Self-Similarity in Random Collision Processes
D. ben-Avraham, Eli Ben-Naim, Katja Lindenberg, Alexandre Rosas
Kinetics of collision processes with linear mixing rules are
investigated analytically. The velocity distribution becomes
self-similar in the long time limit and the similarity functions have
algebraic or stretched exponential tails. The characteristic exponents
are roots of transcendental equations and vary continuously with the
mixing parameters. In the presence of conservation laws, the velocity
distributions become universal.
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