The formation of methane-hydrate precursors at large planar water-methane interfaces has been studied using massively parallel molecular dynamics in systems of varying size from around 10 000 to almost 7 x 10(6) molecules. This process took two distinct steps. First, the concentration of solvated methane clusters increases just inside the aqueous domain via slow diffusion from the methane-water interface, forming "clusters" of solvated methane molecules.

Spatial and velocity statistics of heavy point-like particles in incompressible, homogeneous, and isotropic three-dimensional turbulence is studied by means of direct numerical simulations at two values of the Taylor-scale Reynolds number Re-lambda similar to 200 and Re-lambda similar to 400, corresponding to resolutions of 512(3) and 2048(3) grid points, respectively. Particles Stokes number values range from St approximate to 0.2 to 70.

We consider a simple model for signal transport in the cytoplasm. Following some recent experimental evidences, the standard diffusion model is supplemented by advection operated through an attachement/detachement mechanism along microtubules. This model is given by a system of partial differential equations which are cast in different dimensions and connected by suitable exchange rules. A numerical scheme is introduced and some simulations are presented and discussed to show the performances of our model.

We consider a cell growth model involving a nonlinear system of partial differential equations which describes the growth of two types of cell populations with contact inhibition. Numerical experiments show that there is a parameter regime where, for a large class of initial data, the large time behaviour of the solutions is described by a segregated travelling wave solution with positive wave speed c.

We investigate the role of hydrodynamic interactions on the decision-making and leader-identification processes within a group of fifty small-size active individuals, immersed in a viscous fluid at very low Reynolds number, . A fraction of the individuals is informed about the spatial location of the target, and moves accordingly along a privileged trajectory. The rest of the group has no access to this information, but may draw indirect benefit by following the trajectory of the informed individuals, through a process of leader-identification.

Cavitation in a liquid moving past a constraint is numerically investigated by means of a free-energy lattice Boltzmann simulation based on the van der Waals equation of state. The fluid is streamed past an obstacle, and depending on the pressure drop between inlet and outlet, vapor formation underneath the corner of the sack-wall is observed. The circumstances of cavitation formation are investigated and it is found that the local bulk pressure and mean stress are insufficient to explain the phenomenon.

We consider an initial-boundary value problem for a degenerate pseudoparabolic regularization of a nonlinear forward-backward-forward parabolic equation, with a bounded nonlinearity which is increasing at infinity. We prove existence of suitably defined nonnegative solutions of the problem in a space of Radon measures. Solutions satisfy several monotonicity and regularization properties; in particular, their singular part is nonincreasing and may disappear in finite time.

For clathrate-hydrate polymorphic structure-type (sI versus sII), geometric recognition criteria have been developed and validated. These are applied to the study of the rich interplay and development of both sI and sII motifs in a variety of hydrate-nucleation events for methane and H2S hydrate studied by direct and enhanced-sampling molecular dynamics (MD) simulations.