Counting finite index subgroups and the P. Hall enumeration principle

We apply the P. Hall enumeration principle to count the number of subgroups of a given index in the free pro-p group and the free abelian group. We shall present an infinite family of non-isomorphic pro-p groups with the same zeta function.     

The dielectric response of interfacial water—from the ordered structures to the single hydrated shell

Water is the universal solvent in nature. Does this imply, however, that its interaction with its environment is also a universal feature? While this question maybe too fundamental to be answered by one method only, we present evidence that the broadening of the dielectric spectra of water presents universal features of dipolar interactions with different types of matrixes. If in aqueous solutions the starting point of water’s state can be considered as bulk, with only partial interactions with the solute, then the state of water adsorbed in heterogeneous materials is determined by various hydration centers of the inhomogeneous material (the matrix) and it is significantly different from the bulk. In both cases, the dielectric spectrum of water is symmetrical and can be described by the Cole–Cole (CC) function. The phenomenological model that describes a physical mechanism of the dipole–matrix interaction in complex systems underlying the CC behavior has been applied to water adsorbed in porous glasses. It was then extended to analyses of the dynamic and structural behavior of water in nonionic and ionic aqueous solutions. The same model is then used to analyze the CC relaxation processes observed in clays, aqueous solutions of nucleotides, and amino acids.     

Mobility and Interaction of Heavy Metals in a Natural Soil

We study the mobility and interaction under competing conditions observed for copper ( $\text{ Cu}^{2+}$ ) and zinc ( $\text{ Zn}^{2+}$ ) ions in the context of laboratory-scale experiments performed in natural soil columns. The experiments focus on the analysis of solute breakthrough curves (BTCs) obtained after injection of an aqueous solution containing similar concentrations of the two metal ions into a soil column fully saturated with double deionized water. Transport of the competing ions is tested for the same soil under aerobic and anaerobic conditions. Measurements show that the species with lower affinity for the soil, $\text{ Zn}^{2+}$ , migrates occupying all available adsorption sites, and is then progressively replaced by the ion with higher affinity, $\text{ Cu}^{2+}$ . The two ions are displaced in the system with different effective retardation. The slowest species replaces the sorbed ions, resulting in observed $\text{ Zn}^{2+}$ concentrations that display a non-monotonic behavior in time and which, for a certain period, are larger than the concentration supplied continuously at the inlet. In the absence of a complete geochemical characterization of the system, we show that the measured concentrations of both metals can be interpreted through simple models based on a set of coupled partial differential and algebraic equations, involving a small subset of aqueous and adsorbed species that are present in the system. Depending on the model considered, the relationship between aqueous and adsorbed ion concentrations is described at equilibrium by a Gaines–Thomas (GT) formulation, a competitive Sheindorf–Rebhun–Sheintuch (SRS) isotherm, or an Extended Langmuir (EL) isotherm, respectively. The GT formulation provides the best interpretation of the observed behavior among the models tested. We find that employing these simple models, which account only for the main governing reactive processes, allows reasonable estimation of the observed BTCs in experiments where only partial geochemical datasets are available.     

Preconditioned iterative methods for coupled discretizations of fluid flow problems

Computational fluid dynamics, where simulations require largecomputation times, is one of the areas of application of highperformance computing. Schemes such as the SIMPLE (semi-implicitmethod for pressure-linked equations) algorithm are often usedto solve the discrete Navier-Stokes equations. Generally theseschemes take a short time per iteration but require a largenumber of iterations. For simple geometries (or coarser grids)the overall CPU time is small. However, for finer grids or morecomplex geometries the increase in the number of iterationsmay be a drawback and the decoupling of the differential equationsinvolved implies a slow convergence of rotationally dominatedproblems that can be very time consuming for realistic applications.So we analyze here another approach, DIRECTO, that solves theequations in a coupled way. With recent advances in hardwaretechnology and software design, it became possible to solvecoupled Navier-Stokes systems, which are more robust but implyincreasing computational requirements (both in terms of memoryand CPU time). Two approaches are described here (band blockLU factorization and preconditioned GMRES) for the linear solverrequired by the DIRECTO algorithm that solves the fluid flowequations as a coupled system. Comparisons of the effectivenessof incomplete factorization preconditioners applied to the GMRES(generalized minimum residual) method are shown. Some numericalresults are presented showing that it is possible to minimizeconsiderably the CPU time of the coupled approach so that itcan be faster than the decoupled one.     

Preparation, structural analysis and dielectric properties of Bi x La1−x FeO3 perovskite

Rare earth element substituted bismuth ferrites (BiFeO₃) are of enormous importance as magnetoelectric materials. The polycrystalline samples of Bi _x La_1−x FeO₃ (x=0, 0.2, 0.4, 0.6, 0.8) were prepared by solid-state reaction using standard ceramic method. The single-phase formation of these compounds was confirmed by X-ray diffraction (XRD) studies. The samples with x=0, 0.2, 0.4, 0.6 are found to be orthorhombic while the sample with x=0.8 is triclinic. The dielectric constant (ε′) and dissipation factor (tan δ) were measured in the frequency range 100 Hz to 1 MHz at room temperature and as a function of temperature at certain fixed frequencies (1 kHz, 10 kHz, 100 kHz, 1 MHz). All the samples showed dielectric dispersion. The dielectric constant with temperature shows a broad peak; the peak temperature shifts with frequency which reflects the relaxor-type behavior. The peak above 600 K in the measured temperature range corresponds to antiferromagnetic ordering temperature (Néel temperature). The broadness of the peak changes with composition. The ac conductivity as well as ε′ are found to be maximum for the sample x=0.2 at room temperature.     

From the microscopic to the mesoscopic properties of lyotropic reverse hexagonal liquid crystals

In the present study we aimed to explore a correlation between the microstructural properties of the lyotropic reverse hexagonal phase (HII) of the GMO/tricaprylin/phosphatidylcholine/water system and its mesoscopic structure. The mesoscopic organization of discontinuous and anisotropic domains was examined, in the native state, using environmental scanning electron microscopy. The topography of the HII mesophases was imaged directly in their hydrated state, as a function of aqueous-phase concentration and composition, when a proline amino acid was solubilized into the systems as a kosmotropic (water-structure maker) guest molecule. The domain structures of several dozen micrometers in size, visualized in the environmental scanning electron microscopy, were found to possess fractal characteristics, indicating a discontinuous and disordered alignment of the corresponding internal water rods on the mesoscale. On the microstructural level, SAXS measurements revealed that as water content (Cw) increases the characteristic lattice parameter of the mesophases increases as well. Using the water concentration as the mass measure of the mixtures, a scaling relationship between the lattice parameter and the concentration was found to obey a power law whereby the derived fractal dimension was the relevant exponent, confirming the causal link between the microscopic and mesoscopic organizations. The topography of the HII mesophase was found to be affected by the microstructural parameters and the composition of the samples. Thermal analysis experiments involving these systems further confirmed that the behavior of water underpins both microscopical and mesoscopic features of the systems. It was shown that both the swelling of the lattice parameter and the mesoscopic domains is correlated to the bulk water concentration in the water rods.