Pavlik S. Dynamics of growing rough surfaces

Thesis is devoted to the formation of growing rough surfaces. The features of nonequilibrium growth problem, their scaling description and their differences from equilibrium problems are discussed. The relevance of new factors, such as the anisotropy and the nonlinear diffusion, to the roughening transition is discussed. The scaling properties of the growing rough surfaces with a nonlinear diffusion coefficient are considered. Analytical models based on the new stochastic differential equation with nonlinear diffusion are suggested for justifying scaling. Scaling exponents are derived by the field renormalization-group method (dimensional regularization combined with minimal subtractions). The scaling behavior for a self-organized criticality is studied using minimal-renormalization procedure. Scaling exponents are determined with the field renormalization-group approach. Recent results obtained in thin films deposited onto smooth substrates exhibit an unusual rapid growth of roughness are discussed. The growing rough surfaces with fractional-power nonlinearities are presented. Using the new perturbation theory associated with the expansion over the extent of nonlinearity of the theory (in the power nonlinearity systems), the fluctuation spectrum is calculated up to the second order. It is found that the characteristic functional of growing rough surfaces has the supersymmetric form. The formation of periodic wave patterns on the growing rough surfaces is described. It is shown that one periodic wave is unstable, while the other is stable up to one-dimensional perturbations. The results are obtained using the formalism of supersymmetric quantum mechanics for one-dimensional periodic potentials.