An SDE model for surface roughness progression

A stochastic differential equation (SDE) is derived for modeling the evolution of root mean square surface roughness, , for various deterioration, deposition, or smoothing processes. The model indicates, for deterioration, deposition, or smoothing, that where a and b are nonnegative constants. For small time, 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.