Many-body effects in ice are investigated through a systematic analysis of the lattice energies of several proton ordered and disordered phases, which are calculated with different flexible water models, ranging from pairwise additive (q-TIP4P/F) to polarizable (TTM3-F and AMOEBA) and explicit many-body (MB-pol) potential energy functions. Comparisons with available experimental and diffusion Monte Carlo data emphasize the importance of an accurate description of the individual terms of the many-body expansion of the interaction energy between water molecules for the correct prediction of the energy ordering of the ice phases. Further analysis of the MB-pol results, in terms of fundamental energy contributions, demonstrates that the differences in lattice energies between different ice phases are sensitively dependent on the subtle balance between short-range two-body and three-body interactions, many-body induction, and dispersion energy. By correctly reproducing many-body effects at both short range and long range, it is found that MB-pol accurately predicts the energetics of different ice phases, which provides further support for the accuracy of MB-pol in representing the properties of water from the gas to the condensed phase.
The nonsimilar velocity distribution in a two-dimensional laminar boundary layer with uniform external stream and with either uniform suction or injection is obtained by a series expansion in terms of a mass transfer parameter. The results are compared with more accurate analysis and shown to be in good agreement for a range of values of this parameter. The solution for the velocity distribution is then employed for the calculation of the distributions of energy and element mass fraction when there are imposed requirements for energy and mass balance at the exposed surface of a porous plate with uniform injection. As one example of several possible applications of these solutions, there is computed the flow associated with the injection of hydrogen into an air stream according to the flame sheet model.
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