Multiscale modeling and simulation of soft matter materials

Tuesday, November 4, 2008 - 2:00pm - 2:45pm
EE/CS 3-180
Paul Atzberger (University of California)
We shall discuss a multiscale 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 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 numerical challenges for temporal integration and spatial resolution which we shall address. This includes a time integrator for
the stiff stochastic dynamics and methods
to handle adaptive spatial discretizations of the underlying stochastic partial differential equations. We shall discuss specific applications of the approach, including
the study of lipid flow in bilayer membranes, the shear viscosity of polymer fluids, and the diffusivity of particles in complex fluids.
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