Sydney Dynamics Group: Priya Subramanian -- Formation of complex spatial patterns in systems with two length scales

Dear all, 

Next week, Friday October 9, Priya Subramanian (Oxford) will give a talk at 4pm (Sydney
time) via Zoom.  

Zoom link: https://uni-sydney.zoom.us/j/87496012601 
Meeting ID: 874 9601 2601 

Title: Formation of complex spatial patterns in systems with two length scales 

Abstract: 
Pattern formation in many real world systems such as neural-field models,
reaction-diffusion systems and fluid systems such as the Faraday wave system have
separation of scales leading to nonlinear modal interactions.  A general analysis of
possible terms that can arise via modal interactions is subject to both the choice of a
lattice grid and the ratio between the two length scales $q$.  

In the first half, we are motivated by the observance of different grid states and
superlattice states in experiments of the Faraday wave system.  This leads us to
consider a hexagonal lattice grid and identify families of amplitude equations for
different values of the ratio in the range $0<q<1/2$.  For a chosen case with
$q=1/\sqrt{7}$, we use homotopy methods to investigate the existence and stability of
multiple co-existing superlattice patterns over a range of growth rates for both the
length scales.  

In the second half, we are motivated by the formation of complex self-organised
quasicrystal patterns during crystallisation of soft matter.  We can model these systems
in terms of a conserved pattern forming system within a phase field crystal approach.
For such a soft matter system, with the ratio of length scales in the range $1/2<q<1$,
we look to determine the conditions under which we can find both spatially extended and
localised quasicrystals both in two and three dimensions.  



Past talks can be found on the YouTube channel:
https://www.youtube.com/channel/UCZqgDJ21wbdzMbeIdealpUg/ 

I hope to see you all online.  

Lachlan