An SDE model for surface roughness progression. Issue 1 (2nd January 2020)

• Record Type: Journal Article
• Authors: Allen, E. J.
• Is Part Of: Stochastic analysis and applications. Volume 38:Issue 1(2020)
• Page Start: 171
• Page End: 178
• Publication Date: 2020-01-02
• Subjects: Roughness -- SDE -- model -- deterioration -- deposition -- smoothing; 60H10 -- 74A45 -- 37H10 -- 60H15; Stochastic analysis -- Periodicals; 519.2205
• DOI: 10.1080/07362994.2019.1662805
• Languages: English
• ISSNs: 0736-2994

Abstract

Abstract: A stochastic differential equation (SDE) is derived for modeling the evolution of root mean square surface roughness, R q ( t ), for various deterioration, deposition, or smoothing processes. The model indicates, for deterioration, deposition, or smoothing, that R q ( t ) ≈ R 2 ( 0 ) exp ( − bt ) + a ( 1 − exp ( − bt ) ) where a and b are nonnegative constants. For small time, R q 2 ( t ) approximately changes linearly with time t but approaches a limiting (saturated) value as time increases. Roughness data for eight different physical processes support the model results.