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
- Cluster rearrangements
- Aggregation and self-assembly. Software is available.
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.
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My projects
- Finding zero-temperature transition paths in LJ38 by means of Freidlin's cycles
- Analysis of rearrangements of LJ38 by means of the Transition Path Theory
- Asymptotic spectral analysis of LJ38. Quasi-invariant subsets of states and zero-temperature transition paths in LJ38 and LJ75
- Finite temperature continuation. Eigencurrents. Transition rates for LJ38 and LJ75
- Aggregation from 5- to 14-particle LJ clusters