Simulating dynamical features of escape panic

Avoiding numerical pitfalls in social force models

The social force model of Helbing and Molnár is one of the best known approaches to simulate pedestrian motion, a collective phenomenon with nonlinear dynamics. It is based on the idea that the Newtonian laws of motion mostly carry over to pedestrian motion so that human trajectories can be computed by solving a set of ordinary differential equations for velocity and acceleration. The beauty and simplicity of this ansatz are strong reasons for its wide spread. However, the numerical implementation is not without pitfalls. Oscillations, collisions, and instabilities occur even for very small step sizes. Classic solution ideas from molecular dynamics do not apply to the problem because the system is not Hamiltonian despite its source of inspiration. Looking at the model through the eyes of a mathematician, however, we realize that the right hand side of the differential equation is nondifferentiable and even discontinuous at critical locations. This produces undesirable behavior in the exact solution and, at best, severe loss of accuracy in efficient numerical schemes even in short range simulations. We suggest a very simple mollified version of the social force model that conserves the desired dynamic properties of the original many-body system but elegantly and cost efficiently resolves several of the issues concerning stability and numerical resolution.

Collective motion of humans in mosh and circle pits at heavy metal concerts

Human collective behavior can vary from calm to panicked depending on social context. Using videos publicly available online, we study the highly energized collective motion of attendees at heavy metal concerts. We find these extreme social gatherings generate similarly extreme behaviors: a disordered gaslike state called a mosh pit and an ordered vortexlike state called a circle pit. Both phenomena are reproduced in flocking simulations demonstrating that human collective behavior is consistent with the predictions of simplified models.

The scaling of contact rates with population density for the infectious disease models

Contact rates and patterns among individuals in a geographic area drive transmission of directly-transmitted pathogens, making it essential to understand and estimate contacts for simulation of disease dynamics. Under the uniform mixing assumption, one of two mechanisms is typically used to describe the relation between contact rate and population density: density-dependent or frequency-dependent. Based on existing evidence of population threshold and human mobility patterns, we formulated a spatial contact model to describe the appropriate form of transmission with initial growth at low density and saturation at higher density. We show that the two mechanisms are extreme cases that do not capture real population movement across all scales. Empirical data of human and wildlife diseases indicate that a nonlinear function may work better when looking at the full spectrum of densities. This estimation can be applied to large areas with population mixing in general activities. For crowds with unusually large densities (e.g., transportation terminals, stadiums, or mass gatherings), the lack of organized social contact structure deviates the physical contacts towards a special case of the spatial contact model - the dynamics of kinetic gas molecule collision. In this case, an ideal gas model with van der Waals correction fits well; existing movement observation data and the contact rate between individuals is estimated using kinetic theory. A complete picture of contact rate scaling with population density may help clarify the definition of transmission rates in heterogeneous, large-scale spatial systems.

Nondestructive intervention to multi-agent systems through an intelligent agent

For a given multi-agent system where the local interaction rule of the existing agents can not be re-designed, one way to intervene the collective behavior of the system is to add one or a few special agents into the group which are still treated as normal agents by the existing ones. We study how to lead a Vicsek-like flocking model to reach synchronization by adding special agents. A popular method is to add some simple leaders (fixed-headings agents). However, we add one intelligent agent, called 'shill', which uses online feedback information of the group to decide the shill's moving direction at each step. A novel strategy for the shill to coordinate the group is proposed. It is strictly proved that a shill with this strategy and a limited speed can synchronize every agent in the group. The computer simulations show the effectiveness of this strategy in different scenarios, including different group sizes, shill speed, and with or without noise. Compared to the method of adding some fixed-heading leaders, our method can guarantee synchronization for any initial configuration in the deterministic scenario and improve the synchronization level significantly in low density groups, or model with noise. This suggests the advantage and power of feedback information in intervention of collective behavior.

Geometry dependence of the clogging transition in tilted hoppers

We report the effects of system geometry on the clogging of granular material flowing out of flat-bottomed hoppers with variable aperture size D and with variable angle θ of tilt of the hopper away from horizontal. In general, larger tilt angles make the system more susceptible to clogging. To quantify this effect for a given θ, we measure the distribution of mass discharged between clogging events as a function of aperture size and extrapolate to the critical size at which the average mass diverges. By repeating for different angles, we map out a clogging phase diagram as a function of D and θ that demarcates the regimes of free flow (large D, small θ) and clogging (small D, large θ). We do this for both circular holes and long rectangular slits. Additionally, we measure four types of grain: smooth spheres (glass beads), compact angular grains (beach sand), disklike grains (lentils), and rodlike grains (rice). For circular apertures, the clogging phase diagram is found to be the same for all grain types. For narrow slit apertures and compact grains, the shape is also the same as for circular holes when expressed in terms of projected area of the aperture against the average flow direction. For lentils and rice discharged from slits, the behavior differs and may be due to alignment between grain and slit axes.

Decision-making theories: linking the disparate research areas of individual and collective cognition

In order to maximize their fitness, animals have to deal with different environmental and social factors that affect their everyday life. Although the way an animal behaves might enhance its fitness or survival in regard to one factor, it could compromise them regarding another. In the domain of decision sciences, research concerning decision making focuses on performances at the individual level but also at the collective one. However, between individual and collective decision making, different terms are used resulting in little or no connection between both research areas. In this paper, we reviewed how different branches of decision sciences study the same concept, mainly called speed-accuracy trade-off, and how the different results are on the same track in terms of showing the optimality of decisions. Whatever the level, individual or collective, each decision might be defined with three parameters: time or delay to decide, risk and accuracy. We strongly believe that more progress would be possible in this domain of research if these different branches were better linked, with an exchange of their results and theories. A growing amount of literature describes economics in humans and eco-ethology in birds making compromises between starvation, predation and reproduction. Numerous studies have been carried out on social cognition in primates but also birds and carnivores, and other publications describe market or reciprocal exchanges of commodities. We therefore hope that this paper will lead these different areas to a common decision science.

Analysis of Joint Connectivity Condition for Multiagents With Boundary Constraints

The connectivity of a group of agents in a flocking scenario is caused either by individual's local cohesion interaction mechanism or by external boundary constraints. The latter case is particularly interesting when an individual's cohesion ability is not reliable due to the limitation of communication range. The effect of external boundary constraints on the connectivity property of multiagents has been intensively investigated in natural observation and engineering simulation. A theoretical analysis is given in this paper which reveals that a group of agents in a bounded plane can be almost always jointly connected and hence form a complete flock.

Evacuation of pedestrians from a single room by using snowdrift game theories

Game theory is introduced to simulate the complicated interaction relations among the conflicting pedestrians in a pedestrian flow system, which is defined on a square lattice with the parallel update rule. Modified on the traditional lattice gas model, each pedestrian can move to not only an empty site, but also an occupied site. It is found that each individual chooses its neighbor randomly and occupies the site with the probability W(x→y)=1/1+exp[-(P(x)-U(x))/κ], where P(x) is the x's payoff representing his personal energy, and U(x) is the average payoff of its neighborhood indicating the potential well energy if he stays. Two types of pedestrians are considered, and they interact with their neighbors following the payoff matrix of snowdrift game theory. The cost-to-benefit ratio r=c/(2b-c) (where b is the perfect payoff and c is the labor cost) represents the fear index of the pedestrians in this model. It is found that there exists a moderate value of r leading to the shortest escape time, and the situation for large values of r is better than that for small ones in general. In addition, the pedestrian flow system always arrives at a consistent state in which the two types of walkers have the same number and evolve by the same law irrespectively of the parameters, which can be interpreted as the self-organization effect of pedestrian flow. It is also proven that the time point of the onset of the steady state is unrelated to the scale of the pedestrians and the square lattice. Meanwhile, the system exhibits different dynamics before reaching the consistent state: the number of the two types of walkers oscillates when P(C)>0.5 (i.e., probability to change the present strategy), while no oscillation happens for P(C)≤0.5. Finally, it is shown that a smaller density of pedestrians ρ induces a shorter average escape time.

Financial price dynamics and pedestrian counterflows: a comparison of statistical stylized facts

We propose and document the evidence for an analogy between the dynamics of granular counterflows in the presence of bottlenecks or restrictions and financial price formation processes. Using extensive simulations, we find that the counterflows of simulated pedestrians through a door display eight stylized facts observed in financial markets when the density around the door is compared with the logarithm of the price. Finding so many stylized facts is very rare indeed among all agent-based models of financial markets. The stylized properties are present when the agents in the pedestrian model are assumed to display a zero-intelligent behavior. If agents are given decision-making capacity and adapt to partially follow the majority, periods of herding behavior may additionally occur. This generates the very slow decay of the autocorrelation of absolute return due to an intermittent dynamics. Our findings suggest that the stylized facts in the fluctuations of the financial prices result from a competition of two groups with opposite interests in the presence of a constraint funneling the flow of transactions to a narrow band of prices with limited liquidity.

Patient and impatient pedestrians in a spatial game for egress congestion

Large crowds evacuating through narrow bottlenecks may create clogging and jams that slow down the egress flow. Especially if people try to push towards the exit, the so-called faster-is-slower effect may occur. We propose a spatial game to model the interaction of agents in such situations. Each agent has two possible modes of play that lead to either patient or impatient behavior. The payoffs of the game are derived from simple assumptions and correspond to a hawk-dove game, where the game parameters depend on the agent's location in the crowd and on external conditions. Equilibrium configurations are computed with a myopic best-response rule and studied in both a continuous space and a discrete lattice. We apply the game model to a continuous-time egress simulation, where the patient and impatient agents are given different individual parameter values, which are updated according to the local conditions in the crowd. The model shows how threatening conditions can increase the proportion of impatient agents, which leads to clogging and reduced flows through bottlenecks, even when smooth flows would be possible.

A bio-inspired, motion-based analysis of crowd behavior attributes relevance to motion transparency, velocity gradients, and motion patterns

The analysis of motion crowds is concerned with the detection of potential hazards for individuals of the crowd. Existing methods analyze the statistics of pixel motion to classify non-dangerous or dangerous behavior, to detect outlier motions, or to estimate the mean throughput of people for an image region. We suggest a biologically inspired model for the analysis of motion crowds that extracts motion features indicative for potential dangers in crowd behavior. Our model consists of stages for motion detection, integration, and pattern detection that model functions of the primate primary visual cortex area (V1), the middle temporal area (MT), and the medial superior temporal area (MST), respectively. This model allows for the processing of motion transparency, the appearance of multiple motions in the same visual region, in addition to processing opaque motion. We suggest that motion transparency helps to identify "danger zones" in motion crowds. For instance, motion transparency occurs in small exit passages during evacuation. However, motion transparency occurs also for non-dangerous crowd behavior when people move in opposite directions organized into separate lanes. Our analysis suggests: The combination of motion transparency and a slow motion speed can be used for labeling of candidate regions that contain dangerous behavior. In addition, locally detected decelerations or negative speed gradients of motions are a precursor of danger in crowd behavior as are globally detected motion patterns that show a contraction toward a single point. In sum, motion transparency, image speeds, motion patterns, and speed gradients extracted from visual motion in videos are important features to describe the behavioral state of a motion crowd.

Migration of cells in a social context

In multicellular organisms and complex ecosystems, cells migrate in a social context. Whereas this is essential for the basic processes of life, the influence of neighboring cells on the individual remains poorly understood. Previous work on isolated cells has observed a stereotypical migratory behavior characterized by short-time directional persistence with long-time random movement. We discovered a much richer dynamic in the social context, with significant variations in directionality, displacement, and speed, which are all modulated by local cell density. We developed a mathematical model based on the experimentally identified "cellular traffic rules" and basic physics that revealed that these emergent behaviors are caused by the interplay of single-cell properties and intercellular interactions, the latter being dominated by a pseudopod formation bias mediated by secreted chemicals and pseudopod collapse following collisions. The model demonstrates how aspects of complex biology can be explained by simple rules of physics and constitutes a rapid test bed for future studies of collective migration of individual cells.

Group chase and escape with some fast chasers

We study group chase and escape with some fast chasers. In our model chasers look for the nearest target and move to one of the nearest sites in order to catch the target. On the other hand, targets try to escape from the nearest chaser. When a chaser catches a target, the target is removed from the system and the number of targets decreases. The lifetime of targets, at which all targets caught, decreases as t^{α} with increasing the number of chasers. When there are no fast chasers and the total number of chasers is small, the exponent α is large. When the total number of chasers is large, α becomes small. There is an optimal number of chasers to minimize the cost used in order to catch all targets. However, when we add a few fast chasers, the region with the large α vanishes. The optimal number of chasers vanishes, and the cost monotonically increases with increasing the number of chasers.

Emergent states in dense systems of active rods: from swarming to turbulence

Dense suspensions of self-propelled rod-like particles exhibit a fascinating variety of non-equilibrium phenomena. By means of computer simulations of a minimal model for rigid self-propelled colloidal rods with variable shape we explore the generic diagram of emerging states over a large range of rod densities and aspect ratios. The dynamics is studied using a simple numerical scheme for the overdamped noiseless frictional dynamics of a many-body system in which steric forces are dominant over hydrodynamic ones. The different emergent states are identified by various characteristic correlation functions and suitable order parameter fields. At low density and aspect ratio, a disordered phase with no coherent motion precedes a highly cooperative swarming state with giant number fluctuations at large aspect ratio. Conversely, at high densities weakly anisometric particles show a distinct jamming transition whereas slender particles form dynamic laning patterns. In between there is a large window corresponding to strongly vortical, turbulent flow. The different dynamical states should be verifiable in systems of swimming bacteria and artificial rod-like micro-swimmers.

Collective almost synchronisation in complex networks

This work introduces the phenomenon of Collective Almost Synchronisation (CAS), which describes a universal way of how patterns can appear in complex networks for small coupling strengths. The CAS phenomenon appears due to the existence of an approximately constant local mean field and is characterised by having nodes with trajectories evolving around periodic stable orbits. Common notion based on statistical knowledge would lead one to interpret the appearance of a local constant mean field as a consequence of the fact that the behaviour of each node is not correlated to the behaviours of the others. Contrary to this common notion, we show that various well known weaker forms of synchronisation (almost, time-lag, phase synchronisation, and generalised synchronisation) appear as a result of the onset of an almost constant local mean field. If the memory is formed in a brain by minimising the coupling strength among neurons and maximising the number of possible patterns, then the CAS phenomenon is a plausible explanation for it.

Natural discretization of pedestrian movement in continuous space

Is there a way to describe pedestrian movement with simple rules, as in a cellular automaton, but without being restricted to a cellular grid? Inspired by the natural stepwise movement of humans, we develop a model that uses local discretization on a circle around virtual pedestrians. This allows for movement in arbitrary directions, only limited by the chosen optimization algorithm and numerical resolution. The radii of the circles correspond to the step lengths of pedestrians and thus are model parameters, which must be derived from empirical observation. Therefore, we conducted a controlled experiment, collected empirical data for step lengths in relation with different speeds, and used the findings in our model. We complement the model with a simple calibration algorithm that allows reproducing known density-velocity relations, which constitutes a proof of concept. Further validation of the model is achieved by reenacting an evacuation scenario from experimental research. The simulated egress times match the values reported for the experiment very well. A new normalized measure for space occupancy serves to visualize the results.

Macroscopic limits of individual-based models for motile cell populations with volume exclusion

Partial differential equation models are ubiquitous in studies of motile cell populations, giving a phenomenological description of events which can be analyzed and simulated using a wide range of existing tools. However, these models are seldom derived from individual cell behaviors and so it is difficult to accurately include biological hypotheses on this spatial scale. Moreover, studies which do attempt to link individual- and population-level behavior generally employ lattice-based frameworks in which the artifacts of lattice choice at the population level are unclear. In this work we derive limiting population-level descriptions of a motile cell population from an off-lattice, individual-based model (IBM) and investigate the effects of volume exclusion on the population-level dynamics. While motility with excluded volume in on-lattice IBMs can be accurately described by Fickian diffusion, we demonstrate that this is not the case off lattice. We show that the balance between two key parameters in the IBM (the distance moved in one step and the radius of an individual) determines whether volume exclusion results in enhanced or slowed diffusion. The magnitude of this effect is shown to increase with the number of cells and the rate of their movement. The method we describe is extendable to higher-dimensional and more complex systems and thereby provides a framework for deriving biologically realistic, continuum descriptions of motile populations.

Propagation speed of a starting wave in a queue of pedestrians

The propagation speed of a starting wave, which is a wave of people's successive reactions in the relaxation process of a queue, has an essential role for pedestrians and vehicles to achieve smooth movement. For example, a queue of vehicles with appropriate headway (or density) alleviates traffic jams since the delay of reaction to start is minimized. In this paper, we have investigated the fundamental relation between the propagation speed of a starting wave and the initial density by both our mathematical model built on the stochastic cellular automata and experimental measurements. Analysis of our mathematical model implies that the relation is characterized by the power law αρ-β (β≠1), and the experimental results verify this feature. Moreover, when the starting wave is characterized by the power law (β>1), we have revealed the existence of optimal density, where the required time, i.e., the sum of the waiting time until the starting wave reaches the last pedestrian in a queue and his/her travel time to pass the head position of the initial queue, is minimized. This optimal density inevitably plays a significant role in achieving a smooth movement of crowds and vehicles in a queue.

Breaking arches with vibrations: the role of defects

We present experimental and numerical results regarding the stability of arches against external vibrations. Two-dimensional strings of mutually stabilizing grains are geometrically analyzed and subsequently submitted to a periodic forcing at fixed frequency and increasing amplitude. The main factor that determines the granular arch resistance against vibrations is the maximum angle among those formed between any particle of the arch and its two neighbors: the higher the maximum angle is, the easier it is to break the arch. On the basis of an analysis of the forces, a simple explanation is given for this dependence. From this, interesting information can be extracted about the expected magnitudes of normal forces and friction coefficients of the particles composing the arches.

Mixing times in evolutionary game dynamics

Without mutation and migration, evolutionary dynamics ultimately leads to the extinction of all but one species. Such fixation processes are well understood and can be characterized analytically with methods from statistical physics. However, many biological arguments focus on stationary distributions in a mutation-selection equilibrium. Here, we address the mixing time required to reach stationarity in the presence of mutation. We show that mixing times in evolutionary games have the opposite behavior from fixation times when the intensity of selection increases: in coordination games with bistabilities, the fixation time decreases, but the mixing time increases. In coexistence games with metastable states, the fixation time increases, but the mixing time decreases. Our results are based on simulations and the Wentzel-Kramers-Brillouin approximation of the master equation.

Detection of Primitive Collective Behaviours in a Crowd Panic Simulation Based on Multi-Agent Approach

In case of emergency and evacuation, it is often impossible to interpret manually the complex behaviour of a crowd, essentially due to the lack of staff and time needed to understand a situation. In the literature, a monitored system using data fusion methods makes it possible to perform automatic situation awareness. Using Swarm Intelligence domain, the authors propose an approach based on multi-agent system to simulate and detect primitive collective behaviours emerging from a crowd panic. It enables anticipating collective behaviours in real-time as well as their anomalies according to specific scenarios. Detection is the possibility to learn, recognize and anticipate different behaviours by a probabilistic model. The collective behaviour detection of a crowd panic in real-time is based on a learning method on an extended model of Hidden Markov Model. This paper presents experiments of simulation and detection using an implementation of a virtual environment.

Origin of polar order in dense suspensions of phototactic micro-swimmers

A main question for the study of collective motion in living organisms is the origin of orientational polar order, i.e., how organisms align and what are the benefits of such collective behaviour. In the case of micro-organisms swimming at a low Reynolds number, steric repulsion and long-range hydrodynamic interactions are not sufficient to explain a homogeneous polar order state in which the direction of motion is aligned. An external symmetry-breaking guiding field such as a mechanism of taxis appears necessary to understand this phonemonon. We have investigated the onset of polar order in the velocity field induced by phototaxis in a suspension of a motile micro-organism, the algae Chlamydomonas reinhardtii, for density values above the limit provided by the hydrodynamic approximation of a force dipole model. We show that polar order originates from a combination of both the external guiding field intensity and the population density. In particular, we show evidence for a linear dependence of a phototactic guiding field on cell density to determine the polar order for dense suspensions and demonstrate the existence of a density threshold for the origin of polar order. This threshold represents the density value below which cells undergoing phototaxis are not able to maintain a homogeneous polar order state and marks the transition to ordered collective motion. Such a transition is driven by a noise dominated phototactic reorientation where the noise is modelled as a normal distribution with a variance that is inversely proportional to the guiding field strength. Finally, we discuss the role of density in dense suspensions of phototactic micro-swimmers.

Chasing and escaping by three groups of species

We study group chasing and escaping between three species. In our model, one species acts as a group of chasers for another species and acts as a group of targets for the third species. When a particle is caught by a target, the particle becomes a new chaser. Although the ratio of three species is changed, the total number of particles is conserved. When particles move randomly, the numbers of the three species change periodically but no species seems to become extinct. If particles escape from the nearest chaser and chase the nearest target, the extinction of a species occurs. The extinction induces that of the second species and finally only one species survives.

Reference repulsion in the categorical perception of biological motion

Perceiving biological motion is important for understanding the intentions and future actions of others. Perceiving an approaching person's behavior may be particularly important, because such behavior often precedes social interaction. To this end, the visual system may devote extra resources for perceiving an oncoming person's heading. If this were true, humans should show increased sensitivity for perceiving approaching headings, and as a result, a repulsive perceptual effect around the categorical boundary of leftward/rightward motion. We tested these predictions and found evidence for both. First, observers were especially sensitive to the heading of an approaching person; variability in estimates of a person's heading decreased near the category boundary of leftward/rightward motion. Second, we found a repulsion effect around the category boundary; a person walking approximately toward the observer was perceived as being repelled away from straight ahead. This repulsive effect was greatly exaggerated for perception of a very briefly presented person or perception of a chaotic crowd, suggesting that repulsion may protect against categorical errors when sensory noise is high. The repulsion effect with a crowd required integration of local motion and human form, suggesting an origin in high-level stages of visual processing. Similar repulsive effects may underlie categorical perception with other social features. Overall, our results show that a person's direction of walking is categorically perceived, with improved sensitivity at the category boundary and a concomitant repulsion effect.

Commensurability-dependent transport of a Wigner crystal in a nanoconstriction

We present the first transport measurements of a classical Wigner crystal through a constriction formed by a split-gate electrode. The Wigner crystal is formed on the surface of superfluid helium confined in a microchannel. At low temperatures, the current is periodically suppressed with increasing split-gate voltage, resulting in peaklike transport features. We also present the results of molecular dynamics simulations that reproduce this phenomenon. We demonstrate that, at the split-gate voltages for which the current is suppressed, the electron lattice is arranged such that the stability of particle positions against thermal fluctuations is enhanced. In these configurations, the suppression of transport due to interelectron Coulomb forces becomes important.

Simulating and evaluating the local behavior of small pedestrian groups

Recent advancements in local methods have significantly improved the collision avoidance behavior of virtual characters. However, existing methods fail to take into account that in real life pedestrians tend to walk in small groups, consisting mainly of pairs or triples of individuals. We present a novel approach to simulate the walking behavior of such small groups. Our model describes how group members interact with each other, with other groups and individuals. We highlight the potential of our method through a wide range of test-case scenarios. We evaluate the results from our simulations using a number of quantitative quality metrics, and also provide visual and numerical comparisons with video footages of real crowds.

Bottlenecks in granular flow: when does an obstacle increase the flow rate in an hourglass?

Bottlenecks occur in a wide range of situations from pedestrians, ants, cattle, and traffic flow to the transport of granular materials. We examine granular flow across a bottleneck using simulations of monodisperse disks. Contrary to expectations but consistent with previous work, we find that the flow rate across a bottleneck actually increases if an obstacle is optimally placed before it. Using the hourglass theory and a velocity-density relation, we show that the peak flow rate corresponds to a transition from free flow to congested flow, similar to the phase transition in traffic flow.

Phase transitions in crowd dynamics of resource allocation

We define and study a class of resource allocation processes where gN agents, by repeatedly visiting N resources, try to converge to an optimal configuration where each resource is occupied by at most one agent. The process exhibits a phase transition, as the density g of agents grows, from an absorbing to an active phase. In the latter, even if the number of resources is in principle enough for all agents (g<1), the system never settles to a frozen configuration. We recast these processes in terms of zero-range interacting particles, studying analytically the mean field dynamics and investigating numerically the phase transition in finite dimensions. We find a good agreement with the critical exponents of the stochastic fixed-energy sandpile. The lack of coordination in the active phase also leads to a nontrivial faster-is-slower effect.

Crowd and environmental management during mass gatherings

Crowds are a feature of large cities, occurring not only at mass gatherings but also at routine events such as the journey to work. To address extreme crowding, various computer models for crowd movement have been developed in the past decade, and we review these and show how they can be used to identify health and safety issues. State-of-the-art models that simulate the spread of epidemics operate on a population level, but the collection of fine-scale data might enable the development of models for epidemics that operate on a microscopic scale, similar to models for crowd movement. We provide an example of such simulations, showing how an individual-based crowd model can mirror aggregate susceptible-infected-recovered models that have been the main models for epidemics so far.

Mutual information for the detection of crush

Fatal crush conditions occur in crowds with tragic frequency. Event organizers and architects are often criticised for failing to consider the causes and implications of crush, but the reality is that both the prediction and prevention of such conditions offer a significant technical challenge. Full treatment of physical force within crowd simulations is precise but often computationally expensive; the more common method of human interpretation of results is computationally “cheap” but subjective and time-consuming. This paper describes an alternative method for the analysis of crowd behaviour, which uses information theory to measure crowd disorder. We show how this technique may be easily incorporated into an existing simulation framework, and validate it against an historical event. Our results show that this method offers an effective and efficient route towards automatic detection of the onset of crush.

Least-effort trajectories lead to emergent crowd behaviors

Pedestrian crowds often have been modeled as many-particle systems, usually using computer models known as multiagent simulations. The key challenge in modeling crowds is to develop rules that guide how the particles or agents interact with each other in a way that faithfully reproduces paths and behaviors commonly seen in real human crowds. Here, we propose a simple and intuitive formulation of these rules based on biomechanical measurements and the principle of least effort. We present a constrained optimization method to compute collision-free paths of minimum caloric energy for each agent, from which collective crowd behaviors can be reproduced. We show that our method reproduces common crowd phenomena, such as arching and self-organization into lanes. We also validate the flow rates and paths produced by our method and compare them to those of real-world crowd trajectories.

Improvement of pedestrian flow by slow rhythm

We have developed a simple model for pedestrians by dividing walking velocity into two parts, which are step size and pace of walking (number of steps per unit time). Theoretical analysis on pace indicates that rhythm that is slower than normal-walking pace in a low-density regime increases flow if the flow-density diagram is convex downward in a high-density regime. In order to verify this result, we have performed an experiment with real pedestrians and observed the improvement of flow in a congested situation using slow rhythm.