The peeling of an elastic sheet away from thin layer of viscous fluid is a simply-stated and generic problem, that involves complex interactions between flow and elastic deformation on a range of length scales. 

I will illustrate the possibilities by considering theoretically and experimentally the injection and spread of viscous fluid beneath a flexible elastic lid; the injected fluid forms a blister, which spreads by peeling the lid away at the  perimeter of the blister. Among the many questions to be considered are the mechanisms for relieving the elastic analogue of the contact-line problem, whether peeling is "by bending" or "by pulling", the stability of the peeling front, and the effects of a capillary meniscus when peeling is by air injection. The result is a plethora of dynamical regimes and asymptotic scaling laws.

Using synchronized high-speed video camera, hydrophone and microphone we investigated flow patterns, the impact and secondary sound pulses emitted by oscillating bubbles. On the submerging  drop found short capillary waves produced by small secondary impact droplets. Picturesque filament and grid structures produced by colour drop of mixing fluid registered on the surface of the cavity and crown. Physical model includes discussion of the potential surface energy effects.

The costs to Vodafone of calls terminating on other networks – especially fixed networks – are largely determined by the termination charges levied by other telecoms operators.  We interconnect to several other telecoms operators, who charge differently; within one interconnect operator, costs vary depending on which of their switching centres we deliver calls to, and what the terminating phone number is.  So, while these termination costs depend partly on factors that we cannot control (such as the number called, the call duration and the time of day), they are also influenced by some factors that we can control.  In particular, we can route calls within our network before handing them over from our network to the other telecoms operator; where this “handover” occurs has an impact on termination cost.  
Vodafone would like to develop a repeatable capability to determine call delivery cost efficiency and identify where network routing changes can be made to improve matters, and determine traffic growth forecasts.

In this joint work with D. Ciubotaru, we introduce the notion of local and global indices of Dirac operators for a rational Cherednik algebra H, with underlying reflection group G. In the local theory, I will report on some relations between the (local) Dirac index of a simple module in category O, the graded G-character and the composition series polynomials for standard modules. In the global theory, we introduce an "integral-reflection" module over which we define and compute the index of a (global) Dirac operator and show that the index is independent of the parameters. If time permits, I will discuss some local-global relations.