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NJIT Applied Mathematics Colloquium

Friday, February 5th 2010, 11:30am
Cullimore Lecture Hall II
New Jersey Institute of Technology

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Approximations to Granular Relaxation Flows: Lattices, Limits, Infinite-dimensional Dynamical Systems and Solitons

Denis Blackmore

NJIT

Recent research in particle flow dynamics using long-wave limits of Fermi-Ulam-Pasta lattices and other approximate means of analysis has revealed some fascinating connections between wave propagation phenomena in granular media and infinite-dimensional dynamical systems, including soliton, near soliton and traveling wave behavior. These connections, which have been confirmed by experimental observations, open new vistas for the application of Hamiltonian and near-Hamiltonian functional dynamical systems (PDEs and integro-PDES). Some of our joint research involving these connections, focusing on continuum approximations for relaxation flows (in which a granular configuration is periodically disturbed and given time to settle between successive perturbations) using a method of our devising will be described in some detail. We shall naturally touch on the engineering applications of this research, and also on some new mathematics generated by this approach.