A family of entropy indices constructed in the framework of Tsallis entropy formalism is used to investigate ecological diversity. It represents a new perspective in ecology because a simple equation can incorporate all aspects of α-diversity, from richness to dominance and can be also related to a measure of species rarity. In addition, a generalized Kullback-Leibler distance, constructed in the framework of a nonextensive formalism, is recalled and used as a measure of β-diversity between two systems. These tools are applied to data relative to the macrophytes collected from two not far apart arms of Itaipu Reservoir, in Paraná River basin.

We argue that nonlocal effects represented by fractionary terms in the kinetic energy can be relevant to achieve a satisfactory phenomenological description of the thermal behavior of the specific heat of non-crystalline solids at very low temperature. We propose a simple model formed by the direct sum of two Hamiltonians, one of which is obtained by incorporating fractional derivatives in the kinetic energy of a conventional Hamiltonian, and the other one accounts for the presence of phonons in the system. Some experimental data are used to support the proposed description.

We present a review of our recent progress in the description of the elastic and dynamical properties of the unstable periodic (walls) arising in a nematic liquid crystal sample. The Lonberg criterion for the selection of the period of these walls is analyzed. We present a detailed study of the universal character of these walls, which is the basis for a law of corresponding states of these periodic structures. We show the connection of corresponding states with the constant ratio between the Miesowicz viscosity coefficients. Finally, the collapse of these structures is investigated. We show that it is due to the exponential growth of the fluctuations localized along the lines where the director does not bend at all.

We describe applications of Thermal Lens Spectrometry to study optical and thermal properties of lyotropic liquid crystal. In particular, we refer to methods for measurements of thermal diffusivity anisotropy at different temperatures and as a function of the ferrofluids doping. The theoretical basis for quantitative measurements is discussed together with the advantages and limitations as compared with conventional methods. Finally, future developments of photothermal techniques for these applications are assessed.