ABSTRACT:
I will discuss the physics of mixing and elasticity on random graphs. The results I will show are important step toward understanding on the macroscopic properties of amorphous solids, spin glasses and alike and are also closely related to fields of interest of computer science. The first part of the talk is about elasticity. The physical properties of amorphous solids are far less understood than those of crystalline solids. The analysis of these systems is complicated due to disorder and vastly different interaction strengths present in these materials. I will look at spectral properties of random elastic networks and argue in which sense they provide a good toymodel of disordered solids. Using the Cavity method, a sort of BethePeierls iterative method, I will derive the analytical expressions for the spectral density of such graphs. I will conclude this part by pointing out implications of these results on the physics of amorphous solids. Next I plan to talk about a new type of numerics for mixing on random graphs. These results are about Markov Chain Monte Carlo algorithms and have potential applications in studying granular materials, colloids, protein folding, etc. Most implementations of these algorithms use Markov Chains that obey detailed balance, even though this not a necessary requirement for converging to a steady state. I plan to overview several examples that utilize irreversible Markov Chains, where violating detailed balance has improved the convergence rate. Finally I will pose some open questions and discuss attempts to use nonequilibrium dynamics for efficient sampling.

Condensed Matter Seminar Thursday, December 5, 2013 3:30 PM Physics Building, Room 204 Note special room. 
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