C3

The vast majority of the World's documented meteorite specimens have been collected from Antarctica. This is due to Antarctica’s ice dynamics, which allows for the significant concentration of meteorites onto ice surfaces known as Meteorite Stranding Zones. However, meteorite collection data shows a significant anomaly exists: the proportion of iron-based meteorites are under-represented compared to those found in the rest of the World. Here I explain that englacial solar warming provides a plausible explanation for this shortfall: as meteorites are transported up towards the surface of the ice they become exposed to increasing amounts of solar radiation, meaning it is possible for meteorites with a high-enough thermal conductivity (such as iron) to reach a depth at which they melt their underlying ice and sink back downwards, offsetting the upwards transportation. An enticing consequence of this mechanism is that a sparse layer of  meteorites lies just beneath the surface of these Meteorite Stranding Zones...

Inverse problems arise in many applications. One could solve them by adopting a Bayesian framework, to account for uncertainty which arises from our observations. The solution of an inverse problem is given by a probability distribution. Usually, efficient methods at hand to extract information from this probability distribution involves the solution of an optimization problem, where the objective function is highly nonconvex. In this talk, we explore a reformulation of inverse problems, which helps in convexifying the objective function. We also discuss a method to sample from this probability distribution.

Much of our understanding of the tropospheric dynamics relies on the concept of discrete internal modes. However, discrete modes are the signature of a finite system, while the atmosphere should be modeled as infinite and "is characterized by a single isolated eigenmode and a continuous spectrum" (Lindzen, JAS 2003). Is it then unphysical to use discrete modes? To resolve this issue we obtain an approximate radiation condition at the tropopause --- this yields an EBC. We then use this EBC to compute a new set of vertical modes: the leaky rigid lid modes. These modes decay, with decay time-scales for the first few modes ranging from an hour to a week. This suggests that the rate of energy loss through upwards propagating waves may be an important factor in setting the time scale for some atmospheric phenomena. The modes are not orthogonal, but they are complete, with a simple way to project initial conditions onto them.

The EBC formulation requires an extension of the dispersive wave theory. There it is shown that sinusoidal waves carry energy with the group speed c_g = d omega / dk, where both the frequency omega and wavenumber k are real. However, when there are losses, complex k's and omega's arise, and a more general theory is required. I will briefly comment on this theory, and on how the Laplace Transform can be used to implement generic EBC.

In this talk, I will present two different aspects of the ice flow modelling, including a theoretical part and an applied part. In the theoretical part, I will derive some "mechanical error estimators'', i.e. estimators that can measure the mechanical error between the most accurate ice flow model (Glen-Stokes) and some approximations based on shallowness assumption. To do so, I will follow residual techniques used to obtain a posteriori estimators of the numerical error in finite element methods for non-linear elliptic problems. In the applied part, I will present some simulations of the ice flow generated by the Rhone Glacier, Switzerland, during the last glacial maximum (~ 22 000 years ago), analyse the trajectories taken by erratic boulders of different origins, and compare these results to geomorphological observations. In particular, I will show that erratic boulders, whose origin is known, constitute valuable data to infer information about paleo-climate, which is the most uncertain input of any paleo ice sheet model. 

Orientable manifolds can only have an odd Euler characteristic in dimensions divisible by 4. I will prove the analogous result for spin and string manifolds, where the dimension can only be a multiple of 8 and 16 respectively. The talk will require very little background. I'll go over the definition of spin and string structures, discuss cohomology operations and Poincare duality.

I will present a basic overview of finiteness conditions, group cohomology, and related quasi-isometry invariance results. In particular, I will show that if a group satisfies certain finiteness conditions, group cohomology with group ring coefficients encodes some structure of the `homology at infinity' of a group. This is seen for hyperbolic groups in the work of Bestvina-Mess, which relates the group cohomology to the Čech cohomology of the boundary.

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.