On the existence of characteristic shapes for desert dunes
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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 wordsDesert dune shape fixed point theorem Schauder's theorem
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