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A stochastic method is described for estimating Green's functions (GF's), appropriate to linear advection-diffusion-reaction transport problems, evolving in arbitrary geometries. By allowing straightforward construction of approximate, though high-accuracy GF's, within any geometry, the technique solves the central challenge in obtaining Green's function solutions. In contrast to Monte Carlo solutions of individual transport problems, subject to specific sets of conditions and forcing, the proposed technique produces approximate GF's that can be used: a) to obtain (infinite) sets of solutions, subject to any combination of (random and deterministic) boundary, initial, and internal forcing, b) as high fidelity direct models in inverse problems, and c) as high quality process models in thermal and mass transport design, optimization, and process control problems., Comment: 47 pages, 8 figures

Physical arguments and comparisons with published experimental data suggest that in simple liquids: i) single-molecule-scale viscous forces are produced by temperature-dependent London dispersion forces, ii) viscosity decay with increasing temperature reflects electron cloud compression and attendant suppression of electron screening, produced by increased nuclear agitation, and iii) temperature-dependent self-diffusion is driven by a narrow band of phonon frequencies lying at the low-frequency end of the solid-state-like phonon spectrum. The results suggest that collision-induced electron cloud distortion plays a decisive role in single molecule dynamics: i) electron cloud compression produces short-lived repulsive states and single molecule, self-diffusive hops, while ii) shear-induced distortion generates viscosity and single-molecule-scale viscous drag. The results provide new insight into nonequilibrium molecular dynamics in nonpolar, nonmetallic liquids., Comment: 23 pages, 7 figures