14:00
A stochastic model for linking and predicting spatial patterns in species-rich ecosystems
16:30
Recent applications of and trends in model theory.
Abstract
There are many recent points of contact of model theory and other
parts of mathematics: o-minimality and Diophantine geometry, geometric group
theory, additive combinatorics, rigid geometry,... I will probably
emphasize long-standing themes around stability, Diophantine geometry, and
analogies between ODE's and bimeromorphic geometry.
14:15
14:15
Climate Change and Geoengineering - Marine Cloud Brightening (MCB)
An adaptive finite element algorithm for the solution of time-dependent free-surface incompressible flow problems
Three-wave interactions, quasipatterns and spatio-temporal chaos in the Faraday Wave experiment
Abstract
Three-wave interactions form the basis of our understanding of many
nonlinear pattern forming systems because they encapsulate the most basic
nonlinear interactions. In problems with two comparable length scales, such
as the Faraday wave experiment with multi-frequency forcing, consideration
of three-wave interactions can explain the presence of the spatio-temporal
chaos found in some experiments, enabling some previously unexplained
results to be interpreted in a new light. The predictions are illustrated
with numerical simulations of a model partial differential equation.
16:30
On the Moffatt-Pukhnachov problem
Abstract
The classic coating-flow problem first studied experimentally by Moffat and asymptotically by Pukhnachov in 1977 is reconsidered in the framework of multiple-timescale asymptotics. Two-timescale approximations of the height of the thin film coating a rotating horizontal circular cylinder are obtained from an asymptotic analysis, in terms of small gravitational and capillary parameters, of Pukhnachov's nonlinear evolution for the film thickness. The transition, as capillary effects are reduced, from smooth to shock-like solutions is examined, and interesting large-time dynamics in this case are determined via a multiple-timescale analysis of a Kuramoto-Sivashinsky equation. A pseudo-three-timescale method is proposed and demonstrated to improve the accuracy of the smooth solutions, and an asymptotic analysis of a modified Pukhnachov's equation, one augmented by inertial terms, leads to an expression for the critical Reynolds number above which the steady states first analysed by Moffatt and Pukhnachov cannot be realised. As part of this analysis, some interesting implications of the effects of different scalings on inertial terms is discussed. All theoretical results are validated by either spectral or extrapolated numerics.
Fizzle or Frazzle - Problems with Ignition
Abstract
The phenomenon of ignition is one with which we are all familiar, but which is remarkably difficult to define and model effectively. My own (description rather than definition) is “initiation of a (high temperature) self-sustaining exothermic process”; it may of course be desirable, as in your car’s engine, or highly undesirable, as the cause of many disastrous fires and explosions Both laboratory experiments and numerical simulations demonstrate its extreme sensitivity to external influences, past history and process (essentially chemical) kinetics, but at the heart of all instances there appears to be some “critical” unstable equilibrium state. Though some analytical modelling has been useful in particular cases, this remains in general virgin territory for applied mathematicians – perhaps there is room for some “knowledge transfer” here.