Abstract
Motivated by previous discussions of particle interactions under the Manev potential U(r)=−α/r−ε/r 2, we construct the collision integrals for attractive potentials U(r) satisfying the condition U(r) r 2→−ε as r→0 with ε≥0. For ε=0, we obtain a Boltzmann-type integral with a collision law allowing “spiral” interactions and nonunique correspondence between impact parameter and scattering angle. For ε>0, an additional Smoluchowski-type coagulation integral arises. All these integrals are derived and possible applications are discussed.
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REFERENCES
A. V. Bobylev, The theory of the nonlinear spatially uniform Boltzmann equation for Maxwell molecules, Sov. Sci. Rev. 7:111–233 (1988).
A. V. Bobylev, P. Dukes, R. Illner, and H. D. Victory, On Vlasov-Manev equations, I: Foundations, properties and non-global existence, J. Stat. Phys. 88:885–912 (1997).
R. Illner, H. D. Victory, P. Dukes, and A. V. Bobylev, On Vlasov-Manev equations, II: Local existence and uniqueness, J. Stat. Phys. 91(3/4):625–654 (1998).
C. Cercignani, Theory and Application of the Boltzmann Equation (Springer-Verlag, New York, 1988).
L. D. Landau and E. M. Lifshitz, Mechanics (Pergamon Press, Oxford, 1960).
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Bobylev, A.V., Illner, R. Collision Integrals for Attractive Potentials. Journal of Statistical Physics 95, 633–649 (1999). https://doi.org/10.1023/A:1004543325973
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DOI: https://doi.org/10.1023/A:1004543325973