Measure theoretic derivation of Richardson's equation

T. J. Mackin; C. T. Chen; J. J. Mecholsky; James Patrick Runt

Measure theoretic derivation of Richardson's equation

T. J. Mackin, C. T. Chen, J. J. Mecholsky, James Patrick Runt

Research output: Contribution to journal › Article › peer-review

Abstract

Richardson's empirical equation relating length to measuring scale has been used extensively to assign fractal dimensions to rugged curves. The inconsistency in units, length on one side of the equation vs. fractional units of length on the other has led to considerable debate. This letter presents a derivation of Richardson's equation based upon measure theory. In this context, the constant appearing in Richardson's equation is shown to have a precise meaning; it is the Hausdorff measure of the curve.

Original language	English (US)
Journal	Materials Science and Engineering A
Volume	A186
Issue number	1-2
State	Published - Jan 1 1994

All Science Journal Classification (ASJC) codes

Materials Science(all)
Condensed Matter Physics
Mechanics of Materials
Mechanical Engineering

Cite this

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Measure theoretic derivation of Richardson's equation

Abstract

All Science Journal Classification (ASJC) codes

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