## Collaborative Research: Kinetic Models of Aggregation and Dispersion

**Grant Number:**

**Funding Agency:** National Science Foundation

**PI:** Liu, Jian-Guo

**Effective Dates:** 2015/07-2018/06

**Amount:** $264,120

**Description:** Overview:
In many models of physical systems, coherent
states are formed and maintained by a balance
of competing influences. On the one hand,
focusing, concentration, or aggregation effects
are typically produced by nonlinear mechanisms.
These effects are often counterbalanced by
other processes, usually linear, that disperse,
defocus, fragment, or spread things out in
some way. This proposal concerns a variety of
problems which involve competition of this
kind, whose solution will require the development
of novel and interesting mathematical tools
concerning nonlinear dynamics in high-dimensional
systems..