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Center for Nonlinear Studies |
Many boundary value problems arising in materials science modeling involve complicated boundary shapes and boundary data, making analytic solution based on conventional differential equation methods difficult. Such problems often arise in polymer science where the boundaries correspond to polymer chains, membrane-like structures and adsorbed and grafted polymer layers. This problem also arises in the characterization of the transport properties of synthetic and biologically significant polymers, biological structures such as viruses and cells, as well as in the characterization of nanoparticles such as carbon nanotubes. This general problem is addressed by formulating the problem formally in terms of functional integration and by then estimating the transport property values by numerical path sampling. It is shown that solutions of high accuracy can be obtained by this versatile approach. Particular emphasis is given to the numerical computation of the capacity and polarizability tensors of particles having complex-shape and the many properties related to these quantities (Smoluchowki rate constant for diffusion-limited reactions, intrinsic conductivity, Stokes friction coefficient, intrinsic viscosity, etc.).