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 organised 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.
Original language | English (US) |
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Article number | acf265 |
Journal | Nonlinearity |
Volume | 36 |
Issue number | 10 |
DOIs | |
State | Published - Oct 1 2023 |
Bibliographical note
Publisher Copyright:© 2023 IOP Publishing Ltd & London Mathematical Society.
Keywords
- 35A18
- 35B32
- 35B36
- 92C15
- Swift-Hohenberg equation
- growing domains
- pattern formation
- quenching