Emergent structures in reaction-advection-diffusion systems on a sphere

Physical Review. E
Andrew L KrauseRobert A Van Gorder

Abstract

We demonstrate unusual effects due to the addition of advection into a two-species reaction-diffusion system on the sphere. We find that advection introduces emergent behavior due to an interplay of the traditional Turing patterning mechanisms with the compact geometry of the sphere. Unidirectional advection within the Turing space of the reaction-diffusion system causes patterns to be generated at one point of the sphere, and transported to the antipodal point where they are destroyed. We illustrate these effects numerically and deduce conditions for Turing instabilities on local projections to understand the mechanisms behind these behaviors. We compare this behavior to planar advection which is shown to only transport patterns across the domain. Analogous transport results seem to hold for the sphere under azimuthal transport or away from the antipodal points in unidirectional flow regimes.

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Citations

Aug 12, 2020·Bulletin of Mathematical Biology·Nick P TaylorRobert A Van Gorder
Jun 17, 2018·Physical Review. E·Andrew L KrauseEamonn A Gaffney
Dec 5, 2018·Bulletin of Mathematical Biology·Andrew L KrauseRobert A Van Gorder
Jan 22, 2021·Journal of Mathematical Biology·Robert A Van GorderAndrew L Krause
Mar 20, 2021·Bulletin of Mathematical Biology·Thomas E WoolleyEamonn A Gaffney
Nov 9, 2021·Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences·Andrew L KrauseVáclav Klika

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