Maria Cameron : Analysis of the Lennard-Jones-38 stochastic network

The problem of finding transition paths in the Lennard-Jones cluster of 38 atoms became a benchmark problem in chemical physics due to its beauty and complexity. The two deepest potential minima, the face-centered cubic truncated octahedron and an icosahedral structure with 5-fold rotational symmetry, are far away from each other in the configuration space, which makes problem of finding transition paths between them difficult. D. Wales's group created a network of minima and transition states associated with this cluster. I will present two approaches to analyze this network. The first one, a zero-temperature asymptotic approach, is based on the Large Deviation Theory and Freidlin's cycles. I will show that in the gradient case the construction of the hierarchy of cycles can be simplified dramatically and present a computational algorithm for building a hierarchy of only those Freidlin's cycles associated with the transition process between two given local equilibria. The second approach is the Discrete Transition Path Theory, a finite temperature tool. This approach allows us to establish the range of validity of the zero-temperature asymptotic and describe the transition process at still low but high enough temperatures where the zero-temperature asymptotic approach is no longer valid.

• Category: Applied Math and Analysis
• Duration: 01:34:02
• Date:  May 6, 2013 at 4:25 PM
• Views: 122
• Tags:   seminar, Applied Math And Analysis Seminar