Fernando Vericat

On the Mean Spherical Approximation for Hard Ions and Dipoles

The analytical solution of the mean spherical approximation for the case of equal size ions and different size solvent is reexamined using only two parameters: a polarization parameter λ and a screening parameter Γ. We show that the ion dipole cross energy parameter, which in previous work was obtained solving a cubic equation, can be obtained from a linear algebraic equation. Therefore, the inverse problem of calculating the reduced charge parameter d0 and the reduced dipole parameter d2 from λ and Γ is reduced to a system of two equations: a cubic for d0, and a linear for d2. Simpler expressions for the thermodynamic parameters are also obtained.

New criteria for cluster identification in continuum systems

Two new criteria, that involve the microscopic dynamics of the system, are proposed for the identification of clusters in continuum systems. The first one considers a residence time in the definition of the bond between pairs of particles, whereas the second one uses a life time in the definition of an aggregate. Because of the qualitative features of the clusters yielded by the criteria we call them chemical and physical clusters, respectively. Molecular dynamics results for a Lennard-Jones system and general connectivity theories are presented.

Invariant of dynamical systems: A generalized entropy

In this work the concept of entropy of a dynamical system, as given by Kolmogorov, is generalized in the sense of Tsallis. It is shown that this entropy is an isomorphism invariant, being complete for Bernoulli schemes.

Geometric constructions and multifractal analysis for boundary hyperbolic maps

In this paper we present geometric constructions based on the method by Series for coding geodesics in the hyperbolic disc. For this are used certain special types of one-dimensional maps defined on the boundary of the hyperbolic plane. These types of maps do not require additional assumptions to ensure the existence of Gibbs states. We connect geometrical constructions from limit sets of Fuchsian groups with multifractal analysis by modifying the definition of a local entropy by Takens and Verbitski.

Relations Between Some Quantities in Classical Thermodynamics and Abstract Dynamics. Beyond Hyperbolicity

Formal relationships among statistical mechanics, multifractal analysis, and dynamical systems with weaker conditions than the existence of Markov partitions are presented. The hypotheses we consider are Bowens expansiveness and specification property, so that more general dynamical systems than, for instance, mixing hyperbolic systems can be included in our formalism.

Dielectric properties of natural and demineralized collagen bone matrix

In this paper, measurements of dielectric properties of fluid-saturated cortical and trabecular bovine bones are presented. Results are reported for native and demineralized states from 80 MHz to 1 GHz. A non invasive technique using open-ended coaxial lines is proposed, and compared to invasive configurations. Measurements are performed in time domain and data are processed using system identification techniques in continuous and discrete domains. These are very interesting tools for signal processing when working with time domain spectroscopy data. As a validation test for the system identification technique, data are also obtained in the frequency domain. A clear evidence of relaxation processes around 0.2 to 0.4 GHz is shown, which may be due to the movement of polar side chains of the collagen fibers. A strong difference between the dielectric properties of native and demineralized bones was found. The experiments here reported aim to contribute to a more in-depth knowledge of the relaxation processes due to the fully hydrated collagen matrix and its relation to the mineralized phase.

Clustering and continuum percolation of hard spheres near a hard wall: Monte Carlo simulation and connectedness theory

The effect of a hard wall on the clustering and continuum percolation of a hard spheres fluid is studied using Monte Carlo simulations and connectedness theory. We calculate an averaged pair-connectedness function ρ†(r;z) which is the probability density of finding two particles in the same cluster and separate by a distance r under the assumption that one of them is fixed at a distance z from the wall. We also obtain the mean size S for the cluster containing the fixed sphere and the critical percolation density ρc at which it becomes macroscopically large. Monte Carlo results allow us to conclude that, for given number density and connectedness distance, the wall causes the decrease of S and the increase of ρc in comparison with those found for the bulk in the absence of the wall. Both effects diminish with increasing z. The simulation data also show that, in the presence of the wall, the clusters are eccentric with cylindrical symmetry, slightly flattened in the region of contact with the wall. The the...

Cluster pair correlation function of simple fluids : Energetic connectivity criteria

We consider the clustering of Lennard-Jones particles by using an energetic connectivity criterion proposed long ago by Hill [J. Chem. Phys. 32, 617 (1955)] for the bond between pairs of particles. The criterion establishes that two particles are bonded (directly connected) if their relative kinetic energy is less than minus their relative potential energy. Thus, in general, it depends on the direction as well as on the magnitude of the velocities and positions of the particles. An integral equation for the pair connectedness function, proposed by two of the authors [Phys. Rev. E 61, R6067 (2000)], is solved for this criterion and the results are compared with those obtained from molecular dynamics simulations and from a connectedness Percus-Yevick-type integral equation for a velocity-averaged version of Hills energetic criterion.

An approach to the problem of phase transitions in the continuum

Based on the spectral properties of Ruelle transfer operators, we establish conditions for the absence of phase transitions in the continuum. Our approach differs in several aspects from those which use Kirkwood–Salsburg and Kirkwood–Ruelle operators. In particular the results follow in a concise and relatively direct way.

Statistical mechanics of ion–dipole mixtures: An exactly solvable model in one dimension

The statistical mechanics of a mixture of hard core ions and dipoles, with or without an applied external field, is solved exactly in one dimension using the generating function technique of Baxter. This function is shown to be the solution of a nonlinear Hill‐type equation. In the plasma limit we obtain explicit expressions for the thermodynamic properties of the bulk phase and the potential drop and differential capacitance of the electrical double layer as well. The expressions obtained resemble the mean spherical approximation results.