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CNA Seminar/Colloquium/Joint Pitt-CNA Colloquium

Richard James
University of Minnesota
Title: Viscometry of bulk materials and atomic structures

Abstract: Perhaps the most important deformations in solid mechanics are those that represent the bending, twisting and extension of beams. The most important flows in fluid mechanics are viscometric flows. In both cases these are the motions that, when compared with the corresponding experiments, are used to measure the material constants. We give a universal molecular level interpretation of these motions. We argue that these motions are associated at molecular level with a time-dependent invariant manifold of the equations of molecular dynamics. The mathematical description of the manifold is independent of the nature of the atomic forces and independent of the complexity of the molecules. The presence of this manifold can be used to simplify molecular-level computations, and deliver elastic and viscometric properties in the absence of a constitutive relation. Its presence also suggests a modification of the principle of material frame-indifference, a cornerstone of nonlinear continuum mechanics. Interesting links to theories of turbulence, to the Boltzmann equation, to the dynamics of nanostructures, to the theory of viscometry (and rather directly to research of former Mellon and Carnegie faculty Berry, Brown, Casassa, Coleman, Flory, Markovitz, Noll, Plazek, Williamson) will be briefly discussed. Joint work with Kaushik Dayal, Traian Dumitrica and Stefan Mueller.

Date: Thursday, October 28, 2010
Time: 1:30 pm
Location: Wean Hall 8220
Submitted by:  Irene Fonseca