ncku-talk2013-12-12

NCTS(South)/ NCKU Math Colloquium

DATE 2013-12-12　15:10-16:00

PLACE R204, 2F, NCTS, NCKU

SPEAKER 陳俊全教授（台大數學系）

TITLE Simple PDE Model of Spot Replication

ABSTRACT This is a joint work with Theodore Kolokolnikov. We propose a simple PDE model which exhibits self-replication of spot solutions in any dimension. This model is analysed in one and higher dimensions. In the radially symmetric case, we rigorously demonstrate that the conditions proposed by Nishiura and Ueyama for self-replication are satisfied. In dimension three, two different types of replication mechanisms are analysed.
The first type is due to radially symmetric instability, whereby a spot bifurcates into a ring. The second type is non-radial instability, which causes a spot to deform into a peanut-like shape, and eventually split into two spots. Both types of replication are observed in our model, depending on parameter choice. Numerical simulations are shown confirming our analytical results.

NCTS(South)/ NCKU Math Colloquium

DATE	2013-12-12　15:10-16:00

PLACE	R204, 2F, NCTS, NCKU

SPEAKER	陳俊全教授（台大數學系）

TITLE	Simple PDE Model of Spot Replication

ABSTRACT	This is a joint work with Theodore Kolokolnikov. We propose a simple PDE model which exhibits self-replication of spot solutions in any dimension. This model is analysed in one and higher dimensions. In the radially symmetric case, we rigorously demonstrate that the conditions proposed by Nishiura and Ueyama for self-replication are satisfied. In dimension three, two different types of replication mechanisms are analysed. The first type is due to radially symmetric instability, whereby a spot bifurcates into a ring. The second type is non-radial instability, which causes a spot to deform into a peanut-like shape, and eventually split into two spots. Both types of replication are observed in our model, depending on parameter choice. Numerical simulations are shown confirming our analytical results.