Crowd Dynamics, Volume 1 - Theory, Models, and Safety Problems

von: Livio Gibelli, Nicola Bellomo

Birkhäuser Basel, 2019

ISBN: 9783030051297

Sprache: Englisch

298 Seiten, Download: 9334 KB

Format: PDF, auch als Online-Lesen

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Crowd Dynamics, Volume 1 - Theory, Models, and Safety Problems

	Preface	6
	Contents	8
	Contributors	9
	Behavioral Human Crowds	11
	1 Plan of the Chapter	11
	2 On the Modeling of Crowd Dynamics	12
	3 On the Contents of the Edited Book	18
	4 Critical Analysis and Perspectives	20
	References	22
	Crowd Dynamics in Virtual Reality	25
	1 Introduction	26
	1.1 When to (Not) Use VR	27
	2 VR Studies of Crowd Behavior	29
	2.1 Comparing Virtual and Real Behavior	29
	2.1.1 Walking in VR	30
	2.1.2 Social Interactions in VR	30
	2.1.3 Comparing Crowd Dynamics in Real and Virtual Environments	31
	2.2 Crowd Dynamics in VR	34
	2.2.1 Behavioral Dynamics in VR	36
	2.3 VR Studies of Crowd Evacuation Behavior	38
	3 The Road Ahead	42
	References	43
	Pedestrian Movement in Smoke: Theory, Data and Modelling Approaches	47
	1 Introduction	47
	2 Theory and Data	49
	2.1 Fire Factors	49
	2.1.1 Visibility	50
	2.1.2 Irritancy	52
	2.1.3 Cognitive and Emotional Influences	53
	2.1.4 Tenability	53
	2.2 Pedestrian Factors	54
	2.2.1 Unimpeded Movement Speed	54
	2.2.2 Visual Acuity	54
	2.2.3 Physical Exertion	55
	2.3 Environmental Factors	55
	2.3.1 Geometric Complexity	55
	2.3.2 Way-Finding Systems	56
	2.3.3 Inclination, Stairs and Surface Material	56
	3 Modelling Pedestrian Movement in Smoke	57
	3.1 Modelling the Impact of Reduced Visibility Conditions	59
	3.2 Modelling Way-Finding in Smoke	63
	4 Discussion	65
	5 Conclusion	67
	References	67
	Pedestrian Dynamics: From Empirical Results to Modeling	73
	1 Introduction	73
	2 Empirical Results	74
	2.1 Observables: Flow, Density, and Velocity	75
	2.1.1 Flow	75
	2.1.2 Density	77
	2.1.3 Mean Speed	78
	2.2 Collective Phenomena	79
	2.2.1 Jamming and Clogging	79
	2.2.2 Density Waves, Stop-and-Go Waves	80
	2.2.3 Lane Formation	81
	2.2.4 Other Collective Effects	82
	2.2.5 Emergency Situations, ``Panic''	83
	2.3 Fundamental Diagram	83
	2.3.1 Single-File Movement in Circuit	83
	2.3.2 Pedestrian Movement in Straight Corridor	84
	2.3.3 Pedestrian Movement Through Bottlenecks	85
	2.3.4 Pedestrian Movement on Stairs	86
	2.3.5 Other Geometries	87
	3 Classification of Models	87
	3.1 Acceleration-Based Models	91
	3.2 Velocity-Based Models	93
	3.3 Decision-Based Models	95
	3.3.1 Cellular Automata	96
	3.3.2 Floor Field Model	97
	3.3.3 Other CA Models and Related Approaches	99
	4 Performance of Models: Quantitative and Qualitative ``Benchmarking''	100
	4.1 Stability Analysis	100
	4.2 Verification and Validation	101
	5 Summary	102
	References	103
	One-Dimensional Conservation Laws with Nonlocal Point Constraints on the Flux	113
	1 Introduction	113
	2 Nonlocally Constrained LWR	116
	2.1 Existence and Uniqueness Results	117
	2.2 Finite Volume Approximation	120
	2.3 Examples	122
	3 Locally Constrained ARZ	127
	3.1 Existence and Uniqueness Results	129
	3.2 Example	132
	4 Locally Constrained PT	137
	4.1 Existence Result	138
	4.2 Example	141
	References	143
	Measure-Theoretic Models for Crowd Dynamics	146
	1 Introduction	146
	2 Microscopic and Multi-scale Models	148
	2.1 Microscopic: The Social Force Models	148
	2.1.1 Panic	150
	2.2 Microscopic: Models for Animal Groups	150
	2.3 Microscopic: Cucker-Smale Model	151
	2.4 Multi-scale Models	152
	2.4.1 The Wasserstein Distance	153
	2.4.2 Existence and Uniqueness of Solutions to (6)	155
	2.4.3 Regularity of Interaction Kernels	156
	2.5 Wasserstein Distance and Total Variation Norm	158
	3 Mean-Field Limits of Microscopic Models	160
	3.1 Definition of the Mean-Field Limit	160
	3.2 The Mean-Field Limit of the Helbing-Molnár Model	163
	4 Microscopic Models with Varying Mass	165
	5 Measure Dynamics for Mass-Varying Models	168
	5.1 The Generalized Wasserstein Distance	168
	5.2 The Mean-Field Limit for Mass-Varying Models	169
	References	172
	Numerical Methods for Mean-Field and Moment Modelsfor Pedestrian Flow	175
	1 Introduction	175
	2 Pedestrian Flow Models	178
	2.1 A Microscopic Social Force Model with Optimal Path Computation	178
	2.2 Mean Field and Macroscopic Limits	180
	2.3 Scalar Macroscopic Models	184
	3 Numerical Methods	186
	3.1 Macroscopic Flow Simulation Using Finite-Volume Methods	186
	3.2 Particle Methods for Macroscopic Equations	187
	3.3 A Multi-scale Particle Method Based on the Mean-Field Approximation	189
	4 Numerical Results	189
	4.1 Numerical Transition from Microscopic to Macroscopic Description	189
	4.2 Numerical Comparison of Macroscopic Equations	192
	5 Multigroup Traffic	199
	5.1 The Microscopic Multigroup Model	199
	5.2 The Multigroup Hydrodynamic Model	201
	5.3 The Multigroup Scalar Model	202
	5.4 Numerical Results	203
	5.4.1 Comparison Between Single and Multigroup Pedestrian Flow Models with Weak and Strong Reciprocal Interaction	204
	5.4.2 Comparison Between Models with Weak and Strong Centre of Mass Attraction	204
	5.5 Discussion of Experimental Data	205
	6 Coupling Pedestrian to Traffic Flow	207
	6.1 The Traffic and Pedestrian Flow Model	207
	6.2 The Coupling	208
	6.3 Numerical Methods and Results	209
	7 Conclusions and Outlook	213
	References	214
	Modelling Interactions Between Active and Passive AgentsMoving Through Heterogeneous Environments	218
	1 Introduction	218
	2 Related Contributions	220
	3 Agent-Based Dynamics (Model 1)	221
	3.1 Active Agents	221
	3.2 Passive Agents	224
	3.3 Smoke Effects	226
	4 Results Model 1: Agent-Based Dynamics	227
	5 Lattice Gas Dynamics (Model 2)	231
	6 Results Model 2: Lattice Gas Dynamics	234
	7 Mathematical Aspects of Social Dynamics in Mixed Populations	235
	7.1 Technical Preliminaries, Notation, and Assumptions	236
	7.1.1 Geometry	236
	7.1.2 Function Spaces	236
	7.1.3 Hypotheses	238
	7.1.4 First-Order Social Agents Dynamics	238
	7.2 Well-Posedness	240
	7.3 Background Results	249
	7.3.1 A Regularized Eikonal Equation	249
	7.3.2 Higher Regularity Estimates for the Smoke Concentration	250
	8 Discussion	261
	References	262
	Pedestrian Models Based on Rational Behaviour	265
	1 Introduction	265
	2 A Model with Rational Behaviour	267
	2.1 Perception Stage	268
	2.1.1 Pairwise Encounters	268
	2.1.2 Assumptions on the Heuristics	269
	2.1.3 Global Encounters	270
	2.2 Decision Stage	271
	2.2.1 The Decision Potential	271
	2.2.2 A Choice of Potential	272
	2.3 A Gradient-Based Formulation	272
	2.3.1 Optimality Versus Efficiency	273
	2.4 Summary of the General Model	273
	3 Towards a High-Density Model	274
	3.1 A Frontal Collision	274
	3.2 Grading by Collision Severity	276
	3.3 Modelling Variable Speeds	277
	3.4 Environmental Coercion	280
	3.4.1 Repulsion as Anticipation	283
	3.4.2 Friction and the Fundamental Diagram	284
	3.5 Summary of the Modified Gradient Model	288
	4 Conclusion and Outlook	293
	Supplementary Material	295
	Data Statement	295
	References	295

Crowd Dynamics, Volume 1 - Theory, Models, and Safety Problems

von: Livio Gibelli, Nicola Bellomo

Crowd Dynamics, Volume 1 - Theory, Models, and Safety Problems

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