1. Glossary of Technical Terms Cellular Automata: A regular array of identical finite state automata whose next state is determined solely by their current state and the state of their neighbors. Bosons: Elementary particles that give the agents information about their surroundings. These particles are dropped by the agents when they occupy a cell, and other individuals are attracted to these particles. This can be likened to ants leaving a pheromone trail to signal a pathway for others to follow. Project Description Goal: To accurately model the movement of individuals in a crowd out of a room through a single or multiple exits. Take into account different levels of urgency with regard to the context of the exit circumstances. Expand the model to include different parameters such as individuals pushing or shoving, as well as the possibility for injuries. Take into account human behavior in crowd situations such as maintaining a certain amount of personal space and increased urgency as proximity to the exit increases. Scientific Challenges & Potential Applications To accurately model an individual’s movement while taking into account a certain degree of intelligence and free will. Planning escape routes for buildings. Determining room capacities for building coding. Modeling Crowd Dynamics Brent Morgan 1, 2, Krista Parry 1, 3, Andy Platta 1, 3, Mitch Wilson 1, 4 1 Mathematics, 2 Engineering Physics, 3 Chemistry, 4 Mechanical Engineering Published Models for Crowd Dynamics Simulation of Evacuation Processes Using a Bionics-Inspired Cellular Automaton Model for Pedestrian Dynamics, by Ansgar Kirchner: Introduces the Kirchner Field Model. This model simulates the evacuation of people from a room. People’s movements are determined probabilistically with the probability distribution depending on proximity to the door and the movement of other agents. We will refer to this model as the Kirchner model. Macroscopic Effects of Microscopic Forces Between Agents in Crowd Models, by Colin M. Henein: Implements many of the ideas used in the Kirchner Field Model but adds to it with the addition of a force field that simulates agents pushing. This allows the addition of injuries to the model which render agents immobile. We will refer to this model as the Swarm Force model. Figure 3: Graphs of people remaining in room as a function of time. K d, see key, K s =3. Methodology 1.Used method of direct computer simulation and cellular automata to construct a grid representation of a room with a single exit. 2.Constructed a probability distribution of an individual’s 8 neighboring cells, based on factors such as the proximity to the door, and previous paths of individuals. (Equations shown on right). 3.Determine which individual moves first at each time step based on a Force Determining equation which is inversely related to the distance to the door. 4.Use concepts from Kirchner Field Model [4] and Swarm Force Model [1]; use a dynamic and static field to determine the individual’s most probable move and include injuries of individuals due to pushing or crowding. 5.The static field will be inversely related to the distance to the door, thus the cell that is closer to the door will have a higher probability that the individual will move to it. 6.The dynamic field keeps track of the bosons that individuals have left when previously occupying the cell. This raises the probability of an individual moving to the cell to simulate individuals following others if a path is successful. 7.The dynamic and static fields are weighted differently based on proximity to the door. 8.Pushing is allowed, and if an individual is pushed past the threshold, they will become permanently injured, indicated by a red dot in the following graphs. Results References 1.Henin, C. M. & White, T. Macroscopic Effects of Microscopic Forces Between Agents in Crowd Models. Physica. A 373, 694-712 (2007). 2.Weng, W.G., Pan, L.L., Shen, S.F., Yuan, H.Y. Small-grid Analysis of Discrete Model for Evacuation from a Hall. Physica. A 374, 821-826 (2007). 3.Seyfried, A., Steffen, B., Lippert, T. Basics of Modelling the Pedestrian Flow. Physica A 368, 232-238 (2006). 4.Kirchner, Ansgar & Schadschneider, Andreas. Simulation of Evacuation Processes Using a Bionics-Inspired Cellular Automaton Model for Pedestrian Dynamics. Physica. A 312, 260-276 (2002). Acknowledgments This project was mentored by Jorge Ramirez, whose help is acknowledged with great appreciation. Support from a University of Arizona TRIF (Technology Research Initiative Fund) grant to J. Lega is also gratefully acknowledged. Equations Modified Swarm Force equation : Literature Swarm Force equation: Force Determining equation: Parameters P ij : Probability of individual moving to cell (i, j) N: Normalization coefficient B ij : Normalized dynamic preference factor  ij : Occupancy of the cell (i,j) k D : Dynamic field coefficient k S : Static field coefficient R ij : Normalized static preference factor D ij: : Literature dynamic preference factor S ij : Literature static preference factor  ij : Swarm Force parameter, based on occupancy  ij : Swarm Force parameter, based on walls F ij : Force in determining movement order of individuals (X, Y): Coordinates of the exit door Figure 1: Method determining order of individual movement per time step, depending on the Force Determining equation. Figure 2: Series of screen shots at increasing time steps during one trial with K s =3, K d =2. Active agents denoted in blue, injured agents denoted in red. Figure 4: Plot of number injured as a function of the injury threshold. K s =3, K d =3 Figure 5: Plot of percentage of individuals leaving the room as a function of density of individuals in the room. K s =3, K d =2 Based on our implications of the Swarm and Kirchner models, we found that even with our normalized parameters B ij and R ij, we were able to recreate graphs and movement patterns as in the two comparable models. We were able to observe similar trends regarding parameter values, such as comparing k s and k d. We were also able to verify patterns relating to the injury threshold and the percentage of people that escape given an increasing number of initial individuals. See the accompanying figures for illustrations.