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2018/19 semester 2 events in Mathematics

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Mon 21/01/19 15:00
Dalhousie 1F18
Mathematics Seminar
Prof. Kevin Painter (Heriot-Watt University)
In silico modelling of Green Turtle homing to Ascension Island.
abstract

Abstract

A dot in the vastness of the Atlantic, Ascension Island remains a lifelong goal for the green sea turtles that hatched there, returning as adults every three or four years to nest. This navigating puzzle was brought to the scientific community's attention by Charles Darwin and remains a topic of considerable speculation. Various cues have been suggested, with orientation to geomagnetic field elements and following odour plumes to their island source among the most compelling. We develop agent based and continuous models that model the oriented movement of turtles in the oceanic environment, utilising ocean flow, wind and geomagnetic field data sets. Through a comprehensive in silico investigation we test the hypothesis that multimodal cue following, in which turtles utilise multiple guidance cues, is the most effective strategy. Our analysis shows how population homing efficiency improves as the number of utilised cues is increased, even under “extreme” scenarios where the overall strength of navigating information decreases.

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Mon 28/01/19 14:00
Fulton G20
Mathematics Seminar
Prof. Toby Wood (Newcastle Unversity)
MHD in neutron stars
abstract

Abstract

Neutron stars harbour magnetic fields of up to 10^16 Gauss -- the strongest in the Universe. This field is amplified by rapid contraction and dynamo action during the star's formation, and survives on long timescales because of the star's near-perfect conductivity. In the star's solid crust the field is supported by the flow of electrons, whereas in the superfluid core it is supported by the quantized circulation of protons. The field plays a central role in all the observable phenomena of pulsars, including starquakes, rotational glitches, and giant flares. This talk will review the magneto-hydrodynamics of neutron stars, and the implications for pulsar observations.

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Mon 04/02/19 15:00
Dalhousie 1F18
Mathematics Seminar
Dr. Chiara Saffirio (University of Zurich)
From the many-body quantum dynamics to the Vlasov equation.
abstract

Abstract

We review some results on the joint mean-field and semiclassical limit of the N-body Schrödinger dynamics leading to the Vlasov equation, which is a model in kinetic theory for charged or gravitating particles. The results we present include the case of singular interactions and provide explicit estimates on the convergence rate, using the Hartree-Fock theory for interacting fermions as a bridge between many-body and Vlasov dynamics.

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Tue 19/02/19 15:00
Fulton J20
Mathematics Seminar
Prof. Alan Hood (University of St Andrews)
Solar Avalanches and Cellular Automata: coronal magnetic energy release via an MHD avalanche
abstract

Abstract

Solar flares can be thought of as a sudden and rapid release of a large amount of magnetic energy. Frequently the initial energy release occurs at one location and rapidly spreads along the whole structure. This has been modelled as an avalanche, using cellular automata, based on simple sand-pile models. These models seem to produce characteristics that are similar to solar observations, with the magnetic field existing in a state of self-organised criticality. Any additional stresses to the magnetic field in this state will immediately result in a release of energy. With this approach, large avalanches can model solar flares and lots of small avalanches can model the constant release of magnetic energy needed to heat the solar corona. One issue with this approach is that the cellular automata are based on simple rules that are not derived from the governing equations of Magnetohydrodynamics.

For the first time, we demonstrate how an MHD avalanche can occur in a multi-threaded coronal loop. The implications for coronal heating are discussed.

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Tue 19/02/19 15:00
Fulton J20
Mathematics Seminar
Prof. Alan Hood (University of St Andrews)
Plasma Avalanches
Mon 11/03/19 14:00
Fulton G20
Mathematics Seminar
Dr. Raphael Stuhlmeier (University of Plymouth)
Nonlinear wave interaction for broad-banded, open seas - deterministic and stochastic theory
abstract

Abstract

Nonlinear interaction, along with wind input and dissipation, is one of the key drivers of wave evolution at sea, and is included in every modern wave-forecast model. The mechanism behind the nonlinear interaction terms in such models is based on the kinetic equation for wave spectra first derived by Hasselmann. This does not allow, for example, for statistically inhomogeneous wave fields, and is restricted to very long time-scales.

Beginning with the incompressible Euler equations, one may find simpler deterministic equations for the third-order problem, such as the Zakharov equation or the nonlinear Schrödinger equation. Using these, I will sketch the derivation of a discretized equation for the fast evolution of random, inhomogeneous surface wave fields, along lines first laid out by Crawford, Saffman, and Yuen. This allows for a more general treatment of the stability and long-time behaviour of broad-banded sea states.

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Mon 18/03/19 15:00
Dalhousie 2F15
Mathematics Seminar
Dr. Antonia Wilmot-Smith (University of St Andrews)
Early experiences with using Lecture Capture in a Mathematics department.
abstract

Abstract

This session will discuss the experiences of a department and its students following a University-wide introduction of an optional lecture capture system in 2017/18. Topics include uptake by lecturers and associated philosophies, practicalities from a lecturer perspective, student engagement (how students use the recordings, and how use relates to final grades), and student experience. Some current literature in the field will be reviewed.

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Fri 22/03/19 16:30
Dalhousie 3G02
Mathematics Seminar
Prof. Olivier Pironneau (Univeristé Pierre et Marie Curie)
Mathematics and Supercomputing
abstract

Abstract

Two of the greatest mathematicians of the twentieth century, John von Neumann and Alan Turing, laid the foundations of supercomputing during WWII. Ever since then, the progress of supercomputing is linked with algorithmic discoveries made by mathematicians, as observed by N. Trefethen in a lecture. Conjugate Gradient solvers (M. Hestenes, 1953), Fortran (J. Bachus, 1957), Sorting (D. Knuth, 1963), FFT (J. Cooley, J. Tukey, 1965),the frontal method (B. Iron, 1970), Multigrids (Achi Brandt, 1978), the fast multipole method (V. Rohklin, 1985).

Scientists trained in computer science came late of course, and certainly invented great tools for supercomputing such as the language Pascal (N. Wirth, 1975), but mathematics-trained researchers are also at the origin of many of our tools such as C++ (B.Stroustrup, 1979), Python (G. van Rossum, 2001), MPI and Open MP (J. Dongara, 1991). The Domain Decomposition Method is as old as P. Schwarz (an astronomer, 1870) but the recent developments are mostly due to mathematicians. Yet a number of methods have not yet received sufficient mathematical studies, such as Smooth Particle Hydrodynamics (J. Monaghan, 1977) and model reduction by deep neural network (2010). The supercomputer is a infinite source of mathematical problems!

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Mon 25/03/19 15:00
Dalhousie 2F13
Mathematics Seminar
Dr. Danielle Hilhorst (Universite Paris-Sud)
A stochastic mass conserved Allen-Cahn equation with nonlinear diffusion
abstract

Abstract

In this talk, we prove a well-posedness result for an initial boundary value problem for a stochastic nonlocal reaction-diffusion equation with nonlinear diffusion together with a nul-flux boundary condition. We suppose that the space dimension is arbitrary and that the noise is additive and induced by a Q-Brownian motion. We then shortly discuss the case of linear diffusion with a multiplicative noise, and present an existence and uniqueness result in space dimensions up to 6. This is joint work with Perla El Kettani and Kai Lee.

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