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

Mon 28/01/19 14:00 Fulton G20 Mathematics Seminar  Prof. Toby Wood (Newcastle Unversity) MHD in neutron stars  abstractAbstractNeutron 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 nearperfect 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 magnetohydrodynamics of neutron stars, and the implications for pulsar observations. hide 

Mon 04/02/19 15:00 Dalhousie 1F18 Mathematics Seminar  Dr. Chiara Saffirio (University of Zurich) From the manybody quantum dynamics to the Vlasov equation.
 abstractAbstractWe review some results on the joint meanfield and semiclassical limit of the Nbody 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 HartreeFock theory for interacting fermions as a bridge between manybody 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  abstractAbstractSolar 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 sandpile models. These models seem to produce characteristics that are similar to solar observations, with the magnetic field existing in a state of selforganised 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 multithreaded coronal loop. The implications for coronal heating are discussed. hide 

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 broadbanded, open seas  deterministic and stochastic theory  abstractAbstractNonlinear interaction, along with wind input and dissipation, is one of the key drivers of wave evolution at sea, and is included in every modern waveforecast 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 timescales.
Beginning with the incompressible Euler equations, one may find simpler deterministic equations for the thirdorder 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 longtime behaviour of broadbanded sea states. hide 

Mon 18/03/19 15:00 Dalhousie 2F15 Mathematics Seminar  Dr. Antonia WilmotSmith (University of St Andrews) Early experiences with using Lecture Capture in a Mathematics department.  abstractAbstractThis session will discuss the experiences of a department and its students following a Universitywide 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  abstractAbstractTwo 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 mathematicstrained 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! hide 

Mon 25/03/19 15:00 Dalhousie 2F13 Mathematics Seminar  Dr. Danielle Hilhorst (Universite ParisSud) A stochastic mass conserved AllenCahn equation with nonlinear diffusion  abstractAbstractIn this talk, we prove a wellposedness result for an initial boundary value problem for a stochastic nonlocal reactiondiffusion equation with nonlinear diffusion together with a nulflux boundary condition. We suppose that the space dimension is arbitrary and that the noise is additive and induced by a QBrownian 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. hide 
