I will talk about the boundaries of CAT(0) groups giving definitions, some examples and will state some theorems. I may even prove something if there is time.
The accumulation of surface meltwater on ice shelves can lead to the formation of melt lakes. These structures have been implicated in crevasse propagation and ice-shelf collapse; the Larsen B ice shelf was observed to have a large amount of melt lakes present on its surface just before its collapse in 2002. Through modelling the transport of heat through the surface of the Larsen C ice shelf, where melt lakes have also been observed, this work aims to provide new insights into the ways in which melt lakes are forming and the effect that meltwater filling crevasses on the ice shelf will have. This will enable an assessment of the role of meltwater in triggering ice-shelf collapse. The Antarctic Peninsula, where Larsen C is situated, has warmed several times the global average over the last century and this ice shelf has been suggested as a candidate for becoming fully saturated with meltwater by the end of the current century. Here we present results of a 1-D mathematical model of heat transfer through an idealized ice shelf. When forced with automatic weather station data from Larsen C, surface melting and the subsequent meltwater accumulation, melt lake development and refreezing are demonstrated through the modelled results. Furthermore, the effect of lateral meltwater transport upon melt lakes and the effect of the lakes upon the surface energy balance are examined. Investigating the role of meltwater in ice-shelf stability is key as collapse can affect ocean circulation and temperature, and cause a loss of habitat. Additionally, it can cause a loss of the buttressing effect that ice shelves can have on their tributary glaciers, thus allowing the glaciers to accelerate, contributing to sea-level rise.
Accurate methods for the first-order advection equation, used for example in tracking contaminants in fluids, usually exploit the theory of characteristics. Such methods are described and contrasted with methods that do not make use of characteristics.
Then the second-order wave equation, in the form of a first-order system, is considered. A review of the one-dimensional theory using solutions of various Riemann problems will be provided. In the special case that the medium has the ‘Goupillaud’ property, that waves take the same time to travel through each layer, one can derive exact solutions even when the medium is spatially heterogeneous. The extension of this method to two-dimensional problems will then be discussed. In two-dimensions it is not apparent that exact solutions can be found, however by exploiting a generalised Goupillaud property, it is possible to calculate approximate solutions of high accuracy, perhaps sufficient to be of benchmark quality. Some two-dimensional simulations, using exact one-dimensional solutions and operator splitting, will be described and a numerical evaluation of accuracy will be given.
In this talk I will review mathematical models used to describe the dynamics of ice sheets, and highlight some current areas of active research. Melting of glaciers and ice sheets causes an increase in global sea level, and provides many other feedbacks on isostatic adjustment, the dynamics of the ocean, and broader climate patterns. The rate of melting has increased in recent years, but there is still considerable uncertainty over why this is, and whether the increase will continue. Central to these questions is understanding the physics of how the ice intereacts with the atmosphere, the ground on which it rests, and with the ocean at its margins. I will given an overview of the fluid mechanical problems involved and the current state of mathematical/computational modelling. I will focus particularly on the issue of changing lubrication due to water flowing underneath the ice, and discuss how we can use models to rationalise observations of ice speed-up and slow-down.
I will discuss a couple of techniques often useful to prove quasi-isometric rigidity results for isometry groups. I will then sketch how these were used by B. Kleiner and B. Leeb to obtain quasi-isometric rigidity for the class of fundamental groups of closed locally symmetric spaces of noncompact type.
We will discuss various familiar properties of groups studied in geometric group theory, whether or not they are invariant under quasi-isometry, and why.
One can ask whether the fundamental groups of 3-manifolds are distinguished by their sets of finite quotients. I will discuss the recent solution of this question for Seifert fibre spaces.
I will illustrate how to build families of expanders out of 'very mixing' actions on measure spaces. I will then define the warped cones and show how these metric spaces are strictly related with those expanders.
Humpback whales are iconic mammals at the top of the Antarctic food chain. Their large reserves of lipid-rich tissues such as blubber predispose them to accumulation of lipophilic contaminants throughout their lifetime. Changes in the volume and distribution of lipids in humpback whales, particularly during migration, could play an important role in the pharmacokinetics of lipophilic contaminants such as the organochlorine pesticide hexachlorobenzene (HCB). Previous models have examined constant feeding and nonmigratory scenarios. In the present study, the authors develop a novel heuristic model to investigate HCB dynamics in a humpback whale and its environment by coupling an ecosystem nutrient-phytoplankton-zooplankton-detritus (NPZD) model, a dynamic energy budget (DEB) model, and a physiologically based pharmacokinetic (PBPK) model. The model takes into account the seasonal feeding pattern of whales, their energy requirements, and fluctuating contaminant burdens in the supporting plankton food chain. It is applied to a male whale from weaning to maturity, spanning 20 migration and feeding cycles. The model is initialized with environmental HCB burdens similar to those measured in the Southern Ocean and predicts blubber HCB concentrations consistent with empirical concentrations observed in a southern hemisphere population of male, migrating humpback whales.
It has been conjectured that marine ice sheets (those that
flow into the ocean) are unconditionally unstable when the underlying
bed-slope runs uphill in the direction of flow, as is typical in many
regions underneath the West Antarctic Ice Sheet. This conjecture is
supported by theoretical studies that assume a two-dimensional flow
idealization. However, if the floating section (the ice shelf) is
subject to three-dimensional stresses from the edges of the embayments
into which they flow, as is typical of many ice shelves in Antarctica,
then the ice shelf creates a buttress that supports the ice sheet.
This allows the ice sheet to remain stable under conditions that may
otherwise result in collapse of the ice sheet. This talk presents new
theoretical and experimental results relating to the effects of
three-dimensional stresses on the flow and structure of ice shelves,
and their potential to stabilize marine ice sheets.