Differential Equations and Applications Seminar
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Thu, 15/10/2009 16:30 |
Ricardo Carretero (San Diego State Univ) |
Differential Equations and Applications Seminar  |
DH 1st floor SR |
| Traditional Faraday waves appear in a layer of liquid that is shaken vertically. These patterns can take the form of horizontal stripes, close-packed hexagons, or even squares or quasiperiodic patterns. Faraday waves are commonly observed as fine stripes on the surface of wine in a wineglass that is ringing like a bell when periodically forced. Motivated by recent experiments on Faraday waves in Bose-Einstein condensates we investigate both analytically and numerically the dynamics of cigar-shaped Bose-condensed gases subject to periodic modulation of the strength of the transverse confinement's trap. We offer a fully analytical explanation of the observed parametric resonance yielding the pattern periodicity versus the driving frequency. These results, corroborated by numerical simulations, match extremely well with the experimental observations. | |||
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Thu, 22/10/2009 16:30 |
Norm Zabusky (Rutgers University) |
Differential Equations and Applications Seminar |
DH 1st floor SR |
| An overview of the experiments of Steinbergs group, Theory-and-models and comparison of the applicability of recent reduced models. | |||
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Thu, 29/10/2009 16:30 |
Steve Fitzgerald (EURATOM/UKAEA Fusion Association (Oxford)) |
Differential Equations and Applications Seminar |
DH 1st floor SR |
| Frank-Read sources are among the most important mechanisms of dislocation multiplication, and their operation signals the onset of yield in crystals. We show that the critical stress required to initiate dislocation production falls dramatically at high elastic anisotropy, irrespective of the mean shear modulus. We hence predict the yield stress of crystals to fall dramatically as their anisotropy increases. This behaviour is consistent with the severe plastic softening observed in alpha-iron and ferritic steels as the alpha − gamma martensitic phase transition is approached, a temperature regime of crucial importance for structural steels designed for future nuclear applications. | |||
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Thu, 05/11/2009 16:30 |
Pascale Aussillous (Polytech Marseille) |
Differential Equations and Applications Seminar |
DH 1st floor SR |
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Thu, 12/11/2009 16:30 |
John Hinch (Cambridge) |
Differential Equations and Applications Seminar |
DH 1st floor SR |
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Thu, 19/11/2009 16:30 |
Stephen Creagh (Nottingham) |
Differential Equations and Applications Seminar |
DH 1st floor SR |
| Whispering gallery modes in optical resonators have received a lot of attention as a mechanism for constructing small, directional lasers. They are also potentially important as passive optical components in schemes for coupling and filtering signals in optical fibres, in sensing devices and in other applications. In this talk it is argued that the evanescent field outside resonators that are very slightly deformed from circular or spherical is surprising in a couple of respects. First, even very small deformations seem to be capable of leading to highly directional emission patterns. Second, even though the undelying ray families are very regular and hardly differ from the integrable circular or spherical limit inside the resonator, a calculation of the evanescent field outside it is not straightforward. This is because even very slight nonintegrability has a profound effect on the complexified ray families which guide the external wave to asymptopia. An approach to describing the emitted wave is described which is based on canonical perturbation theory applied to the ray families and extended to comeplx phase space. | |||
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Thu, 26/11/2009 16:30 |
Tim Myers (Centre de Recerca Matematica) |
Differential Equations and Applications Seminar |
DH 1st floor SR |
| Modelling phase change in the presence of a flowing thin liquid film There are numerous physical phenomena that involve a melting solid surrounded by a thin layer of liquid, or alternatively a solid forming from a thin liquid layer. This talk will involve two such problems, namely contact melting and the Leidenfrost phenomenon. Contact melting occurs, for example, when a solid is placed on a surface that is maintained at a temperature above the solid melting temperature. Consequently the solid melts, while the melt layer is squeezed out from under the solid due to its weight. This process has applications in metallurgy, geology and nuclear technology, and also describes a piece of ice melting on a table. Leidenfrost is similar, but involves a liquid droplet evaporating after being placed on a hot substrate. This has applications in cooling systems and combustion of fuel or a drop of water on a hot frying pan. The talk will begin with a brief introduction into one-dimensional Stefan problems before moving on to the problem of melting coupled to flow. Mathematical models will be developed, analysed and compared with experimental results. Along the way the Heat Balance Integral Method (HBIM) will be introduced. This is a well-known method primarily used by engineers to approximate the solution of thermal problems. However, it has not proved so popular with mathematicians, due to the arbitrary choice of approximating function and a lack of accuracy. The method will be demonstrated on a simple example, then it will be shown how it may be modified to significantly improve the accuracy. In fact, in the large Stefan number limit the modified method can be shown to be more accurate than the asymptotic solution to second order. | |||
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Thu, 03/12/2009 16:30 |
Charlie Elliott (Warwick University) |
Differential Equations and Applications Seminar |
OCCAM Common Room (RI2.28) |
| Evolutionary PDEs on stationary and moving surfaces appear in many applications such as the diffusion of surfactants on fluid interfaces, surface pattern formation on growing domains, segmentation on curved surfaces and phase separation on biomembranes and dissolving alloy surfaces. In this talk I discuss three numerical approaches based on:- (I) Surface Finite Elements and Triangulated Surfaces, (II)Level Set Method and Implicit Surface PDEs and (III) Phase Field Approaches and Diffuse Surfaces. | |||
