Roughness Exponent Alpha Research Articles

Inconsistency between height-height correlation and power-spectrum functions of scale-invariant surfaces for roughness exponent alpha ~1.

The height-height correlation function H(r) from a scale-invariant surface is compared with the corresponding power-spectrum function W(q) using a variety of mathematical scaling functions. We show that for a non-self-affine surface with the roughness exponent \ensuremath{\alpha}\ensuremath{\ge}1, one of the asymptotic scaling relations, either H(r)\ensuremath{\sim}${\mathit{r}}^{2\mathrm{\ensuremath{\alpha}}}$ or W(q)\ensuremath{\sim}${\mathit{q}}^{\mathrm{\ensuremath{-}}2\mathrm{\ensuremath{\alpha}}\mathrm{\ensuremath{-}}\mathit{d}}$, can be violated. An inconsistency in the values of \ensuremath{\alpha} also exists between H(r) and W(q) when \ensuremath{\alpha}g0.9. The impact on the data analysis using different experimental methods is discussed.

Dissolution in (1+1) dimensions: a numerical study

The authors study by numerical simulations the growing interfaces due to dissolution in d=(1+1) dimensions. They consider a model based on simple, temperature-dependent microscopic dissolution rules, and they investigate the scaling properties of the growing surface structure. The roughness exponent alpha and the dynamical scaling exponent beta are determined for various temperatures. They report on a complicated temperature dependence of the exponent beta which for the three particular temperatures approaches theoretical limiting values. Also studied is the average nearest-neighbour height difference which follows a linear temperature dependence at saturation.