Progress in Industrial Mathematics at ECMI 2008 by M. Doblaré, J. M. García-Aznar (auth.), Alistair D. Fitt,

By M. Doblaré, J. M. García-Aznar (auth.), Alistair D. Fitt, John Norbury, Hilary Ockendon, Eddie Wilson (eds.)

This quantity is the complaints of the ecu convention on arithmetic for held in London in June 2008. the purpose of the assembly was once to enhance the position of arithmetic as an overarching source for and enterprise. Contributions hide a variety of mathematical innovations and the purposes comprise production and expertise, finance and policy-making, networks, medication, and sport.

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Extra resources for Progress in Industrial Mathematics at ECMI 2008

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15. Cartoon of Chemical Mechanical Polisher. Reproduced from [11] Fig. 16. Cross-section through a polishing pad. Reproduced from [11] Continuum Models: Helping to Guide Industry z 37 z z= s(x,t) Semiconductor Wafer z=d(t) x x (a) Surface of polishing pad before pol- (b) Surface of polishing pad after polishing ishing (c) Probability density function of (d) Probability density function of height of surface before polishing height of surface after polishing Fig. 17. Model of the surface of the polishing pad.

The pressure within the bubble is shown in Fig. 14 and indicates that it increases in the hot region and then decreases in the solidifying region. Note also that, although the bubbles are elongated by the stretching of the glass they can be shown to be shorter than the length that would be predicted by the simple argument about bounding characteristics because the ends pinch-off. Although many assumptions have been made, the continuum model proposed above has been able to provide great insight into the control of holes and the size of bubbles.

On the other hand, image reconstruction refers to the techniques used to create an image of the interior of a body from data collected on its boundary [2]. Mathematically, an image reconstruction can be seen as the solution of an inverse problem in which the cause is inferred from the effect. We will show here two different applications in the oil and medical industries. The first application is the so called history matching problem where we want to estimate the unknown properties of a reservoir, such as its porosity and permeability, from the production data.

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