Ballistic annihilation with continuous isotropic initial velocity distribution.
Ballistic annihilation with continuous initial velocity distributions is investigated in the framework of the Boltzmann equation. The particle density and the rms velocity decay as c approximately t(-alpha) and velocity approximately t(-beta), with the exponents depending on the initial velocity distribution and the spatial dimension d. For instance, in one dimension for the uniform initial velocity distribution beta = 0.230 472ellipsis. In the opposite extreme d-->infinity, the dynamics is universal and beta-->(1-2(-1/2))d(-1). We also solve the Boltzmann equation for Maxwell particles and very hard particles in arbitrary spatial dimension. These solvable cases provide bounds for the decay exponents of the hard sphere gas.
Krapivsky
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PL
Laboaroire de Physique Quantique (UMR C5626 du CNRS), Université Paul Sabatier, Toulouse, France.
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