Asymptotic Fixed-Speed Reduced Dynamics for Kinetic Equations in Swarming

Details Asymptotic Fixed-Speed Reduced Dynamics for Kinetic Equations in Swarming Asymptotic Fixed-Speed Reduced Dynamics for Kinetic Equations in Swarming

2012-02-29

arxiv.org/abs/1202.6557v1

Mathematics

Analysis of PDEs

Scientific paper

We perform an asymptotic analysis of general particle systems arising in collective behavior in the limit of large self-propulsion and friction forces. These asymptotics impose a fixed speed in the limit, and thus a reduction of the dynamics to a sphere in the velocity variables. The limit models are obtained by averaging with respect to the fast dynamics. We can include all typical effects in the applications: short-range repulsion, long-range attraction, and alignment. For instance, we can rigorously show that the Cucker-Smale model is reduced to the Vicsek model without noise in this asymptotic limit. Finally, a formal expansion based on the reduced dynamics allows us to treat the case of diffusion. This technique follows closely the gyroaverage method used when studying the magnetic confinement of charged particles. The main new mathematical difficulty is to deal with measure solutions in this expansion procedure.

Affiliated with

Also associated with

No associations

Rating

Asymptotic Fixed-Speed Reduced Dynamics for Kinetic Equations in Swarming does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Asymptotic Fixed-Speed Reduced Dynamics for Kinetic Equations in Swarming, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Asymptotic Fixed-Speed Reduced Dynamics for Kinetic Equations in Swarming will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-524239