Past Mathematical Geoscience Seminar

22 February 2013
14:30
Abstract
Thermomechanical processes observed in deformable solids under intensive dynamic or quasi-static loadings consist of coupled mechanical, thermal and fracturing stages. The fracturing processes involve formation, motion and interaction of defects in crystals, phase transitions, breaking of bonds between atoms, accumulation of micro-structural damages (pores, cracks), etc. Irreversible deformations, zones of adiabatic shear micro-fractures are caused by these processes. Dynamic fracturing is a complicated multistage process, which includes appearance, evolution and confluence of micro-defects and formation of embryonic micro-cracks and pores that can grow and lead to the breaking-up of bodies with formation of free surfaces. This results in a need to use more advanced mathematical and numerical techniques. This talk presents modelling of irreversible deformation near the tip of a crack in a porous domain containing oil and gas during the hydraulic fracturing process. The governing equations for a porous domain containing oil and gas are based on constructing a mathematical model of thermo-visco-elasto-plastic media with micro-defects (micro-pores) filled with another phase (e.g., oil or/and gas). The micro-pores can change their size during the process of dynamical irreversible deformation. The existing pores can expand or collapse. The model was created by using fundamental thermodynamic principles and, therefore, it is a thermodynamically consistent model. All the processes (i.e., irreversible deformation, fracturing, micro-damaging, heat transfer) within a porous domain are strongly coupled. An explicit normalized-corrected meshless method is used to solve the resulting governing PDEs. The flexibility of the proposed technique allows efficient running using a great number of micro- and macro- fractures. The results are presented, discussed and future studies are outlined.
  • Mathematical Geoscience Seminar
8 February 2013
14:30
Dr Fenwick Cooper
Abstract
We are interested in finding the Probability Density Function (PDF) of high dimensional chaotic systems such as a global atmospheric circulation model. The key difficulty stems from the so called “curse of dimensionality”. Representing anything numerically in a high dimensional space seems to be just too computationally expensive. Methods applied to dodge this problem include representing the PDF analytically or applying a (typically linear) transformation to a low dimensional space. For chaotic systems these approaches often seem extremely ad-hoc with the main motivation being that we don't know what else to do. The Lorenz 95 system is one of the simplest systems we could come up with that is both chaotic and high dimensional. So it seems like a good candidate for initial investigation. We look at two attempts to approximate the PDF of this system to an arbitrary level of accuracy, firstly using a simple Monte-Carlo method and secondly using the Fokker-Planck equation. We also describe some of the (sometimes surprising) difficulties encountered along the way.
  • Mathematical Geoscience Seminar
25 January 2013
14:30
Dr Andrew Wells
Abstract
In many places, the Antarctic and Greenland ice sheets are fringed by tongues of ice floating on the ocean, called ice shelves. Recent observations and modelling suggest that melting and disintegration of the floating ice shelves can impact ice sheet flow, and hence have consequences for sea level rise. Of particular interest are observations of channels and undulations in the ice shelf base, for which the conditions for genesis remain unclear. To build insight into the potential for melting-driven instability of the ice shelf base, this talk will consider a free boundary problem with melting at the ice-ocean interface coupled to a buoyant plume of meltwater confined below a stationary ice shelf. An asymptotic model of turbulent heat transfer in the meltwater plume reveals that melting rates depend on ice-shelf basal slope, with potentially shocking consequences for the evolving ice-shelf geometry
  • Mathematical Geoscience Seminar
30 November 2012
14:30
Abstract
Mesocosm experiments provide a major test bed for models of plankton, greenhouse gas export to the atmosphere, and changes to ocean acidity, nitrogen and oxygen levels. A simple model of a mesocosm plankton ecology is given in terms of a set of explicit natural population dynamics rules that exactly conserve a key nutrient. These rules include many traditional population dynamics models ranging from Lotka-Volterra systems to those with more competitors and more trophic levels coupled by nonlinear processes. The rules allow a definition of an ecospace and an analysis of its behaviour in terms of equilibrium points on the ecospace boundary. Ecological issues such as extinctions, plankton bloom succession, and system resilience can then be analytically studied. These issues are understood from an alternative view point to the usual search for interior equilibrium points and their classification, coupled with intensive computer simulations. Our approach explains why quadratic mortality usually stabilises large scale simulation, but needs to be considered carefully when developing the next generation of Earth System computer models. The ‘Paradox of the Plankton’ and ‘Invasion Theory’ both have alternative, yet straightforward explanations within these rules.
  • Mathematical Geoscience Seminar
16 November 2012
14:30
Dr Andrew J. Hogg
Abstract
Turbidity currents - submarine flows of sediment - are capable of transporting particulate material over large distance. However direct observations of them are extremely rare and much is inferred from the deposits they leave behind, even though the characteristics of their source are often not known. The submarine flows of volcanic ash from the Soufriere Hills Volcano, Monsterrat provide a unique opportunity to study a particle-driven flow and the deposit it forms, because the details of the source are relatively well constrained and through ocean drilling, the deposit is well sampled. We have formed simple mathematical models of this motion that capture ash transport and deposit. Our description brings out two dynamical features that strongly influence the motion and which have previously often been neglected, namely mixing between the particulate flow and the oceanic water and the distribution of sizes suspended by the flow. We show how, in even simple situations, these processes alter our views of how these currents propagate.
  • Mathematical Geoscience Seminar
2 November 2012
14:30
Jonny Kingslake
Abstract
Ice-dammed lakes form next to, on the surface of, and beneath glaciers and ice sheets. Some lakes are known to drain catastrophically, creating hazards, wasting water resources and modulating the flow of the adjacent ice. My work aims to increase our understanding of such drainage. Here I will focus on lakes that form next to glaciers and drain subglacially (between ice and bedrock) through a channel. I will describe how such a system can be modelled and present results from model simulations of a lake that fills due to an input of meltwater and drains through a channel that receives a supply of meltwater along its length. Simulations yield repeating cycles of lake filling and drainage and reveal how increasing meltwater input to the system affects these cycles: enlarging or attenuating them depending on how the meltwater is apportioned between the lake and the channel. When inputs are varied with time, simulating seasonal meteorological cycles, the model simulates either regularly repeating cycles or irregular cycles that never repeat. Irregular cycles demonstrate sensitivity to initial conditions, a high density of periodic orbits and topological mixing. I will discuss how these results enhance our understanding of the mechanisms behind observed variability in these systems.
  • Mathematical Geoscience Seminar
19 October 2012
14:30
Abstract
4D-Var is a widely used data assimilation method, particularly in the field of Numerical Weather Prediction. However, it is highly sequential: integrations of a numerical model are nested within the loops of an inner-outer minimisation algorithm. Moreover, the numerical model typically has a low spatial resolution, limiting the number of processors that can be employed in a purely spatial parallel decomposition. As computers become ever more parallel, it will be necessary to find new dimensions over which to parallelize 4D-Var. In this talk, I consider the possibility of parallelizing 4D-Var in the temporal dimension. I analyse different formulations of weak-constraint 4D-Var from the point of view of parallelization in time. Some formulations are shown to be inherently sequential, whereas another can be made parallel but is numerically ill-conditioned. Finally, I present a saddlepoint formulation of 4D-Var that is both parallel in time and amenable to efficient preconditioning. Numerical results, using a simple two-level quasi-geotrophic model, will be presented.
  • Mathematical Geoscience Seminar
15 June 2012
14:30
Dr Henry Winstanley
Abstract
Respiration is a redox reaction in which oxidation of a substrate (often organic) is coupled to the reduction of a terminal electron acceptor (TEA) such as oxygen. Iron oxides in various mineral forms are abundant in sediments and sedimentary rocks, and many subsurface microbes have the ability to respire using Fe(III) as the TEA in anoxic conditions. This process is environmentally important in the degradation of organic substrates and in the redox-cycling of iron. But low mineral solubility limits the bioavailability of Fe(III), which microbes access primarily through reductive dissolution. For aqueous nutrients, expressions for microbial growth and nutrient uptake rates are standardly based on Monod kinetics. We address the question of what equivalent description is appropriate when solid phase Fe(III) is the electron acceptor.
  • Mathematical Geoscience Seminar
1 June 2012
14:30
Dr Jari Fowkes
Abstract
This talk will consist of two parts. In the first part we will present a motivating application from oil reservoir simulation, namely finding the location and trajectory of an oil producing well which maximises oil production. We will show how such a problem can be tackled through the use of radial basis function (RBF) approximation (also known as Kriging or Gaussian process regression) and a branch and bound global optimization algorithm. In the second part of the talk we will show how one can improve the branch and bound algorithm through the use of Lipschitz continuity of the RBF approximation. This leads to an entirely new global optimization algorithm for twice differentiable functions with Lipschitz continuous Hessian. The algorithm makes use of recent cubic regularisation techniques from local optimization to obtain the necessary bounds within the branch and bound algorithm.
  • Mathematical Geoscience Seminar
18 May 2012
14:30
Dr. Hilmar Gudmundsson
Abstract
Inverse methods are frequently used in geosciences to estimate model parameters from indirect measurements. A common inverse problem encountered when modelling the flow of large ice masses such as the Greenland and the Antarctic ice sheets is the determination of basal conditions from surface data. I will present an overview over some of the inverse methods currently used to tackle this problem and in particular discuss the use of Bayesian inverse methods in this context. Examples of the use of adjoint methods for large-scale optimisation problems that arise, for example, in flow modelling of West-Antarctica will be given.
  • Mathematical Geoscience Seminar

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