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On the existence of characteristic shapes for desert dunes

  • F. J. Bloore
Article
  • 39 Downloads

Abstract

The existence of an angle of reposeα for sand implies that, in any given wind regime, there is at least one configuration of sand dunes which will not be altered by that wind regime. The existence ofα implies that the land forms constitute a convex compact subset of a Banach space, and the result then follows from Shauder's theorem.

Key words

Desert dune shape fixed point theorem Schauder's theorem 

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References

  1. Fryberger, S. G. and Dean, G., 1979, Dune forms and wind regime,in McKee, E. D. (ed.), (p. 137–169) Global Sand Seas, U.S. Geological Survey Professional Paper 1052: U.S. Government Printing Office, Washington, 425 p.Google Scholar
  2. Kolmogorov, A. N. and Fomin, S. V., 1957, Elements of the theory of functions and functional analysis, v. 1, Metric and normed spaces: Graylock Press, Rochester, New York, 129 p.Google Scholar
  3. Mainguet, M. and Callot, Y., 1978, L'Erg de Fachi-Bilma: C.N.R.S., Paris, 184 p.Google Scholar
  4. Simmons, G. F., 1963, Introduction to topology and modern analysis: McGraw-Hill, New York, 372 p.Google Scholar

Copyright information

© Plenum Publishing Corporation 1981

Authors and Affiliations

  • F. J. Bloore
    • 1
  1. 1.Department of Applied Mathematics and Theoretical PhysicsThe UniversityLiverpoolEngland

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