Events

AG dynamics seminar: Nontrivial collective dynamics in a pulse-coupled variant of the Kuramoto model A variant of the Kuramoto model, where the coupling is mediated by delta-pulses sent across a globally coupled network, is investigated upon increasing the coupling strength. The model, which is inspired by the dynamics of leaky integrate and fire neurons, reveals a rather complex collective dynamics. In fact, as soon as the synchronization threshold is overcome, a macroscopic collective dynamics sets in, that appears to be high-dimensional. The macroscopic motion is studied by implementing a standard time-series analysis, while the microscopic (single oscillator) dynamics, is studied with the help of raster plots, phase slips, and single-oscillator Lyapunov exponents.

MAGIC Career Fair

Monday 12th January 2015 at 2pm

MAGIC Public room

Confirmed panelists:

Richard Pinch (GHCQ) and Richard Hill (Atass Sports)
This is a QuestIon and Answer session on jobs opportuniIes aimed specifically at mathematics and statistics PhD students. If you are considering looking for a job this will be an ideal occasion to hear from the panelists what skills they require and to ask them quesIons on how best to approach the job market.
How to attend To attend the MAGIC Career Fair use the Visimeet client to join the MAGIC Public room (meeting ID 55993743) or press the “Connect” button on the MAGIC web site.

http://www1.maths.leeds.ac.uk/~rsturman/ag_dynamics_seminar/wulff.html

MAGIC annual lecture 2014/15

Noether's theorem 100 years on

Professor Elizabeth Mansfield

University of Kent

In 1918, Emmy Noether showed how to calculate conserved quantities for variational problems which have a Lie symmetry, such as invariance under translations and rotations in time and space. Noether obtained the complete result, including the case of invariance under pseudo group actions.
In this talk I will show how Noether's two theorems have been updated to finite difference and to numerical schemes. One outstanding motivation is the desire to incorporate a particular conservation law, potential vorticity, into numerical schemes, needed (I am told) for extreme weather prediction.

In binocular rivalry, conflicting images are presented to the two eyes, and the visual system interprets this combination in sometimes surprising ways. Visual illusions involve ambiguous or incomplete information, presented simultaneously to both eyes. Well-known illusions include the Necker cube, the rabbit/duck illusion, the cartoonist William Ely Hill's 'my wife and my mother-in-law', and the spinning dancer, in which a moving image of a dancer appears to spin in either the clockwise or anticlockwise direction. In 2009 Hugh Wilson proposed a neural network model for high-level decision-making in the brain, based on the phenomenon of binocular rivalry. Diekman, Golubitksy and Wang observed that Wilson networks are useful for understanding rivalry itself. The talk describes ongoing work with Golubitsky and Diekman in which we generalise Wilson networks, and model illusions as well as rivalry. The model corresponds well to several experiments in the literature, and in some cases leads to new predictions.

Applying asymptotics, averaging and reduction by symmetry in Hamilton's principle for the Euler fluid equations governing a rotating, stratified incompressible flow produces the main sequence of GFD approximations. Each model in this sequence of approximations possesses a Kelvin circulation theorem, and conserves energy and potential vorticity (PV). Legendre transforming the symmetry-reduced Lagrangian yields the Lie-Poisson Hamiltonian formulation of GFD and its Eulerian conservation laws, which may be used to classify steady solutions as relative equilibria and determine sufficient conditions for their nonlinear stability.

We propose a method for accounting for model error due to unresolved scales within the context of ensemble Kalman filtering. This method estimates a model error correction to the forecast step by using historical reanalysis increments to build a model error covariance matrix. We compare two different versions of the method; a time-constant model error treatment where the same model error bias correction is added after each forecast, and a time- varying treatment where the bias correction randomly varies with each forecast. We compare both methods with the standard method of dealing with model error through inflation and localization, and illustrate our results with numerical simulations on a low order nonlinear system showing chaotic dynamics. The results show that the filter skill is significantly improved through the proposed model error treatments, and that both methods require far less parameter tuning than the standard approach. This is joint work with Alberto Carrassi.