Matrix Elements of the Linearized Collision Operator
dc.contributor.author | Ford, G. W. | en_US |
dc.date.accessioned | 2010-05-06T23:03:15Z | |
dc.date.available | 2010-05-06T23:03:15Z | |
dc.date.issued | 1968-03 | en_US |
dc.identifier.citation | Ford, G. W. (1968). "Matrix Elements of the Linearized Collision Operator." Physics of Fluids 11(3): 515-521. <http://hdl.handle.net/2027.42/71004> | en_US |
dc.identifier.uri | https://hdl.handle.net/2027.42/71004 | |
dc.description.abstract | The matrix elements of the linearized Boltzmann collision operator with respect to the Burnett functions are constructed for arbitrary power law potentials. The result of Mott‐Smith for elastic spheres appears as a special case. | en_US |
dc.format.extent | 3102 bytes | |
dc.format.extent | 362312 bytes | |
dc.format.mimetype | text/plain | |
dc.format.mimetype | application/pdf | |
dc.publisher | The American Institute of Physics | en_US |
dc.rights | © The American Institute of Physics | en_US |
dc.title | Matrix Elements of the Linearized Collision Operator | en_US |
dc.type | Article | en_US |
dc.subject.hlbsecondlevel | Physics | en_US |
dc.subject.hlbtoplevel | Science | en_US |
dc.description.peerreviewed | Peer Reviewed | en_US |
dc.contributor.affiliationum | Department of Physics, The University of Michigan, Ann Arbor, Michigan | en_US |
dc.description.bitstreamurl | http://deepblue.lib.umich.edu/bitstream/2027.42/71004/2/PFLDAS-11-3-515-1.pdf | |
dc.identifier.doi | 10.1063/1.1691947 | en_US |
dc.identifier.source | Physics of Fluids | en_US |
dc.identifier.citedreference | D. Burnett, Proc. London Math. Soc. 39, 385 (1935). | en_US |
dc.identifier.citedreference | S. Chapman and T. E. Cowling, The Mathematical Theory of Nonuniform Gases (Cambridge University Press, Cambridge, 1958), 2nd ed. | en_US |
dc.identifier.citedreference | C. S. Wang Chang and G. E. Uhlenbeck, University of Michigan Report, Project M999 (1952). | en_US |
dc.identifier.citedreference | H. M. Mott‐Smith, Lincoln Laboratory Group Report V‐2 (1954). | en_US |
dc.identifier.citedreference | See also L. Waldman in Handbuch der Physik, S. Flugge, Ed. (Springer‐Verlag, Berlin, 1960), Vol. 12, Sec. 38. | en_US |
dc.identifier.citedreference | The notation used here is that of G. E. Uhlenbeck and G. W. Ford, Lectures in Statistical Mechanics (American Mathematical Society, Providence, Rhode Island, 1963). | en_US |
dc.identifier.citedreference | See, e.g., L. Landau and S. Lifshitz, Mechanic (Addison‐Wesley Publishing Company, Reading, Massachusetts, 1960), p. 18. Note that for binary scattering the mass must be replaced by the reduced mass m∕2 in their formulas. Equation (3) on p. 78 of Ref. 6 is correct only with this replacement. | en_US |
dc.identifier.citedreference | For spherical harmonics the notation is that of A. R. Edmonds, Angular Momentum in Quantum Mechanics (Princeton University Press, Princeton, New Jersey, 1957), especially pp. 19–24. | en_US |
dc.identifier.citedreference | For Laguerre polynomials the notation is that of W. Magnus and F. Oberhettinger, Formulas and Theorems for the Special Functions of Mathematical Physics (Chelsea Publishing Company, New York, 1949), especially pp. 84–85. | en_US |
dc.identifier.citedreference | Reference 8, p. 63. | en_US |
dc.identifier.citedreference | Reference 9, p. 52. | en_US |
dc.identifier.citedreference | Reference 7, pp. 56–57. | en_US |
dc.identifier.citedreference | Z. Alterman, K. Frankowski, and C. L. Pekeris, Astrophys. J. Suppl. 7, 291 (1962). In their expressions one must put F(θ) = 2−1/2 f4(θ)F(θ)=2−1∕2f4(θ) and λrl = a−2(2Φ0/kT)−1/2 Jlτr.λrl=a−2(2Φ0∕kT)−1∕2Jlτr. The same F(θ) is introduced in Ref. 3, p. 43 and Ref. 6, p. 88, but each of these expressions is in error by a factor of 21/2.21∕2. | en_US |
dc.identifier.citedreference | Reference 9, p. 52. | en_US |
dc.identifier.citedreference | C. L. Pekeris, Z. Alterman, L. Finkelstein, and K. Frankowski, Phys. Fluids 5, 1608 (1962). | en_US |
dc.identifier.citedreference | Reference 2, Chap. 9. See especially pp. 161 and 162. | en_US |
dc.identifier.citedreference | L. Sirovich and J. K. Thurber, in Rarefied Gas Dynamics, J. H. de Leeuw, Ed. (Academic Press Inc., New York, 1966), Vol. I, p. 21. | en_US |
dc.owningcollname | Physics, Department of |
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