arXiv subjects

Johannes Rimmele

Publications and source records attributed to Johannes Rimmele.

3 recordsLinked to original sources

arXiv2026

Stabilization by rough noise for an epitaxial growth model

In this article we study a model from epitaxial thin-film growth. It was originally introduced as a phenomenological model of growth in the presence of a Schwoebbel barrier, where diffusing particles on a terrace are not allowed to jump down at the boundary. Nevertheless, we show that the presence of arbitrarily small space-time white noise due to fluctuations in the incoming particles surprisingly eliminates all nonlinear interactions in the model and thus has the potential to stabilize the dynamics and suppress the growth of hills in these models.

math.PR↗

arXiv2026

Numerical Study of a Surface Growth Model with Singular Noise

We study a stochastic model for epitaxial thin-film growth driven by spatially rough additive noise in a regime where the noise is singular and regularization via truncation in Fourier space is used to give a meaning to the solution, leading to a vanishing nonlinearity in the limit. In order to study this phenomenon numerically, the nonlinearity is discretized by a spectral Galerkin projection, while time integration is performed with an exponential Euler scheme. For roughness stronger than space-time white noise, we derive strong error estimates in $L^p(Ω;C([0,T];\mathcal H^1))$ that display explicitly the interaction between the spatial cut-off, the time step, and the decay of the nonlinear current. We also quantify the growth of the truncated stochastic convolution and the corresponding vanishing rate of the nonlinearity. Numerical experiments illustrate the transition from persistent hill formation to noise-dominated dynamics as the roughness parameter increases.

math.NA↗

arXiv2026

Numerical approximation of nonlinear fourth-order SPDEs with additive space-time white noise

We consider the strong numerical approximation for a fourth-order stochastic nonlinear SPDE driven by space-time white noise on {$d=1,2,3$}-dimensional torus. We consider its full discretisation with a spectral Galerkin scheme in space and Euler scheme in time. We show the convergence with almost spatial rate $2-\frac{d}{2}$ and $\frac{6-d}{4}$-temporal rate obtained mainly via \it{Stochastic Sewing} technique.

math.NA↗