Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-05T15:22:05.810Z Has data issue: false hasContentIssue false
  • English
  • Français

A comparison of mean concentrations in a diffusion problem

Published online by Cambridge University Press:  20 January 2009

A. Brown
A. Brown
Affiliation:
Faculty of Mathematical Studies, University of Southampton Department of Applied Mathematics, Faculty of Science, Australian National University
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In some biological problems, a parasite-host system is immersed in a toxic solution in order to kill off the parasite while leaving the host as little affected as possible. A problem of this type was considered by Clements and Edelstein (2), who treated both the host and the parasite as cylindrical in shape. In a separate paper Clements (1) considered the corresponding problem where the parasite is spherical and the host cylindrical. In both cases, the concentration of the toxic solution at the boundary is taken as having a constant value, c, and the penetration of the poison into the host and parasite is treated as a linear diffusion problem with an appropriate diffusion coefficient. It is assumed also that the host and the parasite are free of the toxic substance initially. The process is terminated when the average concentration in the parasite reaches a lethal level, τ, and the problem is to see how M, the average concentration in the host, is affected by the choice of c (for a given value of τ).

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 24 , Issue 3 , October 1981 , pp. 153 - 170
Copyright
Copyright © Edinburgh Mathematical Society 1981

References

REFERENCES

(1)Clements, J., A simple problem in comparative diffusion, Applicable Analysis 6 (1977), 241–251.Google Scholar
(2)Clements, J. C. and Edelstein, M., A model for a simple diffusion process, Proc. Nova Scotia Inst. of Sc. 27 (1974–1976), 134–143.Google Scholar
(3)Erdelyi, A., Magnus, W., Oberhetttnger, F. and Tricomi, F. G., Higher Transcendental Functions, Vol. 2 (McGraw-Hill, New York, 1953).Google Scholar
(4)Holland, A. S. B., Introduction to the Theory of Entire Functions (Academic Press, New York, 1973).Google Scholar
(5)Watson, G. N., A Treatise on the Theory of Bessel Functions, 2nd Edition (Cambridge University Press, London, 1958).Google Scholar