| In this thesis we explore problems in surface- and diffusion limited growth.; Molecular beam epitaxy, the technique used to grow structures on crystal surfaces, is studied with computer simulations. Our focus is the multilayer stage of this process: how the growth conditions affect the evolution of the forming mounds. We also studied heteroepitaxial systems, where the elastic effects significantly change the growth process, resulting in unusual phenomena like quantum dots.; The second area of research is the evolution of river networks. We propose a coarse grained theory, coupling the equation of the surface erosion with the conservation law of surface water flow. Computer simulation of the model produce patterns which show the statistical properties of natural rivers.; Lastly, we study diffusion limited aggregation (DLA), the discrete model of Laplacian growth. Using DLAs grown in wedge geometry, we show the existence of angular building blocks. In a different approach, using conformal maps, we study the relation between the scaling properties of the model and the Laurent expansion of the map. |
