By Avner Friedman

This is the fourth quantity within the sequence "Mathematics in business Prob lems." the inducement for those volumes is to foster interplay among and arithmetic on the "grass roots"; that's, on the point of spe cific difficulties. those difficulties come from undefined: they come up from versions constructed by means of the economic scientists in ventures directed on the manufac ture of latest or stronger items. even as, those difficulties have the potential of mathematical problem and novelty. to spot such difficulties, i've got visited industries and had discussions with their scientists. many of the scientists have consequently offered their difficulties within the IMA Seminar on commercial difficulties. The ebook relies on questions raised within the seminar and next discussions. each one bankruptcy is dedicated to 1 of the talks and is self-contained. The chap ters often offer references to the mathematical literature and an inventory of open difficulties that are of curiosity to the economic scientists. For a few difficulties partial resolution is indicated in short. The final bankruptcy of the e-book incorporates a brief description of recommendations to a few of the issues raised within the 3rd quantity, in addition to references to papers during which such strategies were published.

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**Extra info for Mathematics in Industrial Problems: Part 4**

**Sample text**

3 Orientation of colloidal magnetically switchable particles Most magnetic media in use today are made by dispersing small magnetic particles in an organic binder and coating the resultant mixture on a support material. The magnetic particles are typically nonspherical and have a magnetization that can change in direction but not in magnitude. Each particle has two stable directions of magnetization, opposite to one another, but aligned with the principal axis of the particle. Because of this coupling of the particle magnetization to the particle axis, the orientation of particles in a magnetic media product contributes to the output level of a recorded magnetic signal and the signal-to-noise ratio.

J. Solids Structures, 25 (1989), 249-265 1. Real-world free boundary problems 17 [22] F. Essenburg, On the significance of the inclusion of the effect of transverse normal strain in problems involving beams with surface constraints, J. Appl. , 42 (1975),127-132. [23] B. Bu and A. Friedman, A free boundary problem arising in superconductor modeling, Asymptotic Analysis, to appear. , agents which prevent a casting from sticking to the mold), lubrication, and biocompatability of artificial implants.

In video applications, particle orientation affects picture sharpness and brightness, and in data recording applications, it affects bit density and error performance. Fluid flows and magnetic fields are effective in orienting particles and both are used in standard manufacturing processes. On October 12, 1990 Richard D. Olmsted from 3M Company presented a kinetic theory which describes the orientation of magnetic particles subjected both to fluid flow and to the external magnetic field. E. F. Snider from the University of British Columbia is an extension of a Statistical Mechanics approach which they had developed in earlier papers [1] [2] to study kinetic theory of dilute polymers.