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SUMMARY:Understanding Turing patterns in heterogeneous reaction-diffusion
systems - Prof Robert A. Van Gorder (Department of Mathematics and Statist
ics University of Otago)
DTSTART;VALUE=DATE-TIME:20230217T140000Z
DTEND;VALUE=DATE-TIME:20230217T150000Z
UID:https://talks.ox.ac.uk/talks/id/22df42d8-93f8-445f-b700-8d7c82c662e8/
DESCRIPTION:The Turing pattern is a key concept in the modern study of rea
ction-diffusion systems\, with Turing patterns proposed a possible explana
tion for the spatial structure observed in myriad physical\, chemical\, an
d biological systems. Real-world systems are not always so clean as ideali
zed Turing systems\, and in this talk we will take up the case of more mes
sy reaction-diffusion systems involving explicit space or time dependence
in diffusion or reaction terms. Turing systems of this nature arise in sev
eral applications\, such as when a Turing system is studied on a growing s
ubstrate\, is subjected to a temperature gradient\, or is immersed within
a fluid flow. The analysis of these messy Turing systems is not as straigh
tforward as in the idealized case\, with the explicit space or time depend
ence greatly complicating or even preventing most standard routes of analy
sis. Motivated by patterning in phenomena involving explicit space or time
dependence\, and by the interesting mathematical challenges inherent in t
he study of such systems\, in this talk we consider the following question
s:\n\n* Is it possible to obtain generalizations of the Turing instability
conditions for non-autonomous\, spatially heterogeneous reaction-diffusio
n systems?\n* What can one say about predicting nascent patterns in these
systems?\n* What role does explicit space or time dependence play in selec
ting fully developed patterns in these systems?\n* Is it possible to explo
it this space or time dependence in order to manipulate the form of emerge
nt patterns?\n\nWe will also highlight some of the applications opened up
by the analysis of heterogeneous Turing systems.\nSpeakers:\nProf Robert A
. Van Gorder (Department of Mathematics and Statistics University of Otago
)
LOCATION:Mathematical Institute (L3)\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/22df42d8-93f8-445f-b700-8d7c82c662e8/
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DESCRIPTION:Talk:Understanding Turing patterns in heterogeneous reaction-d
iffusion systems - Prof Robert A. Van Gorder (Department of Mathematics an
d Statistics University of Otago)
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