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Active Particles, Volume 1

Advances in Theory, Models, and Applications

  • Book
  • © 2017

Overview

Editors:
  1. Nicola Bellomo

    1. Department of Mathematical Sciences, King Abdulaziz University, Jeddah, Saudi Arabia

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  2. Pierre Degond

    1. Department of Mathematics, Imperial College London, London, United Kingdom

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    You can also search for this editor in PubMed   Google Scholar

  3. Eitan Tadmor

    1. CSCAMM, University of Maryland, College Park, USA

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    You can also search for this editor in PubMed   Google Scholar

  • Explores the most recent advances and methods for applications of active particles
  • Contributing authors are leading researchers in their respective areas
  • Numerous applications of active particles covered, such as biological network formation, population learning, and vehicular traffic flow
  • Includes supplementary material: sn.pub/extras

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Table of contents (10 chapters)

  1. Front Matter

    Pages i-x
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  2. Continuum Modeling of Biological Network Formation

    • Giacomo Albi, Martin Burger, Jan Haskovec, Peter Markowich, Matthias Schlottbom
    Pages 1-48

  3. Recent Advances in Opinion Modeling: Control and Social Influence

    • Giacomo Albi, Lorenzo Pareschi, Giuseppe Toscani, Mattia Zanella
    Pages 49-98

  4. Interaction Network, State Space, and Control in Social Dynamics

    • Aylin Aydoğdu, Marco Caponigro, Sean McQuade, Benedetto Piccoli, Nastassia Pouradier Duteil, Francesco Rossi et al.
    Pages 99-140

  5. Variational Mean Field Games

    • Jean-David Benamou, Guillaume Carlier, Filippo Santambrogio
    Pages 141-171

  6. Sparse Control of Multiagent Systems

    • Mattia Bongini, Massimo Fornasier
    Pages 173-228

  7. A Kinetic Theory Approach to the Modeling of Complex Living Systems

    • Diletta Burini, Livio Gibelli, Nisrine Outada
    Pages 229-258

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

    • José A. Carrillo, Young-Pil Choi, Sergio P. Perez
    Pages 259-298

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

    • Young-Pil Choi, Seung-Yeal Ha, Zhuchun Li
    Pages 299-331

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

    • M. Di Francesco, S. Fagioli, M. D. Rosini, G. Russo
    Pages 333-378

  11. Mean Field Limit for Stochastic Particle Systems

    • Pierre-Emmanuel Jabin, Zhenfu Wang
    Pages 379-402
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Keywords

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; andstochastic 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.

Editors and Affiliations

  • Department of Mathematical Sciences, King Abdulaziz University, Jeddah, Saudi Arabia

    Nicola Bellomo

  • Department of Mathematics, Imperial College London, London, United Kingdom

    Pierre Degond

  • CSCAMM, University of Maryland, College Park, USA

    Eitan Tadmor

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