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Stochastic porous-medium equation in one dimension
Maximilien Bernard1,2, Andrei A Fedorenko3, Pierre Le Doussal1
1l'Ecole Normale Supérieure, Laboratoire de Physique de , CNRS, ENS and PSL Université, Sorbonne Université, Université Paris Cité, 24 rue Lhomond, 75005 Paris, France.
None:
We study the porous medium equation (PME) in one space dimension in the presence of additive nonconservative white noise and interpreted as a stochastic growth equation for the height field of an interface. We predict the values of the two growth exponents α and β using the functional renormalization group. Extensive numerical simulations show agreement with the predicted values for these exponents; however, they also show anomalous scaling with an additional local exponent α_{loc} as well as multiscaling originating from broad distributions of local height differences. The stationary measure of the stochastic PME is found to be well described by a random walk model related to a Bessel process. This model allows for several predictions about the multiscaling properties.
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