Calculation of the linear kernel of the collision integral for the hard-sphere potential |
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Authors: | L A Bakaleinikov E Yu Flegontova A Ya énder and I A énder |
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Institution: | (1) Campus Saint-Jean, University of Alberta 8406, 91 Street, Edmonton, Alberta, T6C 4G9, Canada |
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Abstract: | The expansion of a distribution function in spherical harmonics transforms the Boltzmann equation into a system of integro-differential
equations with kernels depending only of the magnitudes of velocities. The kernels can be expressed in terms of the sums including
the matrix elements (MEs) of the collision integral. The kernels are constructed using new results of ME calculations; analysis
of errors is carried out with the help of analytic expressions for kernels, which were derived by Hilbert and Hecke for the
hard-sphere model. The concept of generalized matrix elements is introduced and their asymptotic representation is constructed
for large values of indices. Analytic expressions for the contribution from MEs with large indices to the kernels are constructed.
The high accuracy of the construction of a kernel using MEs is demonstrated. |
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Keywords: | |
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