Scaling of rough surfaces with nonlinear diffusion

Scaling relations for contour lines of rough surfaces.

Equilibrium and nonequilibrium 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 i...

Nonlinear optical phenomena on rough surfaces of metal thin films

Nonlinear optical phenomena on rough self-affine metal surfaces are theoretically studied. Placing nonlinearly polarizable molecules on such surfaces results in strong enhancement of optical nonlinearities. A quasistatic approximation is used to calculate local-enhancement factors for the second and third harmonic generation, degenerate four-wave mixing, and nonlinear Kerr effect. The calculati...

Heterogeneous Multiscale FEM for Diffusion Problems on Rough Surfaces

We present a finite element method for the numerical solution of diffusion problems on rough surfaces. The problem is transformed to an elliptic homogenization problem in a two dimensional parameter domain with a rapidly oscillating diffusion tensor and source term. The finite element method is based on the heterogeneous multiscale methods of E and Engquist [Commun. Math. Sci., 1 (2003), pp. 87...

Solving Diffusion Equations with Rough Coefficients in Rough Grids

operators, in this case, the divergence =? and the gradient =: A finite-difference algorithm for the numerical solution of diffusion problems in strongly heterogeneous and nonisotropic media is constructed for logically rectangular grids. The performance of this algorithm is comparable to other algorithms for problems with a ­u ­t 5 = · K =u 1 f. (1.1) smooth coefficients and regular grids, and...

Modeling Rough Surfaces