scholarly journals Long Time Behavior of Particle Systems in the Mean Field Limit

2007 ◽  
Vol 5 (5) ◽  
pp. 11-19 ◽  
Author(s):  
Emanuele Caglioti ◽  
Frédéric Rousset
Keyword(s):  
Mean Field ◽  
Particle Systems ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Field Limit ◽  
Mean Field Limit ◽  
Long Time ◽  
The Mean

Long Time Estimates in the Mean Field Limit

2008 ◽  
Vol 190 (3) ◽  
pp. 517-547 ◽  
Author(s):  
E. Caglioti ◽  
F. Rousset
Keyword(s):  
Mean Field ◽  
Field Limit ◽  
Mean Field Limit ◽  
Time Estimates ◽  
Long Time ◽  
The Mean

Well-posedness and asymptotic behavior of an aggregation model with intrinsic interactions on sphere and other manifolds

2021 ◽  
pp. 1-53
Author(s):  
Razvan C. Fetecau ◽  
Hansol Park ◽  
Francesco S. Patacchini
Keyword(s):  
Riemannian Manifolds ◽  
Collective Behavior ◽  
Mean Field ◽  
Sufficient Conditions ◽  
Well Posedness ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Long Time ◽  
The Mean ◽  
Particle Approximation

We investigate a model for collective behavior with intrinsic interactions on Riemannian manifolds. We establish the well-posedness of measure-valued solutions (defined via mass transport) on sphere, as well as investigate the mean-field particle approximation. We study the long-time behavior of solutions to the model on sphere, where the primary goal is to establish sufficient conditions for a consensus state to form asymptotically. Well-posedness of solutions and the formation of consensus are also investigated for other manifolds (e.g., a hypercylinder).

scholarly journals Instantaneous control of interacting particle systems in the mean-field limit

2020 ◽  
Vol 405 ◽  
pp. 109181 ◽  
Author(s):  
Martin Burger ◽  
René Pinnau ◽  
Claudia Totzeck ◽  
Oliver Tse ◽  
Andreas Roth
Keyword(s):  
Interacting Particle Systems ◽  
Mean Field ◽  
Particle Systems ◽  
Field Limit ◽  
Mean Field Limit ◽  
Interacting Particle ◽  
The Mean ◽  
Instantaneous Control

scholarly journals The Microscopic Derivation and Well-Posedness of the Stochastic Keller–Segel Equation

2020 ◽  
Vol 31 (1) ◽  
Author(s):  
Hui Huang ◽  
Jinniao Qiu
Keyword(s):  
Existence Of Solutions ◽  
Particle System ◽  
Mean Field ◽  
Field Limit ◽  
Mean Field Limit ◽  
Unique Existence ◽  
Interacting Particle ◽  
Microscopic Derivation ◽  
The Mean ◽  
Limit Result

AbstractIn this paper, we propose and study a stochastic aggregation–diffusion equation of the Keller–Segel (KS) type for modeling the chemotaxis in dimensions $$d=2,3$$ d = 2 , 3 . Unlike the classical deterministic KS system, which only allows for idiosyncratic noises, the stochastic KS equation is derived from an interacting particle system subject to both idiosyncratic and common noises. Both the unique existence of solutions to the stochastic KS equation and the mean-field limit result are addressed.

scholarly journals Limit Theorems and Fluctuations for Point Vortices of Generalized Euler Equations

2021 ◽  
Vol 182 (3) ◽  
Author(s):  
Carina Geldhauser ◽  
Marco Romito
Keyword(s):  
Euler Equations ◽  
Mean Field ◽  
Point Vortices ◽  
Positive Temperature ◽  
Field Limit ◽  
Mean Field Limit ◽  
Large Numbers ◽  
The Mean ◽  
Formal Solutions ◽  
2D Torus

AbstractWe prove a mean field limit, a law of large numbers and a central limit theorem for a system of point vortices on the 2D torus at equilibrium with positive temperature. The point vortices are formal solutions of a class of equations generalising the Euler equations, and are also known in the literature as generalised inviscid SQG. The mean-field limit is a steady solution of the equations, the CLT limit is a stationary distribution of the equations.

Sign in / Sign up

Export Citation Format

Share Document