# Applied Mathematics Seminar

## Seminars in 2016

### Seminars in 2016, Semester 2

Wednesday November 30

Andrew Kels (University of Queensland)

Wednesday November 9

Peter Clarkson (University of Kent)

Wednesday October 19

Herbert Huppert (Cambridge University/University of NSW)

Volcanic eruptions, fluid intrusions and false similarity solutions

Wednesday September 21

Kenji Kajiwara (Kyushu University)

An approach to discrete differential geometry from integrable systems

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(1) deformation of smooth/discrete curves: isoperimetric deformation in the Euclidean plane by (discrete) mKdV equation (2) discrete holomorphic function: a discrete power function and the Painlevé VI equation

In the first half, starting from some historical remarks and basic ideas of integrable systems and their discretization, we explain how the hierarchies of integrable systems naturally arise in the context of deformation theory of plane/space curves. Then we demonstrate a formulation of discrete deformation preserving its integrable nature. In the second half, we present an outline of ongoing project with Nalini Joshi, Nobutaka Nakazono and Yang Shi. We explain how the Painlevé equations arise in the theory of discrete holomorphic functions, and give an explicit formula of a discrete power function by Agafonov and Bobenko in terms of the hypergeometric tau function of the Painlevé VI equation.

Wednesday September 14

Shane Keating (University of New South Wales)

Flavours of Baroclinic Instability in the Global Ocean

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*Charney-Green number*relating the strength of the planetary potential vorticity gradient to the surface buoyancy gradient, and the

*Phillips supercriticality*quantifying the stability of the mean shear profile. Different flavours of baroclinic instability are represented by different regimes in parameter space. Within this framework, hydrographic temperature and salinity profiles are used to form a global atlas of baroclinic instability in the ocean, and regional and seasonal patterns are discussed.

Wednesday August 24

Mathieu Desroches (INRIA Sophia Antipolis)

Canards in piecewise-linear slow-fast systems

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Wednesday July 27

Philippe Guyenne (University of Delaware)

The surface signature of internal waves in the ocean

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Wednesday June 29

Yury Stepanyants (University of Southern Queensland)

Modulational instability of quasi-harmonic wave-trains in rotating fluids.

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### Seminars in 2016, Semester 1

Wednesday May 25

Ngamta (Natalie) Thamwattana, (University of Wollongong)

Applications of calculus of variations for modelling proteins, nucleic acids, polymers and carbon nanostructures

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Wednesday May 18

Darren Engwirda, (Massachusetts Institute of Technology)

Towards optimal simplicial mesh generation in two- and three-dimensions

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Wednesday May 11

Chris Lustri (University of Sydney)

Applications of Exponential Asymptotic Methods

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This talk will be divided into two parts. In the first part, I will discuss how exponential asymptotic methods may be used to obtain information about behaviour that occurs on an exponentially-small scale, and in particular, how such methods uncover behaviour known as the Stokes Phenomenon. In the second part of the talk, I will discuss applications of these methods to problems arising in fluid dynamics, and the study of discrete systems.

Wednesday May 4

Bronwyn Hajek, (University of South Australia)

Viscous extensional flow and Symmetry analysis for reaction-diffusion equations

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In the second part of the talk, I will discuss the application of symmetry techniques to reaction-diffusion equations. These types of equations can be used to describe behaviour in many types of systems such as in population dynamics, cell biology, heat transfer and flow in porous media. Symmetry analysis is a useful technique which allows the construction of analytic solutions, enabling the importance of various system parameters to be determined easily.

Wednesday April 27

Peter van Heijster, (Queensland University of Technology)

A geometric approach to stationary defect solutions in one space dimension

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Wednesday April 6

Marcus Webb, (University of Cambridge)

Computing Spectral Data of Infinite Jacobi Matrices

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Wednesday January 13

Stephen Garrett (University of Leicester)

The stability of the boundary-layer flow over rotating spheres and cones

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