Propagation of chaos: a review of models, methods and applications. II. Applications
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 …
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
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 …
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 …
composed of large numbers of individuals has gained increasing interest from various …
Numerical methods for kinetic equations
In this survey we consider the development and mathematical analysis of numerical
methods for kinetic partial differential equations. Kinetic equations represent a way of …
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
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 …
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
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 …
task to effectively contain the disease spread. In this work, we build a mathematical …
Implicit–explicit schemes for BGK kinetic equations
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 …
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
A framework is introduced for constructing interpretable and truly reliable reduced models
for multiscale problems in situations without scale separation. Hydrodynamic approximation …
for multiscale problems in situations without scale separation. Hydrodynamic approximation …
Particle based gPC methods for mean-field models of swarming with uncertainty
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 …
stochastic mean--field equations which preserve the nonnegativity of the solution. The …
Binary interaction algorithms for the simulation of flocking and swarming dynamics
Microscopic models of flocking and swarming take into account large numbers of interacting
individuals. Numerical resolution of large flocks implies huge computational costs. Typically …
individuals. Numerical resolution of large flocks implies huge computational costs. Typically …