Speaker:

Govind Menon, Brown University

Title:

"Min-driven Clustering"

Abstract:

The study of domain coarsening in the Allen-Cahn equation has several
interesting dynamical aspects such as metastability and connections
with a hierarchy of reduced models for clustering. Motivated by this
problem, we consider a process (`min-driven clustering') that may be
described informally as follows: at each step a random integer $k$ is
chosen with probability $p_k$ and the smallest cluster merges with $k$
randomly chosen clusters.

We study a mean-field model of this process. We prove optimal results
on well-posedness, the approach to self-similarity, and the
classification of eternal solutions. The analysis relies on an
explicit solution formula discovered by Gallay and Mielke, and a
careful choice of time scale.

This is work with Barbara Niethammer (Oxford) and Bob Pego (Carnegie Mellon).