RESUMEN
A sharp interface model of crack propagation as a phase transition process is discussed. We develop a multipole expansion technique to solve this free boundary problem numerically. We obtain steady state solutions with a self-consistently selected propagation velocity and shape of the crack, provided that elastodynamic effects are taken into account. Also, we find a saturation of the steady state crack velocity below the Rayleigh speed, tip blunting with increasing driving force, and a tip splitting instability above a critical driving force.
RESUMEN
A model for the phase transition between partial wetting and dewetting of a substrate has been formulated that explicitly incorporates the hydrodynamic flow during the dewetting process in 1+1 dimensions. The model simulates a fluid layer of finite thickness on a substrate in coexistence with a dry part of the substrate and a gas phase above the substrate. Under nonequilibrium "dewetting" conditions, the front between the dry part and the wet part of the surface moves towards the wet part inducing hydrodynamic flow inside the wet layer. In more general terms, the model handles two immiscible fluids with a freely movable interface in an inhomogeneous external force field. Handling the interface by a new variant of the phase-field model, we obtain an efficient code with well-defined interfacial properties. In particular, the (free) energy can be chosen at will. We demonstrate that our model works well in the viscosity range of creeping flow and we give qualitative results for the higher Reynolds numbers. Connections to experimental realizations are discussed.
RESUMEN
A model for island formation in submonolayer epitaxy has been studied in the presence of elastic strain by means of a Monte Carlo simulation. The description, based on rate equations, leads to scaling predictions for cluster statistics and diffusion rates. We generalize these predictions to include the effects of the repulsive elastic interaction. The elastic interaction is caused by the deformation of the underlying substrate and has a repulsive 1/r(3) character. To enable the efficient simulation of multiparticle surface diffusion with long-range interaction, we employ a multigrid scheme. One particular result is that, with increasing elastic repulsion between the adsorbed particles, the formation of islands is hampered, and island nucleation is deferred to higher coverage values.
RESUMEN
We discuss the stress relaxation in a uniaxially strained solid due to the coarsening of a system of parallel cracks. We emphasize similarities and differences of this process to Ostwald ripening in a first order phase transition. A conventional mean-field approximation breaks down and several independent length scales have to be taken into account. Strong elastic interactions between the cracks determine the growth behavior. We derive scaling laws for the coarsening of the different length scales involved and the time evolution of stress relaxation, finally leading to the equilibrium state of a fractured body. The characteristic size of the cracks grows linearly in time which is much faster than in usual Ostwald ripening.
RESUMEN
We discuss the coarsening process of melt inclusions inside a solid phase. Elastic effects lead to an oblate shape of the particles, resulting in a system with strong diffusional and elastic interactions between inclusions. The usual mean-field approximation breaks down and several independent length scales have to be taken into account. In a system of parallel oriented particles we find scaling laws for the coarsening of the different length scales involved. In particular, the lateral size of the particles obeys a nontrivial growth law, R approximately t(5/12).
RESUMEN
The fractal growth of clusters adsorbed on crystal surfaces has been studied by Monte Carlo simulations. Elastic interactions between the atoms through the substrate have been included. Attractive and repulsive interaction potentials 1/r(3) have been used, including a varying cutoff for the range of interaction. As an important result we find that there exists a crossover radius beyond which the fractal dimension of the cluster corresponds to the fractal dimension of conventional two-dimensional diffusion limited aggregation. The crossover radius itself and the properties of the cluster inside that radius depend sensitively on the details of the interaction. The results have been analyzed by a scaling theory. Furthermore, we have implemented a multigrid scheme which allows for very efficient simulation of a large number of mobile atoms with long-range interaction on the surface.