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6 - Waves in Three Dimensions
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- Book:
- Mathematical Methods for Oscillations and Waves
- Published online:
- 02 April 2020
- Print publication:
- 05 March 2020, pp 146-180
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A flow conservation law for surface processes
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- Journal:
- Advances in Applied Probability / Volume 28 / Issue 1 / March 1996
- Published online by Cambridge University Press:
- 01 July 2016, pp. 13-28
- Print publication:
- March 1996
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The object studied in this paper is a pair (Φ, Y), where Φ is a random surface in
and Y a random vector field on 
. The pair is jointly stationary, i.e. its distribution is invariant under translations. The vector field Y is smooth outside Φ but may have discontinuities on Φ. Gauss' divergence theorem is applied to derive a flow conservation law for Y. For 
this specializes to a well-known rate conservation law for point processes. As an application, relationships for the linear contact distribution of Φ are derived.
and 
. The pair is jointly stationary, i.e. its distribution is invariant under translations. The vector field 
this specializes to a well-known rate conservation law for point processes. As an application, relationships for the linear contact distribution of Φ are derived.