Past Junior Applied Mathematics Seminar

29 May 2012
13:15
Huy Vu
Abstract

 Higher-order transformations are ubiquitous within data management. In relational databases, higher-order queries appear in numerous aspects including query rewriting and query specification. In XML databases, higher-order functions are natural due to the close connection of XML query languages with functional programming. We investigate higher-order query languages that combine higher- order transformations with ordinary database query languages. We define higher-order query languages based on Relational Algebra and XQuery. We also study basic problems for these query languages including evaluation, containment, and type inference. We show that even though evaluating these higher-order query languages is non-elementary, there are subclasses that are polynomially reducible to evaluation for ordinary query languages.

  • Junior Applied Mathematics Seminar
15 May 2012
13:15
Katie Leonard
Abstract

 The use of tissue engineered implants could facilitate unions in situations where there is loss of bone or non-union, thereby increasing healing time, reducing the risk of infections and hence reducing morbidity. Currently engineered bone tissue is not of sufficient quality to be used in widespread clinical practice.  In order to improve experimental design, and thereby the quality of the tissue-constructs, the underlying biological processes involved need to be better understood. In conjunction with experimentalists, we consider the effect hydrodynamic pressure has on the development and regulation of bone, in a bioreactor designed specifically for this purpose. To answer the experimentalists’ specific questions, we have developed two separate models; in this talk I will present one of these, a multiphase partial differential equation model to describe the evolution of the cells, extracellular matrix that they deposit, the culture medium and the scaffold.  The model is then solved using the finite element method using the deal.II library.

  • Junior Applied Mathematics Seminar
1 May 2012
13:15
Lucas Jeub
Abstract
With the advent of powerful computers and the internet, our ability to collect and store large amounts of data has improved tremendously over the past decades. As a result, methods for extracting useful information from these large datasets have gained in importance. In many cases the data can be conveniently represented as a network, where the nodes are entities of interest and the edges encode the relationships between them. Community detection aims to identify sets of nodes that are more densely connected internally than to the rest of the network. Many popular methods for partitioning a network into communities rely on heuristically optimising a quality function. This approach can run into problems for large networks, as the quality function often becomes near degenerate with many near optimal partitions that can potentially be quite different from each other. In this talk I will show that this near degeneracy, rather than being a severe problem, can potentially allow us to extract additional information
  • Junior Applied Mathematics Seminar
6 March 2012
13:30
Emma Warneford
Abstract

Large-scale zonal jets are observed in a wide range of geophysical and astrophysical flows; most strikingly in the atmospheres of the Jovian gas giant planets. Jupiter's upper atmosphere is highly turbulent, with many small vortices, and strong westerly winds at the equator. We consider the thermal shallow water equations as a model for Jupiter's upper atmosphere. Originally proposed for the terrestrial atmosphere and tropical oceans, this model extends the conventional shallow water equations by allowing horizontal temperature variations with a modified Newtonian cooling for the temperature field. We perform numerical simulations that reproduce many of the key features of Jupiter’s upper atmosphere. However, the simulations take a long time to run because their time step is severely constrained by the inertia-gravity wave speed. We filter out the inertia-gravity waves by forming the quasigeostrophic limit, which describes the rapidly rotating (small Rossby number) regime. We also show that the quasigeostrophic energy equation is the quasigeostrophic limit of the thermal shallow water pseudo-energy equation, analogous to the derivation of the acoustic energy equation from gas dynamics. We perform numerical simulations of the quasigeostrophic equations, which again reproduce many of the key features of Jupiter’s upper atmosphere. We gain substantial performance increases by running these simulations on graphical processing units (GPUs).

  • Junior Applied Mathematics Seminar
21 February 2012
13:30
Martin Gould
Abstract

 Determining the price at which to conduct a trade is an age-old problem. The first (albeit primitive) pricing mechanism dates back to the Neolithic era, when people met in physical proximity in order to agree upon mutually beneficial exchanges of goods and services, and over time increasingly complex mechanisms have played a role in determining prices. In the highly competitive and relentlessly fast-paced markets of today’s financial world, it is the limit order book that matches buyers and sellers to trade at an agreed price in more than half of the world’s markets.  In this talk I will describe the limit order book trade-matching mechanism, and explain how the extra flexibility it provides has vastly impacted the problem of how a market participant should optimally behave in a given set of circumstances.

  • Junior Applied Mathematics Seminar
7 February 2012
13:30
Mark Curtis
Abstract

 When modelling the motion of a sperm cell in the female reproductive tract, the Reynolds number is found to be very small, thus allowing the nonlinear Navier-Stokes equations to simplify to the linear Stokes equations stating that pressure, viscous and body forces balance each other at any instant in time. A wide range of analytical techniques can be applied to investigate the Stokes flow past a moving body. In this talk, we introduce various Stokes flow singularities and illustrate how they can provide a handy starting point (ansatz) when trying to determine the form of the flow field around certain bodies, from simple translating spheres to beating sperm tails.

  • Junior Applied Mathematics Seminar
24 January 2012
13:30
Georgios Anastasiades
Abstract

Quantile forecasting of wind power using variability indices
Abstract: Wind power forecasting techniques have received substantial attention recently due to the increasing penetration of wind energy in national power systems.  While the initial focus has been on point forecasts, the need to quantify forecast uncertainty and communicate the risk of extreme ramp events has led to an interest in producing probabilistic forecasts. Using four years of wind power data from three wind farms in Denmark, we develop quantile regression models to generate short-term probabilistic forecasts from 15 minutes up to six hours ahead. More specifically, we investigate the potential of using various variability indices as explanatory variables in order to include the influence of changing weather regimes. These indices are extracted from the same  wind power series and optimized specifically for each quantile. The forecasting performance of this approach is compared with that of some benchmark models. Our results demonstrate that variability indices can increase the overall skill of the forecasts and that the level of improvement depends on the specific quantile.

  • Junior Applied Mathematics Seminar
29 November 2011
13:15
Abstract

Turbidity currents are fast-moving streams of sediment in the ocean 
which have the power to erode the sea floor and damage man-made
infrastructure anchored to the bed. They can travel for hundreds of
kilometres from the continental shelf to the deep ocean, but they are
unpredictable and can occur randomly without much warning making them
hard to observe and measure. Our main aim is to determine the distance
downstream at which the current will become extinct. We consider the
fluid model of Parker et al. [1986] and derive a simple shallow-water
description of the current which we examine numerically and analytically
to identify supercritical and subcritical flow regimes. We then focus on
the solution of the complete model and provide a new description of the
turbulent kinetic energy. This extension of the model involves switching
from a turbulent to laminar flow regime and provides an improved
description of the extinction process. 

  • Junior Applied Mathematics Seminar
18 November 2011
15:30
Abstract

 A common way to replace body tissue is via donors, but as the world population is ageing at an unprecedented rate there will be an even smaller supply to demand ratio for replacement parts than currently exists. Tissue engineering is a process in which damaged body tissue is repaired or replaced via the engineering of artificial tissues. We consider one type of this; a two-phase flow through a rotating high-aspect ratio vessel (HARV) bioreactor that contains a porous tissue construct. We extend the work of Cummings and Waters [2007], who considered a solid tissue construct, by considering flow through the porous construct described by a rotating form of Darcy's equations. By simplifying the equations and changing to bipolar variables, we can produce analytic results for the fluid flow through the system for a given construct trajectory. It is possible to calculate the trajectory numerically and couple this with the fluid flow to produce a full description of the flow behaviour. Finally, coupling with the numerical result for the tissue trajectory, we can also analytically calculate the particle paths for the flow which will lead to being able to calculate the spatial and temporal nutrient density.

  • Junior Applied Mathematics Seminar
1 November 2011
13:15
Abstract
Cell motility is a crucial part of many biological processes including wound healing, immunity and embryonic development. The interplay between mechanical forces and biochemical control mechanisms make understanding cell motility a rich and exciting challenge for mathematical modelling. We consider the two-phase, poroviscous, reactive flow framework used in the literature to describe crawling cells and present a stripped down version. Linear stability analysis and numerical simulations provide insight into the onset of polarization of a stationary cell and reveal qualitatively distinct families of travelling wave solutions. The numerical solutions also capture the experimentally observed behaviour that cells crawl fastest when the surface they crawl over is neither too sticky nor too slippy.
  • Junior Applied Mathematics Seminar

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