2020/08/17 by Lorina Dascal, Dascal, Lorina, Gautam Pai +3
Computer Science · Engineering · Materials Science · Mathematics · #35A15 #35G20 #65M22 #Aluminum Alloy Microstructure Properties #Analysis of PDEs (math.AP) #Block Copolymer Self-Assembly #FOS: Mathematics #Numerical Analysis (math.NA) #Solidification and crystal growth phenomena #cs.NA #math.AP #math.NA #msc:35A15 #msc:35G20 #msc:65M22
paper · pdf · doi:10.48550/arxiv.2008.07654
16 pages, 15 figures
arxiv created 2020/08/17 · openalex publication_date 2020/08/17 · arxiv updated 2020/08/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We propose an extension of the Allen-Cahn model for pattern synthesis on two dimensional curved surfaces. This model is based on a single PDE and it offers improved ability of controlling the type of generated surface patterns via the chosen reaction-diffusion coefficient, thus, obtaining patterns in form of spots, inverted spots, or stripes. We investigate the dependence of the type of the obtained pattern on the new proposed reaction term. An efficient operator splitting scheme is used to discretize the model on a surface. Experiments on surfaces with varying initial conditions illustrate a variety of patterns.