标题： 一维随机多孔介质方程 显示英文标题

标题： The stochastic porous medium equation in one dimension

摘要： 我们研究在存在加性非守恒白噪声的一维空间中的多孔介质方程（PME），并将其解释为界面高度场的随机生长方程。 我们利用功能RG预测了两个生长指数$\alpha$和$\beta$的值。 大量的数值模拟显示这些指数的预测值一致，然而它们也显示了具有额外的“局部”指数$\alpha_{\rm loc}$的异常标度，以及来自局部高度差的广泛分布的多标度。 随机PME的稳态测量被发现可以用一个与贝塞尔过程相关的随机游走模型很好地描述。 该模型允许对多标度性质做出若干预测。 显示英文摘要

摘要： We study the porous medium equation (PME) in one space dimension in presence of additive non-conservative 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 $\alpha$ and $\beta$ using the functional RG. Extensive numerical simulations show agreement with the predicted values for these exponents, however they also show anomalous scaling with an additional "local" exponent $\alpha_{\rm loc}$, 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.