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Widely Applied Mathematics Seminars

# Formation of complex spatial patterns in systems with two length scales

Priya Subaramanian, Research Fellow, University of Oxford

Thursday, Nov 12, 2020
3:00 pm to 4:00 pm | Zoom

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.

Speaker Bio

Priya Subramanian is the Hooke Research Fellow at the Mathematical Institute at the University of Oxford. She received her PhD in Aerospace Engineering from the Indian Institute of Technology Madras in 2012. More information, including a list of papers she has published,. may be found on her website: www.priyasubramanian.com.

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