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- W2081034126 abstract "New mathematical techniques for solving higher dimensional periodic systems are developed. The system is reduced to an equivalent set of one dimensional systems, which are solved by finite difference transform calculus. The resulting solutions are synthesized in the general integral of an associated partial differential equation to form the desired solution. These techniques maintain a higher degree of analytic integrity than the normal mode series expansion method, and allow the handling of sophisticated boundary conditions in an operational manner. The techniques are used to solve physically interesting models of molecules colliding with crystals. The model presented here is a three dimensional, semi-infinite, cubic lattice. The particles obey classical mechanics and interact harmonically with their nearest neighbors. The particle displacement is normal to the surface, and the ratio of the strengths of the longitudinal and transverse harmonic interactions is arbitrary. Lame's constants λ, μ, of the crystal determine this ratio. A normally incident particle of arbitrary mass interacts with the lattice through a truncated harmonic potential of arbitrary strength. The relative motion between this particle and the lattice is determined analytically from the resulting integro-differential equation in the form of a Neumann series. Accommodation coefficients are calculated for the rare gases on tungsten in a range of 100–300 °K. Experimental agreement is quantitative, especially for the heavier gases, A, Kr, Xe." @default.
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- W2081034126 date "1966-01-01" @default.
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- W2081034126 title "Higher dimensional crystal models: A theory of thermal accommodation coefficients" @default.
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- W2081034126 doi "https://doi.org/10.1016/0039-6028(66)90065-3" @default.
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