An accurate cartesian method is devised to simulate incompressible viscous flows past an arbitrary moving body. The Navier-Stokes equations are spatially discretized onto a fixed Cartesian mesh. The body is taken into account via the ghost-cell method and the so-called penalty method, resulting in second-order accuracy in velocity. The accuracy and the efficiency of the solver are tested through two-dimensional reference simulations. To show the versatility of this scheme we simulate a three-dimensional self propelled jellyfish prototype.

We model diffusion-controlled crystal growth as an interference problem. The crystal layers grow by nucleation (initiation of crystallization centers) followed by attachment of molecules to the nucleus. A forming crystal layer completes by either spreading across the length of the crystal or by colliding with another spreading crystal layer. This model differs from the classical Johnson-Mehl-Kolmogorov model in that nucleation happens only on boundaries of a ‘seed’ crystal as opposed to nucleation from random points in a given region. Our results also differ from the limiting results found for this classical model. We use the invariant measure of an embedded Markov process to find the growth rate of the crystal in terms of the nucleation rates. Ergodic theorems are then used to derive explicit formulae for some stationary probabilities.