101 Reproducing crowd turbulence with Verlet integration and agent modeling Albert Gutierrez-Milla 1,2 and Remo Suppi 2 1 Barcelona Supercomputing Center 2 Universitat Autònoma de Barcelona albert.gutierrez@bsc.es, remo.suppi@uab.cat Abstract – High density crowds are risk situations that already had turned some events into disasters. There are particular emerging events in these crowds that had led to dangerous situations. One important phenomenon is named “crowd turbulence”. It is produced by a propagation of forces among the mass and has already been the cause of several tragedies. We present a new approach to its representation and understanding by a hybrid model composed by two parts: physical interaction among the agents, and psychological factors that produce voluntary interactions. The focus of the present work is contributing with a model able to reproduce such events in a computationally efficient way on SIMD architectures. I. INTRODUCTION A crowd under high density conditions is a potential disaster situation. Understanding and developing models to characterize the crowd helps the security assessment process for building design, event planning, evacuation planning, etc. Previous disasters such as Love Parade (Duisburg), or Hajj (Mina)[1] showed that there is still a lack of knowledge and a there is a need of understanding such situations. There is a particular phenomena reproduced in the case of crowds were the pressure is propagated through the mass potentially causing crashed chests. This effect is named “crowd turbulence”. We present a model capable of reproduce crowd turbulence and we implemented a simulator for SIMD architectures using OpenCL. II. MODEL In crowd turbulences, interactions among the bodies are described as a wave propagating forces and the mass inertia. We consider that this event can be model by particle simulation and to complete the model we include human behavior in every person. To model the physics of the movement, navigation and inertia we chose Verlet method which integrates Newton's second law of motion. For the psychological part we use Agent Based Modelling (ABM) to model the voluntary actions of the population. Consequently, bodies of the people are modeled as particles and as agents. Using the second order central method we express the equation of motion as finite differences. Formula 1 shows the equations for coordinates in a bidimensional space. For simplicity we will not consider the mass as variable and the value of the acceleration is a constant defined as a parameter of the model and is applied until the agent reaches its vmax, then only the inertia phase is computed. The velocity chosen for the agents follows a normal distribution with a mean of 1.34m/s and a standard deviation of 0.26m/s[2], navigating towards a specific goal e. When two agents intersect the collision is solved by a simplified technique to solve inelastic collision losing kinetic energy. This is done by using a factor which depends on the intersection between two agents. Even though agents are dragged by the mass in case of turbulence, people do not move as particles. They offer resistance to external interactions and also try to gain free space by pushing others expressing their will. Thus, we model intentional and involuntary pushes. Involuntary take place when a person is moved by the crowd and those are modeled by Verlet integration. Voluntary interactions come from psychological factors and are modeled in every agent. Moreover not every person has a tendency in pushing other. Apathy, empathy or neurotic behavior may have a direct impact in the behavior of people during evacuations. To map these non-homogeneous human treats to the model we describe their tendency to push others. Every agent follows a path declared by a graph were there are some areas named “decisions points” which define the navigation route of the agent. These are nodes, and when the agent is close to it, the goal position e is updated to the next node. We assume that agents know the shortest path and there is no uncertainty added. The size of the agent is modeled by a circle with a dimeter of 0.4m and a standard deviation of 0.1m.