Mathematical Sciences Department Analysis/PDE Seminar
Ryan Goh, Boston University
Thursday, April 24th
1:00pm - 2:00 pm
Title: Growing Patterns
Abstract: Pattern forming systems typically allow for a broad array of coherent states, with varying wavelength and orientation. In the standard situation of formation via small random fluctuations of an unstable homogeneous state, defects disrupt and bound patches of coherent patterns. Growth and heterogeneity is a powerful way to select and control the type of pattern formed in a system. Examples including moving masks in light-sensitive chemical reactions, directional solidification in crystals, varying domain shape in fluid convection. We present recent results on selection when the patterned region expands in time. We use prototypical directional quenching mechanisms to study this situation in a theoretically accessible but application-relevant setting. We find a wealth of wavenumber selection phenomena which can be organized using bifurcation diagrams which depict the wavenumber of a striped state as a function growth rate.