2024/05/30 by Arnd Scheel, Scheel, Arnd, Qiliang Wu +1 · 1 citation
Computer Science · Engineering · Materials Science · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Liquid Crystal Research Advancements #Pattern Formation and Solitons (nlin.PS) #Structural Analysis and Optimization
paper · pdf · doi:10.48550/arxiv.2405.20265
openalex publication_date 2024/05/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate the effect of spatial inhomogeneity on perfectly periodic, self-organized striped patterns in spatially extended systems. We demonstrate that inhomogeneities select a specific translate of the striped patterns and induce algebraically decaying, dipole-type farfield deformations. Phase shifts and leading order terms are determined by effective moments of the spatial inhomogeneity. Farfield decay is proportional to the derivatives of the Green's function of an effective Laplacian. Technically, we use mode filters and conjugacies to an effective Laplacian to establish Fredholm properties of the linearization in Kondratiev spaces. Spatial localization in a contraction argument is gained through the use of an explicit deformation ansatz and a subtle cancellation in Bloch wave space.