Past Industrial and Applied Mathematics Seminar

18 October 2012
16:00
Richard Craster
Abstract
Some striking, and potentially useful, effects in electrokinetics occur for bipolar membranes: applications are in medical diagnostics amongst other areas. The purpose of this talk is to describe the experiments, the dominant features observed and then model the phenomena: This uncovers the physics that control this process. Time-periodic reverse voltage bias across a bipolar membrane is shown to exhibit transient hysteresis. This is due to the incomplete depletion of mobile ions, at the junction between the membranes, within two adjoining polarized layers; the layer thickness depends on the applied voltage and the surface charge densities. Experiments show that the hysteresis consists of an Ohmic linear rise in the total current with respect to the voltage, followed by a decay of the current. A limiting current is established for a long period when all the mobile ions are depleted from the polarized layer. If the resulting high field within the two polarized layers is sufficiently large, water dissociation occurs to produce proton and hydroxyl travelling wave fronts which contribute to another large jump in the current. We use numerical simulation and asymptotic analysis to interpret the experimental results and to estimate the amplitude of the transient hysteresis and the water-dissociation current.
  • Industrial and Applied Mathematics Seminar
11 October 2012
16:00
Martin Everett
Abstract
The use of formal mathematical models in sociology started in the 1940s and attracted mathematicians such as Frank Harary in the 1950s. The idea is to take the rather intuitive ideas described in social theory and express these in formal mathematical terms. Social network analysis is probably the best known of these and it is the area which has caught the imagination of a wider audience and has been the subject of a number of popular books. We shall give a brief over view of the field of social networks and will then look at three examples which have thrown up problems of interest to the mathematical community. We first look at positional analysis techniques and give a formulation that tries to capture the notion of social role by using graph coloration. We look at algebraic structures, properties, characterizations, algorithms and applications including food webs. Our second and related example looks at core-periphery structures in social networks. Our final example relates to what the network community refer to as two-mode data and a general approach to analyzing networks of this form. In all cases we shall look at the mathematics involved and discuss some open problems and areas of research that could benefit from new approaches and insights.
  • Industrial and Applied Mathematics Seminar
14 June 2012
16:00
Abstract
The computational analysis of a mathematical model describing a complex system is often based on the following roadmap: first, an experiment is conceived, in which the measured data are (either directly or indirectly) related to the input data of the model equations; second, such equations are computationally solved to provide iconographic reconstructions of the unknown physical or physiological parameters of the system; third, the reconstructed images are utilized to validate the model or to inspire appropriate improvements. This talk will adopt such framework to investigate three applied problems, respectively in solar physics, neuroscience and physiology. The solar physics problem is concerned with the exploitation of hard X-ray data for the comprehension of energy transport mechanisms in solar flares. The neuroscientific problem is the one to model visual recognition in humans with the help of a magnetocencephalography experiment. Finally, the physiological problem investigates the kinetics of the kidney-bladder system by means of nuclear data.
  • Industrial and Applied Mathematics Seminar
7 June 2012
16:00
Luciano da F. Costa
Abstract
Complex networks have been used to model almost any real-world complex systems. An especially important issue regards how to related their structure and dynamics, which contributes not only for the better understanding of such systems, but also to the prediction of important dynamical properties from specific topological features. In this talk I revise related research developed recently in my group. Particularly attention is given to the concept of accessibility, a new measurement integrating topology and dynamics, and the relationship between frequency of visits and node degree in directed modular complex networks. Analytical results are provided that allow accurate prediction of correlations between structure and dynamics in systems underlain by directed diffusion. The methodology is illustrated with respect to the macaque cortical network.
  • Industrial and Applied Mathematics Seminar
31 May 2012
16:00
Ingenuin Gasser
Abstract
In this seminar we discuss the gas dynamics of chimneys, solar updraft towers and energy towers. The main issue is to discuss simple fluid dynamic models which still describe the main features of the mentioned applications. We focus first on one dimensional compressible models. Then we apply a small Mach number asymptotics to reduce to complexity and to avoid the known problems of fully compressible models in the small Mach number regime. In case of the energy tower in addition we have to model the evaporation process. Finally we obtain a much simpler fluid dynamic model which allows robust and very fast numerical simulations. We discuss the qualitative behaviour and the good agreement with expermental data (in cases such data are available).
  • Industrial and Applied Mathematics Seminar
24 May 2012
16:00
Anne Juel
Abstract
The displacement of a liquid by an air finger is a generic two-phase flow that underpins applications as diverse as microfluidics, thin-film coating, enhanced oil recovery, and biomechanics of the lungs. I will present two intriguing examples of such flows where, firstly, oscillations in the shape of propagating bubbles are induced by a simple change in tube geometry, and secondly, flexible vessel boundaries suppress viscous fingering instability. 1) A simple change in pore geometry can radically alter the behaviour of a fluid displacing air finger, indicating that models based on idealized pore geometries fail to capture key features of complex practical flows. In particular, partial occlusion of a rectangular cross-section can force a transition from a steadily-propagating centred finger to a state that exhibits spatial oscillations via periodic sideways motion of the interface at a fixed location behind the finger tip. We characterize the dynamics of the oscillations and show that they arise from a global homoclinic connection between the stable and unstable manifolds of a steady, symmetry-broken solution. 2) Growth of complex dendritic fingers at the interface of air and a viscous fluid in the narrow gap between two parallel plates is an archetypical problem of pattern formation. We find a surprisingly effective means of suppressing this instability by replacing one of the plates with an elastic membrane. The resulting fluid-structure interaction fundamentally alters the interfacial patterns that develop and considerably delays the onset of fingering. We analyse the dependence of the instability on the parameters of the system and present scaling arguments to explain the experimentally observed behaviour.
  • Industrial and Applied Mathematics Seminar
17 May 2012
16:00
Gavin Brown
Abstract
Feature Selection is a ubiquitous problem in across data mining, bioinformatics, and pattern recognition, known variously as variable selection, dimensionality reduction, and others. Methods based on information theory have tremendously popular over the past decade, with dozens of 'novel' algorithms, and hundreds of applications published in domains across the spectrum of science/engineering. In this work, we asked the question 'what are the implicit underlying statistical assumptions of feature selection methods based on mutual information?' The main result I will present is a unifying probabilistic framework for information theoretic feature selection, bringing almost two decades of research on heuristic methods under a single theoretical interpretation.
  • Industrial and Applied Mathematics Seminar
10 May 2012
16:00
Stefan Llewellyn Smith
Abstract
Hollow vortices are vortices whose interior is at rest. They posses vortex sheets on their boundaries and can be viewed as a desingularization of point vortices. We give a brief history of point vortices. We then obtain exact solutions for hollow vortices in linear and nonlinear strain and examine the properties of streets of hollow vortices. The former can be viewed as a canonical example of a hollow vortex in an arbitrary flow, and its stability properties depend. In the latter case, we reexamine the hollow vortex street of Baker, Saffman and Sheffield and examine its stability to arbitrary disturbances, and then investigate the double hollow vortex street. Implications and extensions of this work are discussed.
  • Industrial and Applied Mathematics Seminar
3 May 2012
16:00
Abstract
Nematic liquid crystals (NLCs) are materials that flow like liquids, but have some crystalline features. Their molecules are typically long and thin, and tend to align locally, which imparts some elastic character to the NLC. Moreover at interfaces between the NLC and some other material (such as a rigid silicon substrate, or air) the molecules tend to have a preferred direction (so-called "surface anchoring"). This preferred behaviour at interfaces, coupled with the internal "elasticity", can give rise to complex instabilities in spreading free surface films. This talk will discuss modelling approaches to describe such flows. The models presented are capable of capturing many of the key features observed experimentally, including arrested spreading (with or without instability). Both 2D and 3D spreading scenarios will be considered, and simple ways to model nontrivial surface anchoring patterns, and "defects" within the flows will also be discussed.
  • Industrial and Applied Mathematics Seminar
26 April 2012
16:00
Mario di Bernardo
Abstract
In a variety of problems in engineering and applied science, the goal is to design or control a network of dynamical agents so as to achieve some desired asymptotic behaviour. Examples include consensus and rendez-vous problems in robotics, synchronization of generator angles in power grids or coordination of oscillations in bacterial populations. A pressing challenge in all of these problems is to derive appropriate analytical tools to prove convergence towards the target behaviour. Such tools are not only invaluable to guarantee the desired performance, but can also provide important guidelines for the design of decentralized control strategies to steer the collective behaviour of the network of interest in a desired manner. During this talk, a methodology for analysis and design of convergence in networks will be presented which is based on the use of a classical, yet not fully exploited, tool for convergence analysis: contraction theory. As opposed to classical methods for stability analysis, the idea is to look at convergence between trajectories of a system of interest rather that at their asymptotic convergence towards some solution of interest. After introducing the problem, a methodology will be derived based on the use of matrix measures induced by non-Euclidean norms that will be exploited to design strategies to control the collective behaviour of networks of dynamical agents. Representative examples will be used to illustrate the theoretical results.
  • Industrial and Applied Mathematics Seminar

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