Scaling Relations for Contour Lines of Rough Surfaces

Understand

Equilibrium and non-equilibrium growth phenomena, e.g., surface growth, generically yields self-affine distributions.

• Analysis of statistical properties of these distributions appears essential in understanding statistical mechanics of underlying phenomena.
• Here, we analyze scaling properties of the cumulative distribution of iso-height loops (i.e., contour lines) of rough self-affine surfaces in terms of loop area and system size.
• Inspired by the Coulomb gas methods, we find the generating function of the area of the loops.