Download Mathematical Modelling of Industrial Processes: Lectures by Stavros Busenberg, Bruno Forte, Hendrik K. Kuiken (auth.), PDF

By Stavros Busenberg, Bruno Forte, Hendrik K. Kuiken (auth.), Vincenzo Capasso, Antonio Fasano (eds.)

The 1990 CIME path on Mathematical Modelling of business strategies got down to illustrate a few advances in questions of commercial arithmetic, i.e.of the functions of arithmetic (with all its "academic" rigour) to real-life difficulties. The papers describe the genesis of the versions and illustrate their correct mathematical features. one of the themesdealt with are: thermally managed crystal development, thermal behaviour of a high-pressure gas-discharge lamp, the sessile-drop challenge, etching techniques, the batch-coil- annealing technique, inverse difficulties in classical dynamics, photograph illustration and dynamical structures, scintillation in rear projections monitors, id of semiconductor properties,pattern acceptance with neural networks. CONTENTS: H.K. Kuiken: Mathematical Modelling of business Processes.- B. uniqueness: Inverse difficulties in arithmetic for Industry.- S. Busenberg: Case stories in business Mathematics.

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Example text

Eq. (16) is a so-called boundary-layer equation. e. much thinner than the length of the cavity. This condition prevails as long as the Peclet number ucl P e = -~- (17) is much larger than unity. In (17) u~ is a typical velocity w i t h i n the layer and length of the cavity. Since, as we have seen, D is very small, P e is usually far than unity. We shall now make use of the result of our discussion on the Schmidt number. the boundary layer the velocity field can be approximated by the first term of a series expansion.

Since the liquid is viscous, the no-slip condition prevails at the wall, so that along with the wall the liquid at the wall is also brought to a stand-still. It is well-known that the subsequent motion of the liquid is given by = 0erf } (10) Let us suppose next that the liquid is an etchant in which the concentration of the active etching component is given by coo. At t = 0 the condition of Eq. (7) suddenly comes into effect. The subsequent concentration profiles will be given by c--cooerf{y/(2nt)½} (11) The error function approaches its asymptotic value, which is equal to unity, exponentially fast.

Appl. Math. J. C. K. Kuiken, J. Appl. Phys. 68, 806-813 (1990). 31 T h e r m a l behaviour of a high-pressure gas-discharge lamp A high-pressure gas-discharge lamp consists of a transparent vessel which may be cylindrical, spherical or otherwise, containing a gas which is at a high pressure at the operating temperature. Within this vessel there are two electrodes between which an electric field can be set up. Electrons leave one of the electrodes, are accelerated by the electric field and move towards the other electrode.

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