Active Particles, Volume 1

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

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.

• 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

• 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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