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Upcoming MBI Seminars:
Tuesday Seminar
Series
Organizer: TBA
Postdoctoral
Seminars
Organizer: Barbara Szomolay
Past MBI Seminars:
2007-2008
Past MBI Seminars:
2006-2007
Past MBI Seminars:
2005-2006
Past
MBI Seminars: 2004-2005
Past
MBI Seminars: 2003-2004
Past
MBI Seminars: 2002-2003
Postdoc Seminars
Monday, September 8, 2008; 10:30-11:30am
MBI Lecture Hall - Jennings Hall, Room 355
Speaker: Dr. Anotida Madzvamuse, University of Sussex, Dept of Mathematics
Title: Turing diffusion-driven instability conditions for reaction-diffusion systems on continuously deforming domains
In this talk, I will extend the Turing diffusion-driven instability conditions for reaction-
diffusion systems from fixed domains to continuously deforming or growing domains for
some growth profiles satisfying the condition that the divergence of the domain velocity is a
constant. By using the arbitrary Lagrangian-Eulerian formulation (ALE), the model equations
on a continuously deforming domain are transformed to a fixed domain at each time,
resulting in a conservative system. Linearising the conservative ALE formulation around a
time-independent solution u_s we show that u_s is a solution of a system of nonlinear
algebraic equations. We further derive and prove the conditions that generalise the classic
Turing parameter space inequalities for the case of growing domains and we show that
these conditions are a function of not only the model parameters in the reaction terms but
also are a function of the divergence of the domain velocity. A fundamental structural
difference between our diffusion-driven instability conditions and those obtained on fixed
domains, is that our results do not enforce cross/pure kinetics thereby demonstrating that
domain growth enlarges the potential range of kinetics which can lead to patterning.
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