It is possible to give a mathematical description
of planktonic populations through
advection-reaction-diffusion equations. We devised a
numerical method that, in the limit of vanishing
diffusivities, recovers the pure advection-reaction
problem. Further details here. (Talk given at XIV
WASCOM, Scicli, July 2007.)

If we assume that a bouncing ball is a rigid
object, and model the impacts by introducing a
restitution coefficient, we find a convergent series
of the times-of-flight. That's inelastic collapse:
what happens after that? (you know it, I know it, but
the restitution-coefficient model won't say!). On
the other hand, if the series of the times-of-flight
diverges, the ball never stops, ...or does it?
(Talk given at the 2007 Symmetry and Perturbation
Theory conference, Otranto, May 2007.)

The standard model *standard model* for interactions among
grains in granular flows leads to the phenomenon of *inelastic
collapse*: clusters of grains undergo infinite collisions in a
finite time. This is not a physical singularity, but a shortcoming
of the model. By tracking the dynamics of internal vibrational
modes of the grains it is possible to avoid the collapse. (Talk
given at the conference "Granular Matter: Mathematical Modeling and
Physical Instances", Reggio Calabria, June 2005. )

Filling Gaps in Chaotic Time Series (In Italian) |

The analysis of time series is particularly hard if the series has
gaps (that is, missing data) having a length greater than the
characteristic predictability time of the series. If the time
series is the expression of a low-dimensional dynamics ruled by a
chaotic attractor, I show how it is possible to fill the gaps with
surrogate data which are consistent with the observed
dynamics. (Internal talk given at my department, May 2005.)

Stommel, a hydrodynamic simulation code (C program) |

Even tough horizontal convection cannot become truly turbulent, it can show time-dependent non-periodic flows. Here I show the results of some numerical simulations carried out at low Prandtl number.

The Anti-Turbulence Theorem | (November 2001) |

Horizontal convection (that is convection forced by a horizontal temperature gradient, rather than by a vertical one, as in the Rayleigh-Bénard case) cannot become "truly turbulent" (Paparella & Young 2002). Of course, in order to give a proof of this statement, one needs first to agree on what is "true turbulence".

Ultimo aggiornamento: 03/12/2007