| Foreword |
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1 | (12) |
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1.1 From Passive to Active Entities |
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1 | (2) |
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1.2 Basics on Crowd Motion Modeling |
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3 | (2) |
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1.3 The Mathematical Standpoint |
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5 | (7) |
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1.4 How to Use this Book? |
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12 | (1) |
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2 One-Dimensional Microscopic Models |
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13 | (24) |
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2.1 Follow-the-Leader Model |
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14 | (16) |
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2.2 Accounting for Inertia/Delays |
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30 | (7) |
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3 Social Force Model, Native and Overdamped Forms |
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37 | (22) |
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3.1 Inertial Social Force Model |
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37 | (12) |
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3.2 Overdamped Social Force Model |
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49 | (7) |
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3.3 Alternative Approaches |
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56 | (3) |
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59 | (24) |
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4.1 One-Dimensional Model |
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59 | (2) |
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4.2 Two-Dimensional Model |
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61 | (3) |
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64 | (2) |
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4.4 Numerical Experiments |
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66 | (2) |
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68 | (8) |
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76 | (7) |
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83 | (14) |
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5.1 Cellular Automata: General Principles |
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84 | (1) |
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85 | (7) |
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5.3 Variations, Extensions |
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92 | (1) |
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5.4 Cellular Automata, Mathematical Issues |
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93 | (4) |
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97 | (14) |
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6.1 Compartment Models: Toy Versions and General Setting |
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97 | (4) |
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101 | (1) |
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102 | (2) |
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6.4 Numerical Illustration |
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104 | (1) |
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6.5 Mathematical Framework: A Cascade of Gradient Flows |
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104 | (7) |
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7 Toward Macroscopic Models |
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111 | (16) |
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7.1 One-Dimensional Macroscopic Traffic Model |
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112 | (3) |
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7.2 Two-Dimensional Models |
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115 | (2) |
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7.3 Granular Models: Hard Congestion |
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117 | (6) |
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123 | (2) |
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7.5 Alternative Macroscopic Models |
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125 | (2) |
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8 Computing Distances and Desired Velocities |
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127 | (18) |
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8.1 Shortest Path Problem on a Graph |
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130 | (2) |
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8.2 Shortest Path on a Domain: The Eikonal Equation |
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132 | (3) |
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8.3 Non-homogenous Domains, Various Extensions |
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135 | (4) |
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8.4 Shortest Paths in a Dynamic Environment |
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139 | (3) |
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8.5 Alternative Way to Compute Desired Velocities |
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142 | (1) |
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143 | (2) |
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9 Data, Observable Phenomena |
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145 | (16) |
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145 | (1) |
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9.2 Proxernics, Interpersonal Distances, Density |
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146 | (2) |
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148 | (1) |
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9.4 Pedestrian Speed, Fundamental Diagram |
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148 | (3) |
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151 | (1) |
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9.6 Capacity Drop Phenomenon |
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151 | (1) |
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9.7 Faster-is-Slower Effect |
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152 | (2) |
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9.8 Influence of an Obstacle |
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154 | (3) |
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157 | (1) |
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9.10 Further Considerations on Human Behavior |
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158 | (3) |
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10 A Wider Look on Characteristic Phenomena in Crowds |
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161 | (16) |
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10.1 Faster-is-Slower Effect |
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161 | (7) |
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10.2 Fluidizing Effect of an Obstacle |
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168 | (2) |
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10.3 Damping, Propagation, and Stop-and-Go Waves |
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170 | (7) |
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177 | (6) |
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A.1 Ordinary Differential Equations |
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177 | (3) |
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A.2 Constrained Optimization |
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180 | (3) |
| Bibliography |
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183 | (6) |
| Index |
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189 | |
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