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Integrals on a moving manifold and geometrical probability

Published online by Cambridge University Press:  01 July 2016

Adrian Baddeley
Adrian Baddeley*
Affiliation:
The Australian National University
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Abstract

For a manifold which is moving and changing with time, consider some numerical property which at each instant is equal to an integral over the manifold. We derive a general expression for the time rate of change of this integral. Corollaries include a precise general form of Crofton's boundary theorem, de Hoff's interface displacement equations (with some new extensions) and a theorem in fluid mechanics.

Keywords

GEOMETRICAL PROBABILITYCROFTON'S THEOREMINTERFACE DISPLACEMENT EQUATIONSSMOOTHLY CHANGING MANIFOLDVELOCITYBOUNDARY VELOCITYBOUNDARY EXPANSION VELOCITYDIFFERENTIAL FORM
Type
Research Article
Information
Advances in Applied Probability , Volume 9 , Issue 3 , September 1977 , pp. 588 - 603
Copyright
Copyright © Applied Probability Trust 1977 

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References

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