Forthcoming Seminars › Seminar Series

Differential Equations and Applications Seminar

Thu, 24/04/2008
16:30 		Margaret Beck (University of Surrey) Differential Equations and Applications Seminar Add to calendar DH 1st floor SR
"Nonlinear stability of time-periodic viscous shocks."
"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."
Thu, 01/05/2008
16:30 		Alan Champneys (Bristol) Differential Equations and Applications Seminar Add to calendar DH 1st floor SR
"Some beyond-all-orders effects for localised structures"
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, 15/05/2008
16:30 		John Brindley (University of Leeds) Differential Equations and Applications Seminar Add to calendar DH 1st floor SR
Fizzle or Frazzle - Problems with Ignition
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, 12/06/2008
16:30 		Marguerite Robinson (University of Limerick) Differential Equations and Applications Seminar Add to calendar DH 1st floor SR
"Modelling Gas-Liquid Bubbly Flows".

For any corrections/updates to these listings, please contact seminars [-at-] maths [dot] ox [dot] ac [dot] uk.

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