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Subject: white noise × WGL Institute: WIAS ×

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    Asymptotics of the eigenvalues of the Anderson Hamiltonian with white noise potential in two dimensions
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2019) Chouk, Khalil; van Zuijlen, Willem
    In this paper we consider the Anderson Hamiltonian with white noise potential on the box [0,L]² with Dirichlet boundary conditions. We show that all the eigenvalues divided by log L converge as L → ∞ almost surely to the same deterministic constant, which is given by a variational formula.
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    On the spinodal dewetting of thin liquid bilayers
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2021) Shiri, Roghayeh; Schmeller, Leonie; Seemann, Ralf; Peschka, Dirk; Wagner, Barbara
    We investigate the spinodal dewetting of a thin liquid polystyrene (PS) film on a liquid polymethylmethacrylate (PMMA) subtrate. Following the evolution of the corrugations of the PS film via in situ measurements by atomic force microscopy (AFM) and those of the PS-PMMA interface via ex situ imaging, we provide a direct and detailed comparison of the experimentally determined spinodal wavelengths with the predictions from linear stability analysis of a thin-film continuum model for the bilayer system. The impact of rough interfaces and fluctuations is studied theoretically by investigating the impact of different choices of initial data on the unstable wavelength and on the rupture time. The key factor is the mode selection by initial data perturbed with correlated colored noise in the linearly unstable regime, which becomes relevant only for liquid bilayers to such an extent. By numerically solving the mathematical model, we further address the impact of nonlinear effects on rupture times and on the morphological evolution of the interfaces in comparison with experimental results.