-increasing breadth and sophistication have been brought to bear. We now have access to vast repositories of data concerning enzymology and regulatory features of enzymes, as well as large-scale datasets containing profiling information of transcripts, protein and metabolite levels. Nevertheless, despite this wealth of data, we remain some way off from being able to rationally engineer plant metabolism or even to predict metabolic responses. Within the past 18 months, rapid progress has been made, with several highly informative plant network interrogations being discussed in the literature. In the present review we will appraise the current state of the art regarding plant metabolic network analysis and attempt to outline what the necessary steps are in order to further our understanding of network regulation.

Mean-field theory for pedestrian outflow through an exit

The average pedestrian flow through an exit is one of the most important indices in evaluating pedestrian dynamics. In order to study the flow in detail, the floor field model, which is a crowd model using cellular automata, is extended by taking into account realistic behavior of pedestrians around the exit. The model is studied by both numerical simulations and cluster analysis to obtain a theoretical expression for the average pedestrian flow through the exit. It is found quantitatively that the effects of exit door width, the wall, and the pedestrian mood of competition or cooperation significantly influence the average flow. The results show that there is a suitable width and position of the exit according to the pedestrians' mood.

Modeling crowd turbulence by many-particle simulations

A recent study [D. Helbing, A. Johansson, and H. Z. Al-Abideen, Phys. Rev. E 75, 046109 (2007)] has revealed a "turbulent" state of pedestrian flows, which is characterized by sudden displacements and causes the falling and trampling of people. However, turbulent crowd motion is not reproduced well by current many-particle models due to their insufficient representation of the local interactions in areas of extreme densities. In this contribution, we extend the repulsive force term of the social force model to reproduce crowd turbulence. We perform numerical simulations of pedestrians moving through a bottleneck area with this model. The transitions from laminar to stop-and-go and turbulent flows are observed. The empirical features characterizing crowd turbulence, such as the structure function and the probability density function of velocity increments, are reproduced well; i.e., they are well compatible with an analysis of video data during the annual Muslim pilgrimage.

Effects of inhomogeneous influence of individuals on an order-disorder transition in opinion dynamics

We study the effects of inhomogeneous influence of individuals on collective phenomena. We focus analytically on a typical model of the majority rule, applied to the completely connected agents. Two types of individuals A and B with different influence activity are introduced. The individuals A and B are distributed randomly with concentrations nu and 1-nu at the beginning and fixed further on. Our main result is that the location of the order-disorder transition is affected due to the introduction of the inhomogeneous influence. This result highlights the importance of inhomogeneous influence between different types of individuals during the process of opinion updating.

Scaling and universality in proportional elections

A most debated topic of the last years is whether simple statistical physics models can explain collective features of social dynamics. A necessary step in this line of endeavor is to find regularities in data referring to large-scale social phenomena, such as scaling and universality. We show that, in proportional elections, the distribution of the number of votes received by candidates is a universal scaling function, identical in different countries and years. This finding reveals the existence in the voting process of a general microscopic dynamics that does not depend on the historical, political, and/or economical context where voters operate. A simple dynamical model for the behavior of voters, similar to a branching process, reproduces the universal distribution.

Effect of traffic rule breaking behavior on pedestrian counterflow in a channel with a partition line

In this paper a partition line is used in the counterflow system to present the default (conventional) traffic rule: pedestrians prefer to walk on a certain side on the road during movement, e.g., the right-hand side in China or the left-hand side in Japan. Based on the counterflow model of Takimoto (model A), we introduced two modified models, i.e., model B and C, to study the effects of a partition line in the consideration of people who do not obey the default traffic rule. Model B represents that factor in time scale, while model C in space scale. In model B, there are pedestrians who cross the partition line but choose not to obey the default traffic rule with a probability p(nor), while in model C, if a pedestrian crosses the partition line and goes away from it further than a certain nonobeying-rule threshold distance d(t), he will not obey the traffic rule. It is found that the behavior of traffic rule breaking influences much the counterflow when it is at the choking flow state rather than at the free moving or stopped state. Furthermore, it is shown that the default traffic rule is not always positive to the counterflow in all situations. It depends on the game result of these two opposite sides: to use the channel width as much as possible and to avoid the interference from the other group as far as possible.

The hard cell: From proteomics to a whole cell model

Proteomics has provided a wealth of data related to the nature of the proteome, including subcellular location, copy number, interaction partners and protein complexes. This raises the question of whether it is feasible to combine these data, together with other data related to overall cellular structure, to construct a static picture of the cell. In this minireview, we discuss these data, and the issues of turning them into whole cell models.

Cellular automaton simulation of pedestrian counter flow considering the surrounding environment

This paper presents a cellular automaton model without step back to simulate the pedestrian counter flow in a channel. The consideration of the surrounding environment when people make judgments on moving directions is added to a random walker model also without step back. Two types of walkers: the right walkers going to the right and the left walkers going to the left are taken into account. The characteristics of counterflow are clarified. Influences of the different interaction radius values and system sizes on movement are studied. Phase transition from free moving to jamming is observed with the increase of entrance density. It is found that the critical entrance density pc at the transition point does not depend on the system size when the interaction radius value is large. Simulation results are represented as a comparison with the random walker model.

Chaos in a one-dimensional compressible flow

We study the dynamics of a one-dimensional discrete flow with open boundaries--a series of moving point particles connected by ideal springs. These particles flow towards an inlet at constant velocity, pass into a region where they are free to move according to their nearest neighbor interactions, and then pass an outlet where they travel with a sinusoidally varying velocity. As the amplitude of the outlet oscillations is increased, we find that the resident time of particles in the chamber follows a bifurcating (Feigenbaum) route to chaos. This irregular dynamics may be related to the complex behavior of many particle discrete flows or is possibly a low-dimensional analogue of nonstationary flow in continuous systems.

Dynamics of crowd disasters: an empirical study

Many observations of the dynamics of pedestrian crowds, including various self-organization phenomena, have been successfully described by simple many-particle models. For ethical reasons, however, there is a serious lack of experimental data regarding crowd panic. Therefore, we have analyzed video recordings of the crowd disaster in Mina/Makkah during the Hajj in 1426H on 12 January 2006. They reveal two subsequent, sudden transitions from laminar to stop-and-go and "turbulent" flows, which question many previous simulation models. While the transition from laminar to stop-and-go flows supports a recent model of bottleneck flows [D. Helbing, Phys. Rev. Lett. 97, 168001 (2006)], the subsequent transition to turbulent flow is not yet well understood. It is responsible for sudden eruptions of pressure release comparable to earthquakes, which cause sudden displacements and the falling and trampling of people. The insights of this study into the reasons for critical crowd conditions are important for the organization of safer mass events. In particular, they allow one to understand where and when crowd accidents tend to occur. They have also led to organizational changes, which have ensured a safe Hajj in 1427H.

The feeding dynamics of broiler chickens

Contrary to a commonly held belief that broiler chickens need more space, there is increasing evidence that these birds are attracted to other birds. Indeed, commercially farmed birds exhibit a range of socially facilitated behaviours, such as increased feeding and preening in response to the presence of other birds. Social facilitation can generate feedback loops, whereby the adoption of a particular behaviour can spread rapidly and suddenly through the population. Here, by measuring the rate at which broiler chickens join and leave a feeding trough as a function of the number of birds already there, we quantify social facilitation. We use these measurements to parameterize a simulation model of chicken feeding behaviour. This model predicts, and further observations of broiler chickens confirm, that social facilitation leads to excitatory and synchronized patterns of group feeding. Such models could prove a powerful tool in understanding how feeding patterns depend on broiler house design.