Lingxing Yao, University of North Carolina at Chapel Hill


Stochastic simulation and inversion methods for microrheology

Abstract:  We assume the Generalized Langevin Equation (GLE) model for thermal fluctuations of passive microbeads in a viscoelastic material. Our goal is to develop tools for direct simulation of GLEs for a known viscoelastic relaxation modulus, and to develop inverse characterization tools for the relaxation modulus from time series of microbead displacement data. We first demonstrate the concepts and tools with the standard Langevin Equation (LE) for viscous fluids, including the relationship between the exact LE solution and autoregressive time series models. Next, the connections between exact solutions and multivariate autoregressive time series models are demonstrated for a class of GLEs. Using this linear multivariate time series model, we show how, given path data of microbeads, one may calculate an exact likelihood function, thereby producing maximum likelihood estimators of parameters in the shear relaxation modulus. For microrheology, these techniques yield storage and loss moduli distributions (e.g. best fit parameter values and variance), and estimates of the best finite model approximation of the complex modulus. We also discuss a new direct simulation algorithm for GLEs using these statistical concepts.

Advisor: Greg Forest (UNC)