Optimal phase distributions for polygonal Fresnel lenses

Polygonal Fresnel zone plates can be configured in a variety of forms depending on the number of sides of the polygon and the number of phase steps used. This contribution deals with some specific polygonal designs that tessellate the plane: triangles, squares, and hexagons. The phase distribution is chosen as a continuous one to form a polygonal kinoform. The selected designs have been simulated and its behaviour compared. Although their performance is worse than the circular Fresnel plate, they may present some other advantages as the tessellation capability, and the possibility to fabricate them as extruded profiles.

First Order Phase Transition in a 3D disordered system

We present a detailed numerical study on the effects of adding quenched impurities to a three dimensional system which in the pure case undergoes a strong first order phase transition (specifically, the ferromagnetic/paramagnetic transition of the site-diluted four states Potts model). We can state that the transition remains first-order in the presence of quenched disorder (a small amount of it) but it turns out to be second order as more impurities are added. A tricritical point, which is studied by means of Finite-Size Scaling, separates the first-order and second-order parts of the critical line. The results were made possible by a new definition of the disorder average that avoids the diverging-variance probability distributions that arise using the standard methodology. We also made use of a recently proposed microcanonical Monte Carlo method in which entropy, instead of free energy, is the basic quantity.

Phase diagram of a polydisperse soft-spheres model for liquids and colloids

The phase diagram of soft spheres with size dispersion is studied by means of an optimized Monte Carlo algorithm which allows us to equilibrate below the kinetic glass transition for all size distributions. The system ubiquitously undergoes a first-order freezing transition. While for a small size dispersion the frozen phase has a crystalline structure, large density inhomogeneities appear in the highly disperse systems. Studying the interplay between the equilibrium phase diagram and the kinetic glass transition, we argue that the experimentally found terminal polydispersity of colloids is a purely kinetic phenomenon.

Entropy production in the early-cosmology pionic phase

We point out that in the early universe, for temperatures in the approximate interval 150-80 MeV (after the quark-gluon plasma), pions carried a large share of the entropy and supported the largest inhomogeneities. Its thermal conductivity (previously calculated) allows the characterization of entropy production due to equilibration (damping) of thermal fluctuations. Simple model distributions of thermal fluctuations are considered and the associated entropy production evaluated.