Maria K. Cameron

University of Maryland, Department of Mathematics

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Lennard-Jones Clusters

Lennard-Jones (LJ) clusters model clusters of rare gases such as Ar, Kr, Xe, Rd and certain synthetic particles. Two problems of interest concerned with small (up to 100 particles) LJ clusters are

These two problems are made mathematically tractable by representing energy landscapes of LJ clusters by stochastic networks in which vertices correspond to local energy minima, edges connect pairs of minima separated by a single saddle, and transition rates along each edge are approximated by Langer's formula adjusted by combinatorial considerations. Powerful methods and software for mapping energy landscapes onto stochastic network were developed by D. Wales' group. An example of such a mapping for LJ7 is shown in the figures below.

LJ network Map energy landscape to network

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