Title: Self-Assembly, Particle Methods, and Lagrangian Coherent Structures Speaker: Philip Du Toit Date/Time: Monday, February 9, 2009, 1:00 – 2:00 pm Location: CSRI Building/Room 90 (Sandia-NM) Brief Abstract: Self-Assembly by Design: Self-Assembly is the process whereby randomly distributed components moving under the influence of short-range mutual interactions, arrange themselves into a globally ordered final configuration. Recent interest in the fabrication of photonic crystals with desired material properties motivates the inverse problem: design the short-range interactions in order to induce self-assembly of the components into a target lattice structure. I will present a fast trend optimization method for the generation of potentials that accomplishes this task. A Particle Method for the EPDiff Equation: We consider a model for active fluid transport described by the EPDiff equation (the Euler-Poincare equation associated with the diffeomorphism group). The EPDiff equation coincides with the Camassa-Holm equation for shallow water waves in one and two dimensions, and with the averaged template matching equation for computer vision in higher dimensions. The EPDiff singular solutions are discontinuities, called peakons. A key feature of peakons is that they carry momentum, and exchange momentum during collisions. I will demonstrate the implementation of a fast parallel particle method that allows for sharp reproduction of peakon solutions and peakon-peakon interactions. Mixing in Geophysical Flows: The method of extracting Lagrangian coherent structures using Liapunov exponents is used to discover surfaces that govern transport in geophysical flows. We observe that transport in synoptic-scale hurricane flows is a low-dimensional process whose salient features are adequately described by the mechanism of lobe dynamics associated with a homoclinic tangle. Similarly, the transport structures observed in three-dimensional hurricane flows lend intensity. The identical homoclinic tangle structure is also observed in mesoscale ocean eddies. CSRI POC: Pavel Bochev, (505) 844-1990 |