Propagation of chaos: a review of models, methods and applications. II. Applications

LP Chaintron, A Diez - arxiv preprint arxiv:2106.14812, 2021‏ - arxiv.org
The notion of propagation of chaos for large systems of interacting particles originates in
statistical physics and has recently become a central notion in many areas of applied …

Vehicular traffic, crowds, and swarms: From kinetic theory and multiscale methods to applications and research perspectives

G Albi, N Bellomo, L Fermo, SY Ha, J Kim… - … Models and Methods …, 2019‏ - World Scientific
This paper presents a review and critical analysis on the modeling of the dynamics of
vehicular traffic, human crowds and swarms seen as living and, hence, complex systems. It …

[ספר][B] Interacting multiagent systems: kinetic equations and Monte Carlo methods

L Pareschi, G Toscani - 2013‏ - books.google.com
The description of emerging collective phenomena and self-organization in systems
composed of large numbers of individuals has gained increasing interest from various …

Numerical methods for kinetic equations

G Dimarco, L Pareschi - Acta Numerica, 2014‏ - cambridge.org
In this survey we consider the development and mathematical analysis of numerical
methods for kinetic partial differential equations. Kinetic equations represent a way of …

[PDF][PDF] Asymptotic preserving (AP) schemes for multiscale kinetic and hyperbolic equations: a review

S ** - Lecture notes for summer school on methods and …, 2010‏ - researchgate.net
Kinetic and hyperbolic equations contain small scales (mean free path/time, Debye length,
relaxation or reaction time, etc.) that lead to various different asymptotic regimes, in which …

Kinetic models for epidemic dynamics in the presence of opinion polarization

M Zanella - Bulletin of Mathematical Biology, 2023‏ - Springer
Understanding the impact of collective social phenomena in epidemic dynamics is a crucial
task to effectively contain the disease spread. In this work, we build a mathematical …

Implicit–explicit schemes for BGK kinetic equations

S Pieraccini, G Puppo - Journal of Scientific Computing, 2007‏ - Springer
In this work a new class of numerical methods for the BGK model of kinetic equations is
presented. In principle, schemes of any order of accuracy in both space and time can be …

Uniformly accurate machine learning-based hydrodynamic models for kinetic equations

J Han, C Ma, Z Ma, WE - Proceedings of the National Academy of …, 2019‏ - pnas.org
A framework is introduced for constructing interpretable and truly reliable reduced models
for multiscale problems in situations without scale separation. Hydrodynamic approximation …

Particle based gPC methods for mean-field models of swarming with uncertainty

JA Carrillo, L Pareschi, M Zanella - arxiv preprint arxiv:1712.01677, 2017‏ - arxiv.org
In this work we focus on the construction of numerical schemes for the approximation of
stochastic mean--field equations which preserve the nonnegativity of the solution. The …

Binary interaction algorithms for the simulation of flocking and swarming dynamics

G Albi, L Pareschi - Multiscale Modeling & Simulation, 2013‏ - SIAM
Microscopic models of flocking and swarming take into account large numbers of interacting
individuals. Numerical resolution of large flocks implies huge computational costs. Typically …