Applied Mathematics Seminars

• 23rd Jan
  2013 On the difference between the hour-glass and clepsydra.
  Lydie Staron (University of Bristol)
  2:00 - Room 1.212 Alan Turing Building
  Abstract (click to view)

  Granular matter is well-known for its ability to flow like a viscous fluid, or resist shear like a solid, depending on the stress state it is subjected to, evolving from one state to the other over a few grain diameters. These complex flow properties are perhaps best illustrated during the discharge of a silo, where rapid motion, slow shear and static equilibrium co-exist at all times. This makes the silo configuration a stringent test for continuum modeling of granular matter. In this seminar, we will present the discharge of the granular silo as a continuum visco-plastic flow, investigate the difference between sand-glasses and water-clocks, and discuss the limitation of the continuum flow-law using discrete grains numerical simulations.

• 30th Jan
  2013 Implementation in OpenFOAM of a general three-phase mixture formulation for dense suspension flows in ambient fluid. Implications for particle-laden and debris flow models.
  Patricio Bohorquez (Univeridad de Jaén)
  2:00 - - Room 1.212 Alan Turing Building
• 30th Jan
  2013 High frequency homogenization: Connecting the Microstructure to the Macroscale.
  Richard Craster (Imperial College, London)
  3:00 - - Room 1.212 Alan Turing Building
  Abstract (click to view)

  It is highly desirable to be able to create continuum equations that embed a known microstructure through effective or averaged quantities such as wavespeeds or shear moduli. The methodology for achieving this at low frequencies and for waves long relative to a microstructure is well-known and such static or quasi-static theories are well developed. However, at high frequencies the multiple scattering by the elements of the microstructure, which is now of a similar scale to the wavelength, requires a dynamic homogenization theory. Many interesting features of, say, periodic media: band gaps, localization etc occur at these higher frequencies. The materials exhibit effective anisotropy and this leads to topical effects such as cloaking/ invisibility, flat lensing, negative refraction and to inducing directional behaviour of the waves within a structure. A general theory will be described and applications to continuum, discrete and frame lattice structures will be outlined. The results and methodology are confirmed versus various illustrative exact/ numerical calculations showing that theory captures, for instance, all angle negative refraction, ultra refraction and localised defect modes.

• 31th Jan
  2013 The role of debris cover on ice ablation.
  Christoph Mayer (Bavarian Academy of Sciences and Humanities)
  2:00 - - Room 1.212 Alan Turing Building
  Abstract (click to view)

  The mass balance of glaciers is usually controlled by the accumulation of snow during cold periods and snow and ice melt during warmer periods. In midlatitudes these periods usually coincide with winter (accumulation) and summer (ablation) seasons. Higher snowfall increases the mass budget, while favorable melt conditions turn the mass balance towards smaller values. The dynamic mass redistribution from the accumulation zone towards the ablation zone follows the mean mass budget of the glacier averaged over several years, where the time span depends on the specific climatic and geometric conditions of the individual glacier. This "low-pass filtering" of general mass balance conditions makes glaciers to useful indicators of the climate evolution, the long term mean of meteorological conditions. This relationship only works well, as long as ablation is a uniform process which relates ice loss directly to the near surface meteorological conditions. In the case of a supra-glacial debris cover, this relationship is influenced by the heat transport through the debris. In dependence of the thermal conditions of the debris material and the geometry of the debris cover either enhanced or reduced ice melt can be observed. The heat transport through the debris cover itself depends on a number of parameters and is difficult to formulate in a uniform solution. The presentation will discuss the general characteristics of ice ablation on debris covered glaciers, present the major parameter and processes influencing the heat transport and summarize the potential solutions of the general problem.

• 6th Feb
  2013 Purely-elastic flow instabilities
  Rob Poole (University of Liverpool)
  2:00 - - Room 1.212 Alan Turing Building
  Abstract (click to view)

  The flow of viscoelastic fluids, e.g. polymer solutions or melts, can often give rise to spectacularly different flow phenomena compared to "simple" Newtonian fluids (water or air). One such manifestation of these differences is that in microfluidic geometries viscoelastic fluid flows can become unstable and time dependent in simple geometries at flow rates much smaller than would arise in the equivalent flow of a Newtonian fluid (typically due to inertial instabilities). Such "purely-elastic" flow instabilities arise as the inherently small scale of microfluidic flows accentuates the viscoelastic behaviour observed: the small length scale simultaneously makes the Reynolds number small and the Deborah or Weissenberg numbers, which characterize the degree of elasticity in the flow, large. In this talk I will discuss how we have been able to numerically model one such experimentally-observed instability. I will then go on to briefly examine a series of purely-elastic instabilities that we have discovered in related geometries and some recent experimental verification of one such truly a priori prediction.

• 27th Feb
  2013 Simple models of low-Reynolds number swimming in confined geometries.
  Darren Crowdy (Imperial College, London)
  2:00 - - Room 1.212 Alan Turing Building
• 6th Mar
  2013 Curved channel flow of Newtonian and shear-thinning fluids.
  Phil Haines (University College, London)
  2:00 - - Room 1.212 Alan Turing Building
  Abstract (click to view)

  In this talk we investigate the Dean instability for fully developed flow in curved channels of finite width, comparing numerical results with linear stability calculations obtained in the infinite aspect ratio limit. The flow is found to support a rich structure that changes significantly with slight changes in channel aspect ratio. This problem is of particular interest for shear-thinning fluids because the undisturbed flow contains points of vanishing shear, suggesting that the constitutive assumptions made in this limit may prove significant.

• 13th Mar
  2013 On the contact-line dynamics of a uniformly evaporating or condensing thin sessile drop.
  James Oliver (University of Oxford)
  2:00 - - Room 1.212 Alan Turing Building
• 20th Mar
  2013 Marine energy resource characterisation around the Finistere Islands.
  Vanesa Magar (University of Plymouth)
  2:00 - - Room 1.212 Alan Turing Building
  Abstract (click to view)

  Island communities are at great risk of fossil fuel scarcity, and particularly vulnerable to damages to fuel and electricity infrastructures. However, as they are surrounded by the ocean, their vulnerability would be reduced with an adequate exploitation of marine energy resources. In this talk we will present two models, one used for wave energy resource characterisation, and another for tidal energy resource characterisation, and show an analysis of marine energy resources around the Islands of Finistere, in the North West of France. This work is a contribution to the Interreg-funded project MERiFIC (Marine Energy in Far Peripheral and Island Communities, http://www.merific.eu).

• 17th Apr
  2013 Freezing of soils and colloidal suspensions.
  Grae Worster (University of Cambridge)
  2:00 - - Room 1.212 Alan Turing Building
• 24th Apr
  2013 Quantum Chemical Topology
  Paul Popelier (University of Manchester)
  2:00 - - Room 1.212 Alan Turing Building
• 8th May
  2013 Cancelled
  Yulii Shikhmurzaev (University of Birmingham)
  2:00 - - Room 1.212 Alan Turing Building
• 15th May
  2013 Experimental Investigation of Large Scale Circulation Generated Over a 2D Turbulent Flow.
  Johann Herault (LPS, ENS, France)
  2:00 - - Room 1.212 Alan Turing Building
  Abstract (click to view)

  One of the striking features of two dimensional turbulence is the presence of large coherent structures, due to the inverse cascade of energy. When the characteristic scale of energy dissipation is larger than the size of the domain, energy accumulates in the largest scale structure which has non zero net angular momentum. This large scale circulation (LSC) breaks the symmetry of the forcing. We report the experimental study of the emergence of this LSC for an electromagnetically forced flow in a liquid metal (GalInStan).

Previous Seminars

• 2012/13 Semester 1
• 2011/12 Semester 2
• 2011/12 Semester 1
• 2010/11 Semester 2
• 2010/11 Semester 1
• 2009/10 Semester 2
• 2009/10 Semester 1
• 2008/09 Semester 2
• 2008/09 Semester 1
• 2007/08 Semester 2