Metastability in stochastic dynamics of disordered mean-field models

We study a class of Markov chains that describe reversible stochastic dynamics of a large class of disordered mean field models at low temperatures. Our main purpose is to give a precise relation between the metastable time scales in the problem to the properties of the rate functions of the corresponding Gibbs measures. We derive the analog of the Wentzell-Freidlin theory in this case, showing that any transition can be decomposed, with probability exponentially close to one, into a deterministic sequence of ``admissible transitions''. For these admissible transitions we give upper and lower bounds on the expected transition times that differ only by a constant. The distribution rescaled transition times are shown to converge to the exponential distribution. We exemplify our results in the context of the random field Curie-Weiss model.Comment: 73pp, AMSTE

Cislunar Trajectory Generation with Sun-Exclusion Zone Constraints Using a Genetic Algorithm and Direct Method Hybridization

Space missions to the Moon have received renewed interest in recent decades. Science missions continue to be sent to the Moon, and several space agencies have aspirations of establishing a human presence on the Moon. With the increased number of artificial objects in cislunar space, the problem of tracking these objects arises. Optical sensors are able to track these objects in deep space. However, optical sensors cannot track objects that are close to the Sun as viewed from the observer. This unobservable region is the Sun-exclusion zone (SEZ). This research attempts to create optimal Moon-Earth transfers which are completely in the SEZ using a genetic algorithm-direct method hybridization. Such transfers demonstrate how much the SEZ can limit optical sensors from maintaining custody of a satellite. Transfers from L1 and L2 Lyapunov orbits to geosynchronous orbit are generated while optimizing fuel and time of flight. Remaining inside of the SEZ is shown to significantly increase the fuel required to make the transfer