Rough surfaces appear everywhere in natural processes as fluid-fluid displacement in porous media, molecular-beam epitaxy growth, electrodeposition, fractures in solids, bacte- rial colony growth, or the motion of flux lines in type-II superconductors. The understanding of the physics of growth processes is of a paramount importance from both a theoretical and technical point of view due to the relevance of the growth surface physics in modern industry. The main aim of this project is to develop a coherent understanding of the kinetic roughening problem in general situations in which the surface is not supposed to verify the usual scaling laws. In view of the recent findings, anomalous scalin is expected to be very common in nature. We plan to study in great detail several growth problems, including both continuous equations and discrete models. The work encompasses renormalization group techniques and a large amount of computer simulation. On the one hand, we will focus our attention on the class of conserved fourth-order equations related to MBE growth in which nonlinear terms give arise to instabilities, which offer interesting examples of spontaneous morphogenesis. In addition, we will investigate the universality class of MBE growth. On the other hand, we plan to study the effect of quenched disorder on surface scaling behaviour and pursue recent analyses of J.M. LOPEZ et. al. and H.J. Jensen et.al. on dynamics of depinnined interfaces.
The main objective is to learn new useful analytical methods, as for Instance functional renormalization group techniques. This project involves collaboration with researchers in Jensen's group, and Prof. Dr. Vvendensky and Dr. L.-H. Tang from the Phvsics Department at the Imperial College, London. It is expected that Theoretical Physics environment at Imperial College, with weekly seminars and a large number of visitors, will act as a source of stimulation for a young researcher and allow the applicant to complement his education by means of an excellent training.