A New Way Of characterizing Surface Roughness
Girish Nathan, Gemunu H. Gunaratne
University of Houston
We propose a new diagnostic for characterizing rough surfaces.
This parameter, called the disorder parameter, is based on the Hessian of the
input field and is initial-configuration independent. The exact form of the
parameter relies on rigid rotational and translational invariance. We identify
a spectrum of moments that can be used to highlight low and high-curvature
regions. In this paper, the method is applied to two recipes of interface
growth, the Ballistic Deposition (BD) and the Restricted Solid-On-Solid (RSOS)
models. It is shown that the behavior of the moments in time is similar to
standard measures of surface roughness - that is, the interface width as a
function of time. One can extract growth and roughness exponents from the
disorder parameter to quantify the growth process. We then apply the method to
the speckle pattern obtained from these growing interfaces and show that the
moments obtained numerically are qualitatively similar to those obtained from
analysis of the surface data. This is not always true for the usual correlation
functions. Therefore, we propose that the disorder parameter might be a good
suppelement to the correlation functions already being used extensively in the
field.