TIME: 3:30 PM

LOCATION: GMCS 314

SPEAKER: Paul Carter, University of CA, Irvine (Department of Mathematics)

ABSTRACT: Motivated by the appearance of desertification fronts between bare soil and vegetation in dryland ecosystems, we consider the dynamics of planar interfaces between stable homogeneous rest states in multi-component reaction diffusion equations. On sloped terrain, one can find stable traveling interfaces, while on flat ground, one finds that long wavelength instabilities along the interface can lead to labyrinthine Turing-like patterns. To study this behavior, using singular perturbation methods, we analyze instability criteria for planar interfaces in reaction diffusion systems, and we examine the effect of terrain slope on the stability of the interfaces. We also explore the implications of these results in other biological applications, including growing tumors and bacterial colonies.

HOST: Efstathis Charalampidis