Growing patterns
Pattern Formation and Solitons
2023-02-28 v1 Analysis of PDEs
Dynamical Systems
Abstract
Pattern forming systems allow for a wealth of states, where wavelengths and orientation of patterns varies and defects disrupt patches of monocrystalline regions. Growth of patterns has long been recognized as a strong selection mechanism. We present here recent and new results on the selection of patterns in situations where the pattern-forming region expands in time. The wealth of phenomena is roughly organized in bifurcation diagrams that depict wavenumbers of selected crystalline states as functions of growth rates. We show how a broad set of mathematical and numerical tools can help shed light into the complexity of this selection process.
Cite
@article{arxiv.2302.13486,
title = {Growing patterns},
author = {Ryan Goh and Arnd Scheel},
journal= {arXiv preprint arXiv:2302.13486},
year = {2023}
}