Growing patterns

2023/02/27 by Ryan Goh, Goh, Ryan, Arnd Scheel +1 · 1 citation
Materials Science · #35A18 #35B32 #35B36 #92C15 #Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Pattern Formation and Solitons (nlin.PS) #Solidification and crystal growth phenomena

paper · pdf · doi:10.48550/arxiv.2302.13486

openalex publication_date 2023/02/27 · openalex created_date 2023/03/03 · openalex updated_date 2026/07/28

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.

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• Global bifurcation of localised 2D patterns emerging from spatial heterogeneity

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