Active Particles, Volume 1

Advances in Theory, Models, and Applications

  • Nicola Bellomo
  • Pierre Degond
  • Eitan Tadmor

Table of contents

  1. Front Matter
    Pages i-x
  2. Giacomo Albi, Martin Burger, Jan Haskovec, Peter Markowich, Matthias Schlottbom
    Pages 1-48
  3. Giacomo Albi, Lorenzo Pareschi, Giuseppe Toscani, Mattia Zanella
    Pages 49-98
  4. Aylin Aydoğdu, Marco Caponigro, Sean McQuade, Benedetto Piccoli, Nastassia Pouradier Duteil, Francesco Rossi et al.
    Pages 99-140
  5. Jean-David Benamou, Guillaume Carlier, Filippo Santambrogio
    Pages 141-171
  6. Mattia Bongini, Massimo Fornasier
    Pages 173-228
  7. Diletta Burini, Livio Gibelli, Nisrine Outada
    Pages 229-258
  8. José A. Carrillo, Young-Pil Choi, Sergio P. Perez
    Pages 259-298
  9. Young-Pil Choi, Seung-Yeal Ha, Zhuchun Li
    Pages 299-331
  10. M. Di Francesco, S. Fagioli, M. D. Rosini, G. Russo
    Pages 333-378
  11. Pierre-Emmanuel Jabin, Zhenfu Wang
    Pages 379-402

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.


Mathematical Kinetic Theory of Active Particles Nonequilibrium Statistical Mechanics Biological Network Formation Opinion Modeling Variational Mean Field Games Sparse Control of Multi-Agent Systems Complex Systems Hydrodynamic Models of Collective Behavior Cucker-Smale Flocking Model Follow-the-Leader Apporximations Vehicular Flows Pedetrian Flows Stochastic Particle Systems

Editors and affiliations

  • Nicola Bellomo
    • 1
  • Pierre Degond
    • 2
  • Eitan Tadmor
    • 3
  1. 1.Department of Mathematical SciencesKing Abdulaziz UniversityJeddahSaudi Arabia
  2. 2.Department of MathematicsImperial College LondonLondonUnited Kingdom
  3. 3.CSCAMMUniversity of MarylandCollege ParkUSA

Bibliographic information