Simulating dynamical features of escape panic

Modeling crowd and trained leader behavior during building evacuation

This article considers animating evacuation in complex buildings by crowds who might not know the structure's connectivity, or who find routes accidentally blocked. It takes into account simulated crowd behavior under two conditions: where agents communicate building route knowledge, and where agents take different roles such as trained personnel, leaders, and followers.

Analytical approach to continuous and intermittent bottleneck flows

We propose a many-particle-inspired theory for granular outflows from a hopper and for the escape dynamics through a bottleneck based on a continuity equation in polar coordinates. If the inflow is below the maximum outflow, we find an asymptotic stationary solution. If the inflow is above this value, we observe queue formation, which can be described by a shock wave equation. We also address the experimental observation of intermittent outflows, taking into account the lack of space in the merging zone by a minimum function and coordination problems by a stochastic variable. This results in avalanches of different sizes even if friction, force networks, inelastic collapse, or delay-induced stop-and-go waves are not assumed. Our intermittent flows result from a random alternation between particle propagation and gap propagation. Erratic flows in congested merging zones of vehicle traffic may be explained in a similar way.

Cellular automaton simulation of pedestrian counter flow with different walk velocities

This paper presents a cellular automaton model without step back for pedestrian dynamics considering the human behaviors which can make judgments in some complex situations. This model can simulate pedestrian movement with different walk velocities through update at different time-step intervals. Two kinds of boundary conditions including periodic and open boundary for pedestrian counter flow are considered, and their dynamical characteristics are discussed. Simulation results show that for periodic boundary condition there are three phases of pedestrian patterns, i.e., freely moving phase, lane formation phase, and perfectly stopped phase at some certain total density ranges. In the stage of lane formation, the phenomenon that pedestrians exceed those with lower walk velocity through a narrow walkway can be found. For open boundary condition, at some certain entrance densities, there are two steady states of pedestrian patterns; but the first is metastable. Spontaneous fluctuations can break the first steady state, i.e., freely moving phase, and run into the second steady state, i.e., perfectly stopped phase.

Boltzmann and hydrodynamic description for self-propelled particles

We study analytically the emergence of spontaneous collective motion within large bidimensional groups of self-propelled particles with noisy local interactions, a schematic model for assemblies of biological organisms. As a central result, we derive from the individual dynamics the hydrodynamic equations for the density and velocity fields, thus giving a microscopic foundation to the phenomenological equations used in previous approaches. A homogeneous spontaneous motion emerges below a transition line in the noise-density plane. Yet, this state is shown to be unstable against spatial perturbations, suggesting that more complicated structures should eventually appear.

Arching in tapped deposits of hard disks

We simulate the tapping of a bed of hard disks in a rectangular box by using a pseudodynamic algorithm. In these simulations, arches are unambiguously defined and we can analyze their properties as a function of the tapping amplitude. We find that an order-disorder transition occurs within a narrow range of tapping amplitudes as has been seen by others. Arches are always present in the system although they exhibit regular shapes in the ordered regime. Interestingly, an increase in the number of arches does not always correspond to a reduction in the packing fraction. This is in contrast with what is found in three-dimensional systems.

Health risks at the Hajj

Annually, millions of Muslims embark on a religious pilgrimage called the "Hajj" to Mecca in Saudi Arabia. The mass migration during the Hajj is unparalleled in scale, and pilgrims face numerous health hazards. The extreme congestion of people and vehicles during this time amplifies health risks, such as those from infectious diseases, that vary each year. Since the Hajj is dictated by the lunar calendar, which is shorter than the Gregorian calendar, it presents public-health policy planners with a moving target, demanding constant preparedness. We review the communicable and non-communicable hazards that pilgrims face. With the rise in global travel, preventing disease transmission has become paramount to avoid the spread of infectious diseases, including SARS (severe acute respiratory syndrome), avian influenza, and haemorrhagic fever. We examine the response of clinicians, the Saudi Ministry of Health, and Hajj authorities to these unique problems, and list health recommendations for prospective pilgrims.

Centrality in networks of urban streets

Centrality has revealed crucial for understanding the structural properties of complex relational networks. Centrality is also relevant for various spatial factors affecting human life and behaviors in cities. Here, we present a comprehensive study of centrality distributions over geographic networks of urban streets. Five different measures of centrality, namely degree, closeness, betweenness, straightness and information, are compared over 18 1-square-mile samples of different world cities. Samples are represented by primal geographic graphs, i.e., valued graphs defined by metric rather than topologic distance where intersections are turned into nodes and streets into edges. The spatial behavior of centrality indices over the networks is investigated graphically by means of color-coded maps. The results indicate that a spatial analysis, that we term multiple centrality assessment, grounded not on a single but on a set of different centrality indices, allows an extended comprehension of the city structure, nicely capturing the skeleton of most central routes and subareas that so much impacts on spatial cognition and on collective dynamical behaviors. Statistically, closeness, straightness and betweenness turn out to follow similar functional distribution in all cases, despite the extreme diversity of the considered cities. Conversely, information is found to be exponential in planned cities and to follow a power-law scaling in self-organized cities. Hierarchical clustering analysis, based either on the Gini coefficients of the centrality distributions, or on the correlation between different centrality measures, is able to characterize classes of cities.

Modeling bursts and heavy tails in human dynamics

The dynamics of many social, technological and economic phenomena are driven by individual human actions, turning the quantitative understanding of human behavior into a central question of modern science. Current models of human dynamics, used from risk assessment to communications, assume that human actions are randomly distributed in time and thus well approximated by Poisson processes. Here we provide direct evidence that for five human activity patterns, such as email and letter based communications, web browsing, library visits and stock trading, the timing of individual human actions follow non-Poisson statistics, characterized by bursts of rapidly occurring events separated by long periods of inactivity. We show that the bursty nature of human behavior is a consequence of a decision based queuing process: when individuals execute tasks based on some perceived priority, the timing of the tasks will be heavy tailed, most tasks being rapidly executed, while a few experiencing very long waiting times. In contrast, priority blind execution is well approximated by uniform interevent statistics. We discuss two queuing models that capture human activity. The first model assumes that there are no limitations on the number of tasks an individual can handle at any time, predicting that the waiting time of the individual tasks follow a heavy tailed distribution P(tau(w)) approximately tau(w)(-alpha) with alpha=3/2. The second model imposes limitations on the queue length, resulting in a heavy tailed waiting time distribution characterized by alpha=1. We provide empirical evidence supporting the relevance of these two models to human activity patterns, showing that while emails, web browsing and library visitation display alpha=1, the surface mail based communication belongs to the alpha=3/2 universality class. Finally, we discuss possible extension of the proposed queuing models and outline some future challenges in exploring the statistical mechanics of human dynamics.

The principles of collective animal behaviour

In recent years, the concept of self-organization has been used to understand collective behaviour of animals. The central tenet of self-organization is that simple repeated interactions between individuals can produce complex adaptive patterns at the level of the group. Inspiration comes from patterns seen in physical systems, such as spiralling chemical waves, which arise without complexity at the level of the individual units of which the system is composed. The suggestion is that biological structures such as termite mounds, ant trail networks and even human crowds can be explained in terms of repeated interactions between the animals and their environment, without invoking individual complexity. Here, I review cases in which the self-organization approach has been successful in explaining collective behaviour of animal groups and societies. Ant pheromone trail networks, aggregation of cockroaches, the applause of opera audiences and the migration of fish schools have all been accurately described in terms of individuals following simple sets of rules. Unlike the simple units composing physical systems, however, animals are themselves complex entities, and other examples of collective behaviour, such as honey bee foraging with its myriad of dance signals and behavioural cues, cannot be fully understood in terms of simple individuals alone. I argue that the key to understanding collective behaviour lies in identifying the principles of the behavioural algorithms followed by individual animals and of how information flows between the animals. These principles, such as positive feedback, response thresholds and individual integrity, are repeatedly observed in very different animal societies. The future of collective behaviour research lies in classifying these principles, establishing the properties they produce at a group level and asking why they have evolved in so many different and distinct natural systems. Ultimately, this research could inform not only our understanding of animal societies, but also the principles by which we organize our own society.

Symmetry Breaking in Escaping Ants

The phenomenon of herding is a very general feature of the collective behavior of many species in panic conditions, including humans. It has been predicted theoretically that panic-induced herding in individuals confined to a room can produce a nonsymmetrical use of two identical exit doors. Here we demonstrate the existence of that phenomenon in experiments, using ants as a model of pedestrians. We show that ants confined to a cell with two symmetrically located exits use both exits in approximately equal proportions to abandon it in normal conditions but prefer one of the exits if panic is created by adding a repellent fluid. In addition, we are able to reproduce the observed escape dynamics in detail using a modification of a previous theoretical model that includes herding associated with a panic parameter as a central ingredient. Our experimental results, combined with theoretical models, suggest that some features of the collective behavior of humans and ants can be quite similar when escaping under panic.

Dynamics of prey-flock escaping behavior in response to predator's attack

The dynamic behavior of prey-flock in response to predator's attack was investigated by using molecular dynamics (MD) simulations in a two-dimensional (2D) continuum model. By locally applying interactive forces between prey individuals (e.g. attraction, repulsion, and alignment), a coherently moving state in the same direction was obtained among individuals in prey-flock. When a single predator was introduced to the prey population, the prey-flock was correspondingly deformed by the predator's continuous attacks towards the prey-flock's center. In response to the predator's attack, three regimes in the flock size (compression (Regime I), expansion (Regime II), compression (Regime III)) were revealed if the predator's attack speed (kappa) was comparatively low to the escape speed of prey-flock. If noise was added to the predator's attacking course, a higher degree of variation was observed in the patterns of compression and expansion in the prey-flock size. However, the scaling behavior in the changes in prey-flock size was present in different levels of noise with the increase in predation risk (R) when kappa takes an appropriately low value. During the procedure of escaping, order breaking in alignment (phi) of prey population was observed, while the degree of alignment was dependent upon the changes in parameters of kappa and R.

Analytical investigation of oscillations in intersecting flows of pedestrian and vehicle traffic

In two intersecting many-particle streams, one can often find the emergence of oscillatory patterns. Here, we investigate the interaction of pedestrians with vehicles, when they try to cross a road. A numerical study of this coupled pedestrian-vehicle delay problem has been presented in a previous paper. Here, we focus on the analytical treatment of the problem, which requires us to use a simplified car-following model. Our analytical results for the transition to oscillatory pedestrian and traffic flows and the average waiting times are well supported by numerical evaluations and give a detailed picture of the collective dynamics emerging when pedestrians try to cross a road. The mathematical expressions allow one to identify the dependence on model parameters such as the vehicle or pedestrian arrival rate, and the safety factor of pedestrian gap acceptance. We also calculate a formula for the vehicle time gap distribution, which corresponds to the departure time contribution of a M/D/1 queue characterized by Poissonian distributed Markovian arrivals, 1 service channel, and deterministic departures.

Computational models of collective behavior

Computational models of human collective behavior offer promise in providing quantitative and empirically verifiable accounts of how individual decisions lead to the emergence of group-level organizations. Agent-based models (ABMs) describe interactions among individual agents and their environment, and provide a process-oriented alternative to descriptive mathematical models. Recent ABMs provide compelling accounts of group pattern formation, contagion and cooperation, and can be used to predict, manipulate and improve upon collective behavior. ABMs overcome an assumption that underlies much of cognitive science--that the individual is the crucial unit of cognition. The alternative advocated here is that individuals participate in collective organizations that they might not understand or even perceive, and that these organizations affect and are affected by individual behavior.

Centrifugal force model for pedestrian dynamics

In this paper, a centrifugal force model is developed for pedestrian dynamics. The effects of both the headway and the relative velocity among pedestrians are taken into account, which can be expressed by a "centrifugal force" term in dynamic equation. The jamming probability due to the arching at exits for crowd flows is provided. A quantitative analysis of the crowd flowing out of a hall shows that the average leaving time T is a function of the exit width W in negative power. The related simulation indicates that the proposed model is able to reproduce the self-organization phenomena of lane formation for sparse flows.

Moving backward noisily

We discuss the fundamental physical differences and the mathematical interconnections of counterintuitive transport and response properties in Brownian motion far from equilibrium. After reviewing the ubiquity of such effects in physical and other systems, we illustrate the general properties on paradigmatic models for both individually and collectively acting Brownian particles.

The origin of bursts and heavy tails in human dynamics

The dynamics of many social, technological and economic phenomena are driven by individual human actions, turning the quantitative understanding of human behaviour into a central question of modern science. Current models of human dynamics, used from risk assessment to communications, assume that human actions are randomly distributed in time and thus well approximated by Poisson processes. In contrast, there is increasing evidence that the timing of many human activities, ranging from communication to entertainment and work patterns, follow non-Poisson statistics, characterized by bursts of rapidly occurring events separated by long periods of inactivity. Here I show that the bursty nature of human behaviour is a consequence of a decision-based queuing process: when individuals execute tasks based on some perceived priority, the timing of the tasks will be heavy tailed, with most tasks being rapidly executed, whereas a few experience very long waiting times. In contrast, random or priority blind execution is well approximated by uniform inter-event statistics. These finding have important implications, ranging from resource management to service allocation, in both communications and retail.

Heterogeneous beliefs, segregation, and extremism in the making of public opinions

The connection between contradictory public opinions, heterogeneous beliefs, and the emergence of majority- or minority-induced extremism is studied, extending our former two-state dynamic opinion model. Agents are attached to a social-cultural class. At each step they are distributed randomly in different groups within their respective classes to evolve locally by majority rule. In case of a tie the group adopts one or another opinion with respective probabilities k and (1-k) . The value of k accounts for the average of individual biases driven by the existence of heterogeneous beliefs within the corresponding class. It may vary from class to class. The process leads to extremism with a full polarization of each class along one opinion. For homogeneous classes the extremism can be along the initial minority making it minority induced. In contrast, heterogeneous classes exhibit more balanced dynamics, which results in a majority-induced extremism. Segregation among subclasses may produce a coexistence of opinions at the class level, thus averting global extremism. Insight into the existence of contradictory public opinions in similar social-cultural neighborhoods is given.

An agent-based approach for modeling molecular self-organization

Agent-based modeling is a technique currently used to simulate complex systems in computer science and social science. Here, we propose its application to the problem of molecular self-assembly. A system is allowed to evolve from a separated to an aggregated state following a combination of stochastic, deterministic, and adaptive rules. We consider the problem of packing rigid shapes on a lattice to verify that this algorithm produces more nearly optimal aggregates with less computational effort than comparable Monte Carlo simulations.

Discrete-element modelling: methods and applications in the environmental sciences

This paper introduces a Theme Issue on discrete-element modelling, based on research presented at an interdisciplinary workshop on this topic organized by the National Institute of Environmental e-Science. The purpose of the workshop, and this collection of papers, is to highlight the opportunities for environmental scientists provided by (primarily) off-lattice methods in the discrete-element family, and to draw on the experiences of research communities in which the use of these methods is more advanced. Applications of these methods may be conceived in a wide range of situations where dynamic processes involve a series of fundamental entities (particles or elements) whose interaction results in emergent macroscale structures. Indeed, the capacity of these methods to reveal emergent properties at the meso- and macroscale, that reflect microscale interactions, is a significant part of their attraction. They assist with the definition of constitutive material properties at scales beyond those at which measurement and theory have been developed, and help us to understand self-organizing behaviours. The paper discusses technical issues including the contact models required to represent collision behaviour, computational aspects of particle tracking and collision detection, and scales at which experimental data are required and choices about modelling style must be made. It then illustrates the applicability of DEM and other forms of individual-based modelling in environmental and related fields as diverse as mineralogy, geomaterials, mass movement and fluvial sediment transport processes, as well as developments in ecology, zoology and the human sciences where the relationship between individual behaviour and group dynamics can be explored using a partially similar methodological framework.

Experiment, theory, and simulation of the evacuation of a room without visibility

We study the evacuation process from a smoky room by means of experiments and simulations. People in a dark or smoky room are mimicked by "blind" students wearing eye masks. The evacuation of the disoriented students from the room is observed by video cameras, and the escape time of each student is measured. We find that the disoriented students exhibit a distinctly different behavior compared to a situation in which people can see their environment. Our experimental results are related to a theoretical approach and reproduced by an extended lattice gas model taking into account the empirically observed behavior. Our particular focus is on the mean value and distribution of escape times. For a large number of people in the room, the escape time distribution is wide because of jamming. Surprisingly, adding more exits does not improve the situation in the expected way, since most people use the exit that is discovered first, which may be viewed as a kind of herding effect based on nonlocal, but direct acoustic interactions. Moreover, the average escape time becomes minimal for a certain finite number of people in the dark or smoky room. These nonlinear effects have practical implications for emergency evacuation and the planning of safer buildings.

Particle-based multidimensional multispecies biofilm model

In this paper we describe a spatially multidimensional (two-dimensional [2-D] and three-dimensional [3-D]) particle-based approach for modeling the dynamics of multispecies biofilms growing on multiple substrates. The model is based on diffusion-reaction mass balances for chemical species coupled with microbial growth and spreading of biomass represented by hard spherical particles. Effectively, this is a scaled-up version of a previously proposed individual-based biofilm model. Predictions of this new particle-based model were quantitatively compared with those obtained with an established one-dimensional (1-D) multispecies model for equivalent problems. A nitrifying biofilm containing aerobic ammonium and nitrite oxidizers, anaerobic ammonium oxidizers, and inert biomass was chosen as an example. The 2-D and 3-D models generally gave the same results. If only the average flux of nutrients needs to be known, 2-D and 1-D models are very similar. However, the behavior of intermediates, which are produced and consumed in different locations within the biofilm, is better described in 2-D and 3-D models because of the multidirectional concentration gradients. The predictions of 2-D or 3-D models are also different from those of 1-D models for slowly growing or minority species in the biofilm. This aspect is related to the mechanism of biomass spreading or advection implemented in the models and should receive more attention in future experimental studies.

Onset of collective and cohesive motion

We study the onset of collective motion, with and without cohesion, of groups of noisy self-propelled particles interacting locally. We find that this phase transition, in two space dimensions, is always discontinuous, including for the minimal model of Vicsek et al. [Phys. Rev. Lett. 75, 1226 (1995)]] for which a nontrivial critical point was previously advocated. We also show that cohesion is always lost near onset, as a result of the interplay of density, velocity, and shape fluctuations.

Self-organized queuing and scale-free behavior in real escape panic

Numerical investigations of escape panic of confined pedestrians have revealed interesting dynamical features such as pedestrian arch formation around an exit, disruptive interference, self-organized queuing, and scale-free behavior. However, these predictions have remained unverified because escape panic experiments with real systems are difficult to perform. For mice escaping out of a water pool, we found that for a critical sampling rate the escape behavior exhibits the predicted features even at short observation times. The mice escaped via an exit in bursts of different sizes that obey exponential and (truncated) power-law distributions depending on exit width. Oversampling or undersampling the mouse escape rate prevents the observation of the predicted features. Real systems are normally subject to unavoidable constraints arising from occupancy rate, pedestrian exhaustion, and nonrigidity of pedestrian bodies. The effect of these constraints on the dynamics of real escape panic is also studied.

Lattice gas simulation of experimentally studied evacuation dynamics

We study the evacuation process from a classroom by means of experiments and simulations. The evacuation of students from a classroom is observed by video cameras, and the escape time of each student is measured. Our experimental results are compared with simulations based on a lattice gas model of pedestrian flows. We find that the empirically identified inefficiencies of the evacuation process can be well reproduced. Our particular focus is on the spatial dependence of the escape times on the initial positions, which is highly significant. The escape time distribution turns out to be rather broad due to a jamming (queuing) of the students at the exit, which determines not only the saturation flow (capacity) but also the temporal characteristics of the evacuation dynamics.

Friction effects and clogging in a cellular automaton model for pedestrian dynamics

We investigate the role of conflicts in pedestrian traffic, i.e., situations where two or more people try to enter the same space. Therefore a recently introduced cellular automaton model for pedestrian dynamics is extended by a friction parameter mu. This parameter controls the probability that the movement of all particles involved in a conflict is denied at one time step. It is shown that these conflicts are not an undesirable artifact of the parallel update scheme, but are important for a correct description of the dynamics. The friction parameter mu can be interpreted as a kind of an internal local pressure between the pedestrians which becomes important in regions of high density, occurring, e.g., in panic situations. We present simulations of the evacuation of a large room with one door. It is found that friction has not only quantitative effects, but can also lead to qualitative changes, e.g., of the dependence of the evacuation time on the system parameters. We also observe similarities to the flow of granular materials, e.g., arching effects.

Collective Memory and Spatial Sorting in Animal Groups

We present a self-organizing model of group formation in three-dimensional space, and use it to investigate the spatial dynamics of animal groups such as fish schools and bird flocks. We reveal the existence of major group-level behavioural transitions related to minor changes in individual-level interactions. Further, we present the first evidence for collective memory in such animal groups (where the previous history of group structure influences the collective behaviour exhibited as individual interactions change) during the transition of a group from one type of collective behaviour to another. The model is then used to show how differences among individuals influence group structure, and how individuals employing simple, local rules of thumb, can accurately change their spatial position within a group (e.g. to move to the centre, the front, or the periphery) in the absence of information on their current position within the group as a whole. These results are considered in the context of the evolution and ecological importance of animal groups.

Excitation of rotational modes in two-dimensional systems of driven Brownian particles

Models of active Brownian motion in two-dimensional (2D) systems developed earlier are investigated with respect to the influence of linear attracting forces and external noise. Our consideration is restricted to the case that the driving is rather weak and that the forces show only weak deviations from radial symmetry. In this case an analytical study of the bifurcations of the system is possible. We show that in the presence of external linear forces with only small deviations from radial symmetry, the system develops rotational excitations with left-right symmetry, corresponding to limit cycles in the 4D phase space, the corresponding distribution has the form of a hoop or a tire in the 4D space. In the last part we apply the theory to swarms of Brownian particles that are held together by weak and attracting forces, which lead to cluster formation. Since near the center the potential is at least approximately parabolic and near to the radial symmetry, the swarm develops rotational modes of motion with left-right symmetry.

Agent-based modeling: methods and techniques for simulating human systems

Agent-based modeling is a powerful simulation modeling technique that has seen a number of applications in the last few years, including applications to real-world business problems. After the basic principles of agent-based simulation are briefly introduced, its four areas of application are discussed by using real-world applications: flow simulation, organizational simulation, market simulation, and diffusion simulation. For each category, one or several business applications are described and analyzed.