We present an overview of recent results on localized pattern formation in
non-local PDEs that arise in swarming and particle self-assembly models. We
begin by computing the non-local stability analysis for particles which
bifurcate away from radially symmetric states such as rings and spheres.
The linear theory accurately characterizes the rich array of localized
patterns which have been observed in the fully nonlinear problem in two and
three dimensions. This aspect of the theory allows us to solve the inverse
problem of designing specified potentials which assemble into targeted
patterns. Time permitting, we will also show how to leverage this
mathematical theory to provide, for the first time, a purely isotropic
physical model that produces spherical assemblies at the nano scale, such
as viral capids.
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Last modified: April 11 2016 - 18:14:43