Burgers dynamics with Weibull-class Poisson point process initial conditions produces self-similar evolution and explicit analytical expressions for velocity distributions, void and shock multiplicities, and correlation functions with stretched-exponential tails whose exponents range from 1 to ∞.
It is related to the void probabilityPvoid(x)by Pvoid(x) = Z ∞ x dx′nvoid(x′) (x′ −x),whencen void(> x) =− dPvoid dx =−R ′ α(x), n void(x) = d2Pvoid dx2 =R ′′ α(x)
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Burgers dynamics for Poisson point process initial conditions of the Weibull class
Burgers dynamics with Weibull-class Poisson point process initial conditions produces self-similar evolution and explicit analytical expressions for velocity distributions, void and shock multiplicities, and correlation functions with stretched-exponential tails whose exponents range from 1 to ∞.