Abstract

Pattern formation in the presence of slowly-varying spatio-temporal heterogeneities has application in diverse areas, including biology, chemistry, and fluid dynamics. This talk will discuss front and patterned solutions in the presence of parameter ramps which moderate the instability of a homogeneous equilibrium state. In this talk we discuss ramps which vary slowly in space, and rigidly propagate in time, as well as those which are slowly-vary in time, but are homogeneous in space. In the former, we will show how, the front location and selected pattern is governed by slow passage between convective and absolute instability which can be characterized as a slow passage near a fold bifurcation using projective coordinates and geometric singular perturbation theory. If the ramp does not propagate, then fronts are governed by slow-passage through a pitchfork bifurcation and a connecting solution of the Painléve-II equation. In the latter case of homogeneous temporal quench, we show a pointwise linearized analysis paired with a Burgers’ modulational approximation can predict the patterned front.

 

WebEx Link: https://nationaltaiwanuniversity-ksz.my.webex.com/nationaltaiwanuniversity-ksz.my/j.php?MTID=m65196702b2080b4d2f4687a275b45175

 

Organizers: Chueh-Hsin Chang (CCU), Jia-Yuan Dai (NTHU), Bo-Chih Huang (CCU), Chih-Chiang Huang (CCU), Chang-Hong Wu (NYCU)