Active Particles, Volume 4 Theory, Models, Applications

This edited volume collects nine surveys that present the state-of-the-art in modeling, qualitative analysis, and simulation of active particles, focusing on specific applications in the natural sciences. As in the preceding Active Particles volumes, it blends diverse applications that demonstrate the interdisciplinary nature of the subject and the various mathematical tools available. Contributions were selected with the aim of covering a variety of viewpoints, from modeling the interactions in collective dynamics of animals and in population dynamics; through neural-networks, semi-supervised learning, and Monte Carlo methods in optimization; to kinetic and continuum theories with applications to aggregations and birth-and-death processes.  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.

1 Consistency of Semi-supervised Learning, Stochastic Tug-of-War Games, and the p-Laplacian.- 2 Discrete Minimizers of the Interaction Energy in Collective Behavior.- 3 Large-Population Limits of Non-Exchangeable Particle Systems.- 4 Models of Animal Behavior as Active Particle Systems with Nonreciprocal Interactions.- 5 Bayesian Sampling Using Interacting Particles.- 6 Aggregation-Diffusion Phenomena.- 7 Conservative Semi-Lagrangian Methods for Kinetic Equations.- 8 Large Population Limit of Interacting Population Dynamics via Generalized Gradient Structures.- 9 Adjoint Monte Carlo Method.

Eitan Tadmor is a Distinguished University Professor at the University of Maryland, College Park. Previously, he held professorship positions at Tel-Aviv University and at UCLA, where he was the founding co-director of IPAM.  He was also a Senior Fellow at ETH-ITS in Zurich, and held a FSMP Chair of excellence hosted at Sorbonne University.

Tadmor’s work on the interplay between analytical theories and computational aspects of time-dependent problems, with applications to shock waves, kinetic transport, image processing and collective dynamics, was awarded the SIAM-ETH Henrici prize and AMS-SIAM Norbert Wiener prize in Applied Mathematics. He is an AMS and SIAM Fellow, and member of Academia Europaea and the European Academy of Sciences.

José Antonio Carrillo is Professor of the Analysis of Nonlinear Partial Differential Equations at the Mathematical Institute and Tutorial Fellow in Applied Mathematics at The Queen's College, University of Oxford. He held professorship positions at Imperial College London, the Universitat Autònoma de Barcelona, and the Universidad de Granada. He served as chair of the Applied Mathematics Committee of the European Mathematical Society. He was awarded the GAMM 2006 Richard Von-Mises prize for young researchers, a 2012 Wolfson Research Merit Award by the Royal Society, and the 2022 Echegaray Medal of the Royal Spanish Academy of Sciences.

He works on kinetic and nonlinear nonlocal diffusion equations. He has contributed to the theoretical and numerical analysis of these PDE models, and their simulation in different applications such as collective behaviour and self-organization, and their implications in mathematical biology, control engineering and global optimization. He is a SIAM Fellow, and member of the Royal Spanish Academy of Sciences, Academia Europaea and the European Academy of Sciences.