Industrial and Applied Mathematics Seminar
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Thu, 24/05 16:00 |
Anne Juel (Manchester) |
Industrial and Applied Mathematics Seminar  |
DH 1st floor SR |
| 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. | |||
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Thu, 31/05 16:00 |
Ingenuin Gasser (Universität Hamburg) |
Industrial and Applied Mathematics Seminar |
DH 1st floor SR |
| 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). | |||
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Thu, 07/06 16:00 |
Luciano da F. Costa (Brazil University of São Paulo) |
Industrial and Applied Mathematics Seminar |
DH 1st floor SR |
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Thu, 14/06 16:00 |
Michele Piana (Universita' di Verona Italy) |
Industrial and Applied Mathematics Seminar |
DH 1st floor SR |
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Thu, 11/10 16:00 |
Martin Everett (University of Manchester) |
Industrial and Applied Mathematics Seminar |
DH 1st floor SR |
| 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. | |||
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Thu, 18/10 16:00 |
Richard Craster (Imperial College London) |
Industrial and Applied Mathematics Seminar |
DH 1st floor SR |
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Thu, 25/10 16:00 |
John Hinch (Cambridge DAMTP) |
Industrial and Applied Mathematics Seminar |
DH 1st floor SR |
| We study a thin liquid film on a vertical fibre. Without gravity, there is a Rayleigh-Plateau instability in which surface tension reduces the surface area of the initially cylindrical film. Spherical drops cannot form because of the fibre, and instead, the film forms bulges of roughly twice the initial thickness. Large bulges then grow very slowly through a ripening mechanism. A small non-dimensional gravity moves the bulges. They leave behind a thinner film than that in front of them, and so grow. As they grow into large drops, they move faster and grow faster. When gravity is stronger, the bulges grow only to finite amplitude solitary waves, with equal film thickness behind and in front. We study these solitary waves, and the effect of shear-thinning and shear-thickening of the fluid. In particular, we will be interested in solitary waves of large amplitudes, which occur near the boundary between large and small gravity. Frustratingly, the speed is only determined at the third term in an asymptotic expansion. The case of Newtonian fluids requires four terms. | |||
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Thu, 01/11 16:00 |
Peter Kramer (RPI) |
Industrial and Applied Mathematics Seminar |
DH 1st floor SR |
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Thu, 08/11 16:00 |
Industrial and Applied Mathematics Seminar |
DH 1st floor SR | |
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Thu, 15/11 16:00 |
Ryan Barnett (Imperial College London) |
Industrial and Applied Mathematics Seminar |
DH 1st floor SR |
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Thu, 22/11 16:00 |
Industrial and Applied Mathematics Seminar |
DH 1st floor SR | |
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Thu, 29/11 16:00 |
Jesús San Martin (Universidad Politécnica de Madrid) |
Industrial and Applied Mathematics Seminar |
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| RI.0.48 | |||
