Modeling and Simulation of Soft Matter Materials using Stochastic Immersed Boundary Methods
Paul Atzberger (UCSB)


We shall discuss a modeling and simulation formalism for soft matter materials taking into account hydrodynamic interactions and thermal fluctuations. A specific motivation is the study of lipid bilayer membranes and polymer fluids taking into account microstructure degrees of freedom. The approach is based on an extension of the immersed boundary method, where hydrodynamic interactions of the composite system are handled by an approximate treatment of the fluid-structure stresses.   The microstructures (lipid molecules / polymers) are represented by Lagrangian degrees of freedom which are coupled to an Eulerian representation of the fluid, treated at the level of continuum mechanics. Thermal fluctuations are incorporated in the formalism by an appropriate stochastic forcing of the fluid-structure equations in accordance with the principles of statistical mechanics.  The theoretical formalism presents a number of theoretical and numerical challenges.  This includes time integration for the stiff stochastic dynamics and methods to handle spatial discretizations of the underlying stochastic partial differential equations. We shall discuss specific applications of the approach to the study of lipid flow in bilayer membranes, the shear viscosity of polymer fluids, and the diffusivity of particles in complex fluids.