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About this book

This volume collects ten surveys on the modeling, simulation, and applications of active particles using methods ranging from mathematical kinetic theory to nonequilibrium statistical mechanics. The contributing authors are leading experts working in this challenging field, and each of their chapters provides a review of the most recent results in their areas and looks ahead to future research directions. The approaches to studying active matter are presented here from many different perspectives, such as individual-based models, evolutionary games, Brownian motion, and continuum theories, as well as various combinations of these. Applications covered include biological network formation and network theory; opinion formation and social systems; control theory of sparse systems; theory and applications of mean field games; population learning; dynamics of flocking systems; vehicular traffic flow; and stochastic particles and mean field approximation. Mathematicians and other members of the scientific community interested in active matter and its many applications will find this volume to be a timely, authoritative, and valuable resource.

Table of Contents

Frontmatter

2017 | OriginalPaper | Chapter

Continuum Modeling of Biological Network Formation

Giacomo Albi, Martin Burger, Jan Haskovec, Peter Markowich, Matthias Schlottbom

2017 | OriginalPaper | Chapter

Recent Advances in Opinion Modeling: Control and Social Influence

Giacomo Albi, Lorenzo Pareschi, Giuseppe Toscani, Mattia Zanella

2017 | OriginalPaper | Chapter

Interaction Network, State Space, and Control in Social Dynamics

Aylin Aydoğdu, Marco Caponigro, Sean McQuade, Benedetto Piccoli, Nastassia Pouradier Duteil, Francesco Rossi, Emmanuel Trélat

2017 | OriginalPaper | Chapter

Variational Mean Field Games

Jean-David Benamou, Guillaume Carlier, Filippo Santambrogio

2017 | OriginalPaper | Chapter

Sparse Control of Multiagent Systems

Mattia Bongini, Massimo Fornasier

2017 | OriginalPaper | Chapter

A Kinetic Theory Approach to the Modeling of Complex Living Systems

Diletta Burini, Livio Gibelli, Nisrine Outada

2017 | OriginalPaper | Chapter

A Review on Attractive–Repulsive Hydrodynamics for Consensus in Collective Behavior

José A. Carrillo, Young-Pil Choi, Sergio P. Perez

2017 | OriginalPaper | Chapter

Emergent Dynamics of the Cucker–Smale Flocking Model and Its Variants

Young-Pil Choi, Seung-Yeal Ha, Zhuchun Li

2017 | OriginalPaper | Chapter

Follow-the-Leader Approximations of Macroscopic Models for Vehicular and Pedestrian Flows

M. Di Francesco, S. Fagioli, M. D. Rosini, G. Russo

2017 | OriginalPaper | Chapter

Mean Field Limit for Stochastic Particle Systems

Pierre-Emmanuel Jabin, Zhenfu Wang
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