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Matrix Elements of the Linearized Collision Operator
dc.contributor.authorFord, G. W.en_US
dc.date.accessioned2010-05-06T23:03:15Z
dc.date.available2010-05-06T23:03:15Z
dc.date.issued1968-03en_US
dc.identifier.citationFord, 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.urihttps://hdl.handle.net/2027.42/71004
dc.description.abstractThe 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.extent3102 bytes
dc.format.extent362312 bytes
dc.format.mimetypetext/plain
dc.format.mimetypeapplication/pdf
dc.publisherThe American Institute of Physicsen_US
dc.rights© The American Institute of Physicsen_US
dc.titleMatrix Elements of the Linearized Collision Operatoren_US
dc.typeArticleen_US
dc.subject.hlbsecondlevelPhysicsen_US
dc.subject.hlbtoplevelScienceen_US
dc.description.peerreviewedPeer Revieweden_US
dc.contributor.affiliationumDepartment of Physics, The University of Michigan, Ann Arbor, Michiganen_US
dc.description.bitstreamurlhttp://deepblue.lib.umich.edu/bitstream/2027.42/71004/2/PFLDAS-11-3-515-1.pdf
dc.identifier.doi10.1063/1.1691947en_US
dc.identifier.sourcePhysics of Fluidsen_US
dc.identifier.citedreferenceD. Burnett, Proc. London Math. Soc. 39, 385 (1935).en_US
dc.identifier.citedreferenceS. Chapman and T. E. Cowling, The Mathematical Theory of Nonuniform Gases (Cambridge University Press, Cambridge, 1958), 2nd ed.en_US
dc.identifier.citedreferenceC. S. Wang Chang and G. E. Uhlenbeck, University of Michigan Report, Project M999 (1952).en_US
dc.identifier.citedreferenceH. M. Mott‐Smith, Lincoln Laboratory Group Report V‐2 (1954).en_US
dc.identifier.citedreferenceSee also L. Waldman in Handbuch der Physik, S. Flugge, Ed. (Springer‐Verlag, Berlin, 1960), Vol. 12, Sec. 38.en_US
dc.identifier.citedreferenceThe 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.citedreferenceSee, 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.citedreferenceFor 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.citedreferenceFor 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.citedreferenceReference 8, p. 63.en_US
dc.identifier.citedreferenceReference 9, p. 52.en_US
dc.identifier.citedreferenceReference 7, pp. 56–57.en_US
dc.identifier.citedreferenceZ. 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.citedreferenceReference 9, p. 52.en_US
dc.identifier.citedreferenceC. L. Pekeris, Z. Alterman, L. Finkelstein, and K. Frankowski, Phys. Fluids 5, 1608 (1962).en_US
dc.identifier.citedreferenceReference 2, Chap. 9. See especially pp. 161 and 162.en_US
dc.identifier.citedreferenceL. 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.owningcollnamePhysics, Department of


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