Multiscale Modeling of Pedestrian Dynamics

✍ Scribed by Emiliano Cristiani, Benedetto Piccoli, Andrea Tosin (auth.)

Publisher: Springer International Publishing
Year: 2014
Tongue: English
Leaves: 271
Series: MS&A 12
Edition: 1
Category: Library

No coin nor oath required. For personal study only.

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-xvi
Front Matter....Pages 1-1
An Introduction to the Modeling of Crowd Dynamics....Pages 3-27
Problems and Simulations....Pages 29-52
Psychological Insights....Pages 53-69
Front Matter....Pages 71-71
An Overview of the Modeling of Crowd Dynamics....Pages 73-107
Multiscale Modeling by Time-Evolving Measures....Pages 109-135
Basic Theory of Measure-Based Models....Pages 137-168
Evolution in Measure Spaces with Wasserstein Distance....Pages 169-194
Generalizations of the Multiscale Approach....Pages 195-219
Back Matter....Pages 221-262

✦ Subjects

Partial Differential Equations; Complex Systems; Mathematical Applications in the Physical Sciences; Mathematical Modeling and Industrial Mathematics; Game Theory, Economics, Social and Behav. Sciences; Applications of Mathematics

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