Unexpected Outcomes: Propagating Light Rays in the Atmosphere, a New Technique for Solving Partial Differential Equations

Neville Fowkes

Abstract


Problems that arise out of an industrial context normally have clear cut objectives, and the results are usually important in context but of limited general interest. Sometimes, however, the investigations lead to results that are both unexpected and of much broader interest. Two such investigations are described here. In the first problem an investigation of the propagation of light rays across the ocean leads to new results concerning optical distortion. In the second problem a surface tension investigation leads to an entirely new technique for solving partial differential equations.


Keywords


Optical refraction; boundary tracing; partial differential equations; exact solutions

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References


Anderson, M. L. Boundary Tracing Methods for Partial Differential Equations. PhD thesis, School of Mathematics and Statistics, University of Western Australia. 2003. (Thesis or Dissertation)

Anderson, M.L., Bassom, A.P., Fowkes, N.D. Boundary tracing and boundary value problems: II. Applications. Proceedings of the Royal Society A-Mathematical Physical and Engineering Sciences. 463, pp. 1925-1938. 2007. (Conference Proceedings)

Anderson, M.L., Bassom, A.P., Fowkes, N.D. Boundary tracing and boundary value problems: I. Theory. Proceedings of the Royal Society A-Mathematical Physical and Engineering Sciences. 463, pp. 1909-1924. 2007. (Conference Proceedings)

Anderson, M.L., Bassom, A.P., Fowkes, N. D. Exact solutions of the Laplace - Young equation. Proceedings of the Royal Society A-Mathematical Physical and Engineering Sciences. 462, pp. 3645-3656. . 2006. (Conference Proceedings)

Anderssen, R. S., R.P. Hale, & J. R. M. Radok. The simulation with mathematical models of ion uptake by growing roots. Plant and Soil. 30, 2, 271 - 298. 1969. (Journal)

Landau, L. D., and E. M. Lifshitz. Fluid Mechanics. Pergamon Press, 230 - 237. 1987. (Book)

Lehn, W. H. A simple parabolic model for the optics of the atmospheric surface layer, Appl. Math. Modeling, 447 - 54. 1985. (Journal)

McNabb, A., Wake, G. C., Lambourne, R. D. & R. S. Anderssen. Theoretical derivation of rules of thumb for freezing times. Inverse Problems. 633 - 642. 1991. (Book)

Nener, B. D., Fowkes, N. D., & L. Borredon. Analytical models of optical refraction in the troposphere. J. Opt. Soc. Am. A. 5, 267 - 75. 2003. (Journal)

Rees, W. G., & C.H.F. Glover. Inversion of atmospheric refraction data. J. Opt. Soc. Am. A, 330 -- 39. 1991. (Journal)




DOI: http://dx.doi.org/10.5614%2Fj.math.fund.sci.2014.46.3.3

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