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Scott McKinley : Fluctuating Hydrodynamics of Polymers in Dilute Solution

In 1953, the physicist P.E. Rouse proposed to model polymers in dilute solution by taking the polymer to be a series of beads connected by Gaussian springs. Neglecting inertia, the dynamics are set by a balance between the thermal fluctuations in the fluid and the elastic restoring force of the springs. One year later, B. Zimm noted that a polymer will interact with itself through the fluid in a qualitatively meaningful way. In this talk, we consider a more recent Langevin equation approach to dealing with hydrodynamic self-interaction. This involves coupling the continuum scaling limit of the Rouse model with stochastically forced time-dependent Stokes equations. The resulting pair of parabolic SPDE, with non-linear coupled forcing, presents a number of mathematical challenges. On the way to providing an existence and uniqueness result, we shall take time to develop relevant stochastic tools, and consider the modeling implications of certain technical results.

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