| Description |
1 online resource |
| Series |
MS & A, Modeling, Simulation and Applications, 2037-5255 ; volume 12 |
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MS & A (Series) ; volume 12
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| Contents |
880-01 1 An Introduction to the Modeling of Crowd Dynamics -- 2 Problems and Simulations -- 3 Psychological Insights -- 4 An Overview of the Modeling of Crowd Dynamics -- 5 Multiscale Modeling by Time-Evolving Measures -- 6 Basic Theory of Measure-Based Models -- 7 Evolution in Measure Spaces with Wasserstein Distance -- 8 Generalizations of the Multiscale Approach -- 9 Appendices: A Basics of Measure and Probability Theory; B Pseudo-Code for the Multiscale Algorithm |
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880-01/(S Machine generated contents note: pt. I Pedestrian Behavior: Phenomenology and Simulations -- 1. Introduction to the Modeling of Crowd Dynamics -- 1.1. Modeling-Oriented Phenomenological Issues -- 1.1.1. Behavioral Rules -- 1.1.2. Self-Organization -- 1.2. Preliminary Reasonings on Mathematical Modeling -- 1.2.1. Crowds as a Living Complex System -- 1.2.2. Scaling and Representation -- 1.2.3. Critical Analysis -- 1.3. Interplay Between Modeling and Experimenting -- 1.3.1. Fundamental Diagrams -- 1.3.2. Data on Emerging Collective Behaviors -- 1.3.3. Data on Individual Behaviors and on Interactions -- 1.4. Book Contribution -- 1.4.1. Multiscale Approach -- 1.4.2. Generalizations and Applications to Other Fields -- 1.4.3. Purpose and Structure of the Book -- 1.5. Bibliographical Notes -- 2. Problems and Simulations -- 2.1. Informal Introduction to the Multiscale Model -- 2.2. Effects of Repulsion -- 2.3. Metric vs. Topological Attraction -- 2.4. Flow Through a Bottleneck -- 2.5. Crossing Flows -- 2.5.1. Lane Formation -- 2.5.2. Intermittent Flow -- 2.6. Social Groups and One-Many Interactions -- 2.7. Bibliographical Notes -- 3. Psychological Insights -- 3.1. Wide Literatures -- 3.2. Specific Characteristics of Pedestrians -- 3.2.1. Cognitive Maps -- 3.2.2. Geographical and Social Features -- 3.2.3. Self-Organization and Re-organization -- 3.3. Models for the Single Pedestrian -- 3.3.1. 2/3 Power Law and Other Empirical Laws -- 3.3.2. Models of Path Choice -- 3.4. Experimental Settings and Measurements -- 3.4.1. Experimental Setting -- 3.4.2. Measurements -- 3.4.3. Comparison of Different Experimental Settings -- 3.5. Bibliographical Notes -- pt. II Modeling and Mathematical Problems -- 4. Overview of the Modeling of Crowd Dynamics -- 4.1. Microscopic Models -- 4.1.1. Force Models -- 4.1.2. Maury and Venel's Model -- 4.1.3. Cellular Automata Models -- 4.1.4. Discrete Choice Models -- 4.2. Macroscopic Models -- 4.2.1. Fundamental Diagram -- 4.2.2. Coscia and Canavesio's Model -- 4.2.3. Colombo and Rosini's Model -- 4.2.4. Maury et al.'s Model -- 4.2.5. Nonlocal Models -- 4.2.6. Bellomo and Dogbe's Model -- 4.3. Mesoscopic Models -- 4.3.1. Dogbe's Model -- 4.3.2. Bellomo and Bellouquid's Model -- 4.4. Models for Rational Pedestrians -- 4.4.1. Arechavaleta et al.'s Model -- 4.4.2. Hoogendoorn and Bovy's Microscopic Model -- 4.4.3. Eikonal Equation and Minimum Time Problems -- 4.4.4. Hughes' Model -- 4.4.5. Hoogendoorn and Bovy's Macroscopic Model -- 4.4.6. Mean Field Game Models -- 4.4.7. Playing with Rationality -- 4.5. Bibliographical Notes -- 5. Multiscale Modeling by Time-Evolving Measures -- 5.1. Conservation Laws by Time-Evolving Measures -- 5.2. Velocity from Planning and Interactions -- 5.2.1. Desired Velocity -- 5.2.2. Interaction Velocity -- 5.2.3. Metric and Topological Interactions -- 5.3. Recovering Single-Scale Models -- 5.3.1. Microscopic Models -- 5.3.2. Macroscopic Models -- 5.4. Multiscale Model -- 5.5. Multiscale Numerical Scheme -- 5.5.1. Discrete-in-Time Model -- 5.5.2. Spatial Approximation -- 5.5.3. Algorithm -- 5.6. Two-Population Models -- 5.7. Bibliographical Notes -- 6. Basic Theory of Measure-Based Models -- 6.1. Phenomenological Model with Perception -- 6.2. From the Phenomenological to a Mathematical-Physical Model -- 6.3. Probabilistic Interpretation -- 6.4. Uniqueness and Continuous Dependence of the Solution -- 6.5. Existence of the Solution -- 6.6. Approximation of the Solution -- 6.7. Spatial Structure of the Solution -- 6.8. Study of Pedestrian Velocity Models -- 6.9. Bibliographical Notes -- 7. Evolution in Measure Spaces with Wasserstein Distance -- 7.1. Homogeneous Nonlinear Evolution Equation -- 7.2. Transport Equation, Optimal Transportation, and the Wasserstein Distance -- 7.2.1. Wasserstein Distance Under the Action of Flows -- 7.2.2. Existence and Uniqueness of Solutions -- 7.3. Lagrangian and Eulerian Numerical Schemes -- 7.3.1. Discrete Lagrangian Scheme with Velocity of Centers -- 7.3.2. Eulerian Scheme -- 7.4. Interaction Velocities for Pedestrians -- 7.5. Transport Equation with Source -- 7.6. Generalized Wasserstein Distance -- 7.7. Existence and Uniqueness of Solutions for the Transport Equation with Source -- 7.8. Bibliographical Notes -- 8. Generalizations of the Multiscale Approach -- 8.1. Second Order Time-Evolving Measures -- 8.1.1. Phenomenological Microscopic Model -- 8.1.2. Mathematical-Physical Model -- 8.1.3. Mass and Momentum Equations -- 8.1.4. Monokinetic Solutions -- 8.2. Multidimensional Multiscale Coupling -- 8.3. Space-Time-Dependent Multiscale Coupling -- 8.4. More General ODE-PDE Coupling -- 8.4.1. Coupling the Heat Equation and the Brownian Motion -- 8.4.2. Numerical Approximation of the Coupled Equation -- 8.5. Conclusions -- 8.6. Bibliographical Notes -- A. Basics of Measure and Probability Theory -- A.1. Measurable Spaces, Measures, and Measurable Functions -- A.1.1. Sets and Operations with Sets -- A.1.2. σ-Algebras and Measurable Spaces -- A.1.3. Measures -- A.1.4. Measurable Functions -- A.2. Integration with Respect to an Abstract Measure -- A.3. Decomposition of a Measure -- A.4. Probabilities -- A.4.1. Events, Operations with Events, and σ-Algebras -- A.4.2. Probability Measures -- A.4.3. Random Variables -- A.4.4. Integrals of Random Variables -- A.5. Product Spaces, Marginals, and Disintegration of a Measure -- A.6. Wasserstein Distance in Probability Spaces -- A.7. Measures as Distributions -- A.8. Bibliographical Notes -- B. Pseudo-code for the Multiscale Algorithm -- B.1. Preliminaries -- B.2. Pseudo-code |
| Summary |
This book presents mathematical models and numerical simulations of crowd dynamics. The core topic is the development of a new multiscale paradigm, which bridges the microscopic and macroscopic scales taking the most from each of them for capturing the relevant clues of complexity of crowds. The background idea is indeed that most of the complex trends exhibited by crowds are due to an intrinsic interplay between individual and collective behaviors. The modeling approach promoted in this book pursues actively this intuition and profits from it for designing general mathematical structures susceptible of application also in fields different from the inspiring original one. The book considers also the two most traditional points of view: the microscopic one, in which pedestrians are tracked individually, and the macroscopic one, in which pedestrians are assimilated to a continuum. Selected existing models are critically analyzed. The work is addressed to researchers and graduate students |
| Analysis |
mathematische natuurkunde |
|
mathematical physics |
|
systemen |
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systems |
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wiskunde |
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mathematics |
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partial differential equations |
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wiskundige modellen |
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mathematical models |
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toegepaste wiskunde |
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applied mathematics |
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speltheorie |
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game theory |
|
Mathematics (General) |
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Wiskunde (algemeen) |
| Bibliography |
Includes bibliographical references and index |
| Subject |
Pedestrians -- Psychology
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Pedestrian traffic flow -- Mathematical models
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BUSINESS & ECONOMICS -- Industries -- Transportation.
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TRANSPORTATION -- Public Transportation.
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Pedestrians -- Psychology
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| Form |
Electronic book
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| Author |
Piccoli, Benedetto
|
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Tosin, Andrea.
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| ISBN |
9783319066202 |
|
331906620X |
|
3319066196 |
|
9783319066196 |
|
9783319066219 |
|
3319066218 |
|
9783319361215 |
|
331936121X |
|
