A systematic approach will be presented for describing materials, macromolecules and fluids at increasingly coarser scales, and for deriving corresponding coarse-level Hamiltonians, based either on a given fine-scale Hamiltonian or, more fundamentally, on quantum chemistry. The coarse levels can be used for orders-of-magnitude acceleration of equilibrium and/or dynamics simulations, avoiding slow-downs and attraction-basin traps typical to single-level simulations. They may also lead to "macroscopic equations", enabling simulations of indefinitely large systems.
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