Glass Transition in a 2D Lattice Model

The dynamics of compaction of hard cross-shaped pentamers on the 2D square lattice is investigated. The addition of new particles is controlled by diffusive relaxation. It is shown that the filling process terminates at a glassy phase with a limiting coverage density \rho_{rcp}=0.171626(3), lower than the density of closest packing \rho_{cp}=0.2, and the long time filling rate vanishes like (\rho_{rcp}-\rho(t))^2. For the entire density regime the particles form an amorphous phase, devoid of any crystalline order. Therefore, the model supports a stable random packing state, as opposed to the hard disks system. Our results may be relevant to recent experiments studying the clustering of proteins on bilayer lipid membranes

Stochastic light concentration from 3D to 2D reveals ultraweak chemi- and bioluminescence

For countless applications in science and technology, light must be concentrated, and concentration is classically achieved with reflective and refractive elements. However, there is so far no efficient way, with a 2D detector, to detect photons produced inside an extended volume with a broad or isotropic angular distribution. Here, with theory and experiment, we propose to stochastically transform and concentrate a volume into a smaller surface, using a high- albedo Ulbricht cavity and a small exit orifice through cavity walls. A 3D gas of photons produced inside the cavity is transformed with a 50% number efficiency into a 2D Lambertian emitting orifice with maximal radiance and a much smaller size. With high-albedo quartz-powder cavity walls ( P = 99.94%), the orifice area is 1/( 1 - P) approximate to 1600 times smaller than the walls' area. When coupled to a detectivity-optimized photon-counter ( D = 0.015 photon- 1 s1/ 2 cm) the detection limit is 110 photon s- 1 L- 1. Thanks to this unprecedented sensitivity, we could detect the luminescence produced by the non-catalytic disproportionation of hydrogen peroxide in pure water, which has not been observed so far. We could also detect the ultraweak bioluminescence produced by yeast cells at the onset of their growth. Our work opens new perspectives for studying ultraweak luminescence, and the concept of stochastic 3D/2D conjugation should help design novel light detection methods for large samples or diluted emitters