  We investigate the dynamics of elastic microstructures within a fluid that
are subjected to thermal fluctuations. We perform analysis to obtain
systematically simplified descriptions of the mechanics in the limiting regimes
when (i) the coupling forces that transfer momentum between the fluid and
microstructures is strong, (ii) the mass of the microstructures is small
relative to the displaced mass of the fluid, and (iii) the response to stresses
results in hydrodynamics that relax rapidly to a quasi-steady-state relative to
the motions of the microstructure. We derive effective equations using a
singular perturbation analysis of the Backward Kolmogorov equations of the
stochastic process. Our continuum mechanics description is based on the
Stochastic Eulerian Lagrangian Method (SELM) which provides a framework for
approximation of the fluid-structure interactions when subject to thermal
fluctuations.
