In some cells pairing of homologous chromosomes happens at particular moments during the cell life cycle. A Statistical
Mechanics model based on some experimental data is presented and discussed here for this phenomenon.
Under this model, chromosomes pair at special regions whose interaction is mediated by some molecules which
diffuse in cells' nuclei and can bind them. Concentration of these molecules acts as a switch for pairing: at low
concentrations chromosomes move independently one from another whereas if concentration is above a certain
threshold value, chromosomes colocalize. Monte Carlo simulations of this model have been performed to test its
eficiency and the effect on pairing levels of chromosomal binding sites deletions.
We discuss some recent results on Statistical Mechanics approach to dense granular media. In particular, by analytical mean field investigation we derive the phase diagram of monodisperse and bydisperse granular assemblies. We show that "jamming" corresponds to a phase transition from a "fluid" to a "glassy" phase, observed
when crystallization is avoided. The nature of such a "glassy" phase turns out to be the same found in mean field models for glass formers. This gives quantitative evidence to the idea of a unified description of the "jamming" transition in granular media and thermal systems, such as glasses. We also discuss mixing/segregation transitions in binary mixtures and their connections to phase separation and "geometric" effects.