Using Von Mises-fisher Distribution for Polymer Conformation Analysis in Multi-scale Framework

In this study we consider the statistical representation of polymer conformations, which is very important when modeling rheology at macroscopic scales. It is impossible to track all relevant microscopic variables for each polymer in a polymer-laden solution due to the huge number degrees of freedom associated with such fluids. We applied this approach to one of the most descriptive kinetic models of polymer, Kramers bead-rod model, where the probability density function models the angle of each rod with respect to the fixed coordinate axes. Towards this goal we apply mixture of von Mises-Fisher distribution for modeling a polymer conformation. The Expectation-Maximization based clustering algorithms are used to estimate the conformation given the ensemble of polymers. Both distribution sampling and parameters estimation have been implemented in parallel using CPU and GPU based platforms.