Date: Friday, October 24, 2014
Location: 1084 East Hall (3:00 PM to 4:00 PM)
Title: SelfAssembly: Variational models, Energy Landscapes, and Metastability
Abstract: Selfassembly, a process in which a disordered system of preexisting components forms an organized structure or pattern, is both ubiquitous in nature and important for the synthesis of many designer materials. In this talk, we will address three variational models for selfassembly from the point of view of mathematical analysis and computation.
The first is a nonlocal perturbation of Coulombictype to the wellknown GinzburgLandau/CahnHilliard free energy. The functional has a rich and complex energy landscape with many metastable states. I will present a simple method for assessing whether or not a particular computed metastable state is a global minimizer. The method is based upon finding a ``suitable" global quadratic lower bound to the free energy.
The second model is a purely geometric and finitedimensional paradigm for selfassembly which generalizes the notion of centroidal Voronoi tessellations from points to rigid bodies. Using a level set formulation, we a priori fix the geometry for the structures and consider selfassembly entirely dictated by distance functions. I will introduce a novel fast algorithm for simulations in two and three space dimensions.
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Speaker: Rustum Choksi
Institution: McGill University
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