Past Mathematical Geoscience Seminar

14 March 2014
14:15
Heather Viles
Abstract
Microbial biofilms grow on most rock and stone surfaces and may play critical roles in weathering. With climate change and improving air quality in many cities in Europe biofilms are growing rapidly on many historic stone buildings and posing practical problems for heritage conservation. With many new field and lab techniques available it is now possible to identify the microbes present and start to clarify their roles. We now need help modelling microbial biofilm growth and impacts in order to provide better advice for conservators.
  • Mathematical Geoscience Seminar
14 February 2014
14:15
Abstract
Hazardous geophysical mass flows, such as snow avalanches, debris-flows and pyroclastic flows, often spontaneously develop large particle rich levees that channelize the flow and enhance their run-out. Measurements of the surface velocity near an advancing flow front have been made at the United States Geological Survey (USGS) debris-flow flume, where 10m^3 of water saturated sand and gravel are allowed to flow down an 80m chute onto a run-out pad. In the run-out phase the flow front is approximately invariant in shape and advances at almost constant speed. By tracking the motion of surface tracers and using a simple kinematic model, it was possible to infer bulk motion as incoming material is sheared towards the front, over-run and shouldered to the side. At the heart of the levee formation process is a subtle segregation-mobility feedback effect. Simple models for particle segregation and the depth-averaged motion of granular avalanches are described and one of the first attempts is made to couple these two types of models together. This process proves to be non-trivial, yielding considerable complexity as well as pathologies that require additional physics to be included.
  • Mathematical Geoscience Seminar
31 January 2014
14:15
Mauro Werder
Abstract
Jakobshavn Isbrae and many other fast flowing outlet glaciers of present and past ice sheets lie in deep troughs which often have several overdeepened sections. To make their fast flow possible their bed needs to be slippery which in turn means high basal water pressures. I will present a model of subglacial water flow and its application to Jakobshavn. I find that, somewhat surprisingly, the reason for Jakobshavn's fast flow might be the pressure dependence of the melting point of ice. The model itself describes the unusual fluid dynamics occurring underneath the ice; it has an interesting mathematical structure that presents computational challenges.
  • Mathematical Geoscience Seminar
6 December 2013
14:15
Daniel Goldberg
Abstract
Stick-slip behavior is a distinguishing characteristic of the flow of Whillans Ice Stream. Distinct from stick-slip on northern hemisphere glaciers, which is generally attributed to supraglacial melt, the behavior is thought be be controlled by fast processes at the bed and by tidally-induced stress. Modelling approaches to studying this phenomenon typically consider ice to be an elastically-deforming solid (e.g. Winberry et al, 2008; Sergienko et al, 2009). However, there remains a question of whether irreversible, i.e. viscous, deformation is important to the stick-slip process; and furthermore whether the details of stick-slip oscillations are important to ice stream evolution on longer time scales (years to decades). To address this question I use two viscoelastic models of varying complexity. The first is a modification to the simple block-and-slider models traditionally used to examine earthquake processes on a very simplistic fashion. Results show that the role of viscosity in stick-slip depends on the dominant stress balance. These results are then considered in the context of a continuum description of a viscoelastic ice stream with a rate-weakening base capable of exhibiting stick-slip behavior. With the continuum model we examine the spatial and temporal aspects of stick-slip, their dependence on viscous effects, and how this behavior impacts the mean flow. Different models for the evolution of basal shear stress are examined in the experiments, with qualitatively similar results. A surprising outcome is that tidal effects, while greatly affecting the spectrum of the stick-slip cycle, may have relatively little effect on the mean flow.
  • Mathematical Geoscience Seminar
22 November 2013
14:15
Philip Stier
Abstract
Clouds play a key role in the climate system. Driven by radiation, clouds power the hydrological cycle and global atmospheric dynamics. In addition, clouds fundamentally affect the global radiation balance by reflecting solar radiation back to space and trapping longwave radiation. The response of clouds to global warming remains poorly understood and is strongly regime dependent. In addition, anthropogenic aerosols influence clouds, altering cloud microphysics, dynamics and radiative properties. In this presentation I will review progress and limitations of our current understanding of the role of clouds in climate change and discuss the state of the art of the representation of clouds and aerosol-cloud interactions in global climate models, from (slightly) better constrained stratiform clouds to new frontiers: the investigation of anthropogenic effects on convective clouds.
  • Mathematical Geoscience Seminar
25 October 2013
14:15
William Newman
Abstract
Many years ago, Mark Kac was consulted by biologist colleague Lamont Cole regarding field-based observations of animal populations that suggested the existence of 3-4 year cycles in going from peak to peak. Kac provided an elegant argument for how purely random sequences of numbers could yield a mean value of 3 years, thereby establishing the notion that pattern can seemingly emerge in random processes. (This does not, however, mean that there could be a largely deterministic cause of such population cycles.) By extending Kac's argument, we show how the distribution of cycle length can be analytically established using methods derived from random graph theory, etc. We will examine how such distributions emerge in other natural settings, including large earthquakes as well as colored Brownian noise and other random models and, for amusement, the Standard & Poor's 500 index for percent daily change from 1928 to the present. We then show how this random model could be relevant to a variety of spatially-dependent problems and the emergence of clusters, as well as to memory and the aphorism "bad news comes in threes." The derivation here is remarkably similar to the former and yields some intriguing closed-form results. Importantly, the centroids or "centers of mass" of these clusters also yields clusters and a hierarchy then emerges. Certain "universal" scalings appear to emerge and scaling factors reminiscent of Feigenbaum numbers. Finally, as one moves from one dimension to 2, 3, and 4 dimensions, the scaling behaviors undergo modest change leaving this scaling phenomena qualitatively intact. Finally, we will show how that an adaptation of the Langevin equation from statistical physics provides not simply a null-hypothesis for matching the observation of 3-4 year cycles, but a remarkably simple model description for the behavior of animal populations.
  • Mathematical Geoscience Seminar
14 June 2013
14:30
Dr. Anthony Anderson
Abstract
Colloidal suspensions do not freeze uniformly; rather, the frozen phase (e.g. ice) becomes segregated, trapping bulk regions of the colloid within, which leads to a fascinating variety of patterns that impact both nature and technology. Yet, despite the central importance of ice segregation in several applications, the physics are poorly understood in concentrated systems and continuum models are available only in restricted cases. I will discuss a particular set of steady-state ice segregation patterns that were obtained during a series of directional solidification experiments on concentrated suspensions. As a case study, I will focus of one of these patterns, which is very reminiscent of ice lenses observed in freezing soils and rocks; a form of ice segregation which underlies frost heave and frost weathering. I will compare these observations against an extended version of a 'rigid-ice' model used in previous frost heave studies. The comparison between theory and experiment is qualitatively correct, but fails to quantitatively predict the ice-lensing pattern. This leaves open questions about the validity of the assumptions in 'rigid-ice' models. Moreover, 'rigid-ice' models are inapplicable to the study of other ice segregation patterns. I conclude this talk with some possibilities for a more general model of freezing colloidal suspensions.
  • Mathematical Geoscience Seminar

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