Forthcoming events in this series


Thu, 15 May 2008

16:30 - 17:30
DH 1st floor SR

Fizzle or Frazzle - Problems with Ignition

John Brindley
(University of Leeds)
Abstract

The phenomenon of ignition is one with which we are all familiar, but which is remarkably difficult to define and model effectively. My own (description rather than definition) is “initiation of a (high temperature) self-sustaining exothermic process”; it may of course be desirable, as in your car’s engine, or highly undesirable, as the cause of many disastrous fires and explosions Both laboratory experiments and numerical simulations demonstrate its extreme sensitivity to external influences, past history and process (essentially chemical) kinetics, but at the heart of all instances there appears to be some “critical” unstable equilibrium state. Though some analytical modelling has been useful in particular cases, this remains in general virgin territory for applied mathematicians – perhaps there is room for some “knowledge transfer” here.

Thu, 01 May 2008
16:30
DH 1st floor SR

"Some beyond-all-orders effects for localised structures"

Alan Champneys
(Bristol)
Abstract

This talk shall examine a range of problems where nonlinear waves or coherent structures are localised to some portion of a domain. In one spatial dimension, the problem reduces to finding homoclinic connections to equilibria. Two canonical problems emerge when higher-order spatial terms are considered (either via fourth-order operators or discreteness effects). One involves so-called snaking bifurcation diagrams where a fundamental state grows an internal patterned layer via an infinite sequence of fold bifurcations. The other involves the exact vanishing of oscillatory tails as a parameter is varied. It is shown how both problems arise from certain codimension-two limits where they can be captured by beyond-all-orders analysis. Dynamical systems methods can then be used to explain the kind of structures that emerge away from these degenerate points. Applications include moving discrete breathers in atomic lattices, discrete solitons in optical cavities, and theories for two-dimensional localised patterns using Swift-Hohenberg theory.

Thu, 24 Apr 2008
16:30
DH 1st floor SR

"Nonlinear stability of time-periodic viscous shocks."

Margaret Beck
(University of Surrey)
Abstract

"Time-periodic shocks in systems of viscous conservation laws are shown to be nonlinearly stable. The result is obtained by representing the evolution associated to the linearized, time-periodic operator using a contour integral, similar to that of strongly continuous semigroups. This yields detailed pointwise estimates on the Green's function for the time-periodic operator. The evolution associated to the embedded zero eigenvalues is then extracted.

Stability follows from a Gronwall-type estimate, proving algebraic decay of perturbations."

Tue, 15 Apr 2008
14:00
DH 2nd floor SR

Disappearing bodies and ghost vortices

Ian Eames
(University College, London)
Abstract

In many dispersed multiphase flows droplets, bubbles and particles move and disappear due to a phase change. Practical examples include fuel droplets evaporating in a hot gas, vapour bubbles condensing in subcooled liquids and ice crystals melting in water. After these `bodies' have disappeared, they leave behind a remnant `ghost' vortex as an expression of momentum conservation.

A general framework is developed to analyse how a ghost vortex is generated. A study of these processes is incomplete without a detailed discussion of the concept of momentum for unbounded flows. We show how momentum can be defined unambiguously for unbounded flows and show its connection with other expressions, particularly that of Lighthill (1986). We apply our analysis to interpret new observations of condensing vapour bubble and discuss droplet evaporation. We show that the use of integral invariants, widely applied in turbulence, introduces a new perspective to dispersed multiphase flows