Multidimensional potential energy surfaces for systems larger than about 15 atoms are so complex that interpreting their topographies and the consequent dynamics requires statistical analyses of their minima and saddles. Sequences of minimum-saddle-minimum points provide a characterization of such surfaces. Two examples, Ar 19 and (KCI) 32 , illustrate how topographies govern tendencies to form glasses or “focused” structures, for example, crystals or folded proteins. Master equations relate topographies to dynamics. The balance between glass-forming and structure-seeking characters of a potential energy surface seems governed by sawtooth versus staircase topography and the associated collectivity of the growth process after nucleation.

A statistically based method of characterizing the topography of a multidimensional potential surface classifies not only local minima and saddles but entire basins containing many minima, and divides separating basins and monotonic sequences of local minima within each basin. The data, so classified, fold readily into the formalisms of chemical kinetic isomerization theory and master equations to provide a connection between that topography and the dynamics on the surface. This analysis, in particular, permits an interpretation of the glass-forming or ‘‘focusing’’ character of the surface. The method is illustrated with a model system derived, with simplifications, from the 19-atom Lennard-Jones cluster. The method also leads naturally to control problems including the determination of optimum conditions for forming glasses or selected structures, such as particular crystal structures or folded protein structures.

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An adaptive method is presented to optimize schedules for the simulated annealing of clusters and nanoscale particles. The method, based on both molecular-dynamics simulations and a set of master equations, is applied to a model configuration space for which the exact optimal schedule can also be found. The adaptive method is demonstrably suitable for optimizing larger and more realistic systems than can be treated by an exact method, even one based on a statistical-sample master equation.

We present theoretical and experimental investigations of current filaments in thin n-GaAs films in the regime of low-temperature impurity breakdown. Simulations combining a Monte Carlo approach for the scattering and generation-recombination processes with a drift-diffusion model on a two-dimensional spatial domain yield detailed information about the distribution of the electron densities, electron temperature, current density and electric field. The theory is confirmed by spatially resolved measurements using a novel technique of quenched photoluminescence.