Non-linear Poisson-Boltzmann Theory for Swollen Clays

The non-linear Poisson-Boltzmann equation for a circular, uniformly charged platelet, confined together with co- and counter-ions to a cylindrical cell, is solved semi-analytically by transforming it into an integral equation and solving the latter iteratively. This method proves efficient, robust, and can be readily generalized to other problems based on cell models, treated within non-linear Poisson-like theory. The solution to the PB equation is computed over a wide range of physical conditions, and the resulting osmotic equation of state is shown to be in fair agreement with recent experimental data for Laponite clay suspensions, in the concentrated gel phase.Comment: 13 pages, 4 postscript figure

População no sistema prisional português: evolução e tendências entre 2000 e 2017

Este artigo apresenta uma reflexão sobre as principais tendências identificadas na evolução da população recenseada no sistema prisional português, entre 2000 e 2017. Partindo de uma análise que cruza as alterações no campo do direito penal com os dados estatísticos oficiais e relatórios e estudos nacionais e internacionais sobre a aplicação da pena de prisão no país, pretende-se compreender e identificar alguns dos desafios colocados ao sistema pelo movimento da população prisional, assim como pelas mudanças registadas no perfil desta população. A evolução e tendências identificadas permitem indagar sobre o impacto da lei e contribuir para identificar alguns dos caminhos que falta traçar em resposta aos imperativos legais internacionais em matéria da população a cumprir pena privativa de liberdade

Correlation functions in ionic liquid at coexistence with ionic crystal. Results of the Brazovskii-type field theory

Correlation functions in the restricted primitive model are calculated within a field-theoretic approach in the one-loop self-consistent Hartree approximation. The correlation functions exhibit damped oscillatory behavior as found before in the Gaussian approximation [Ciach at. al., J. Chem. Phys. {\bf 118}, 3702 (2003)]. The fluctuation contribution leads to a renormalization of both the amplitude and the decay length of the correlation functions. The renormalized quantities show qualitatively different behavior than their mean-field (MF) counterparts. While the amplitude and the decay length both diverge in MF when the $\lambda$-line is approached, the renormalized quantities remain of order of unity in the same dimensionless units down to the coexistence with the ionic crystal. Along the line of the phase transition the decay length and the period of oscillations are independent of density, and their values in units of the diameter of the ions are $\alpha_0^{-1}\approx 1$ and $2\pi/\alpha_1\approx 2.8$ respectively.Comment: 21 pages including 9 figure

Algunos ejemplos de Realpolitik en las fuentes griegas

Se comentan algunos ejemplos de textos legales que muestran un enfoque decididamente realista, inspirado por un principio de racionalismo práctico y una total autonomía en la aplicación de la inteligencia humana a la previsión y resolución de los problemas de la vida en comunidad. Los testimonios analizados primero, son epigráficos: una arcaica inscripción de Quíos (VII-VI), cuya mención de una µïùìc äèíïóÝè indujo a considerarla un temprano ejemplo de constitución democrática, y los códigos legales, en forma de Imprecaciones Públicas, recogidos en dos inscripciones procedentes de Teos (490-470). Finalmente se insiste en el paralelismo de estos testimonios directos con un texto literario, la Ciropedia de Jenofonte.Using some fragments of archaic legal texts, and of Xenophon's Cyropaedia, we show the dominant role, within the Ancient Greek World, of a principle of practical rationality to deal with the problems arising from life of the human communities. A principle relying upon a full authonomy of the human mind. The fragments belong to a Chios' inscription (VII-VI), usually seen as an early remain of a democratic constitution because of its mentioning of a µïùìc äèíïóÝè, and to the law codes on two inscriptions from Teos (490-470), written in the form of public imprecations. An akin method is suggested for the political strategies shown by the literary hero of Xenophon's Cyropaedia

Charge Oscillations in Debye-Hueckel Theory

The recent generalized Debye-Hueckel (GDH) theory is applied to the calculation of the charge-charge correlation function G_{ZZ}(r). The resulting expression satisfies both (i) the charge neutrality condition and (ii) the Stillinger-Lovett second-moment condition for all T and rho_N, the overall ion density, and (iii) exhibits charge oscillations for densities above a "Kirkwood line" in the (rho_N,T) plane. This corrects the normally assumed DH correlations, and, when combined with the GDH analysis of the density correlations, leaves the GDH theory as the only complete description of ionic correlation functions, as judged by (i)-(iii), (iv) exact low-density (rho_N,T) variation, and (v) reasonable behavior near criticality.Comment: 6 pages, EuroPhys.sty (now available on archive), 1 eps figur

Effective Magnetic Hamiltonian and Ginzburg Criterion for Fluids

We develop further the approach of Hubbard and Schofield (Phys.Lett., A40 (1972) 245), which maps the fluid Hamiltonian onto a magnetic one. We show that all coefficients of the resulting effective Landau-Ginzburg-Wilson (LGW) Hamiltonian may be expressed in terms of the compressibility of a reference fluid containing only repulsive interactions, and its density derivatives; we calculate the first few coefficients in the case of the hard-core reference fluid. From this LGW-Hamiltonian we deduce approximate mean-field relations between critical parameters and test them on data for Lennard-Jones, square-well and hard-core-Yukawa fluids. We estimate the Ginzburg criterion for these fluids.Comment: 4 pages, LaTeX, To appear in Phys.Rev.

The liquid-vapor interface of an ionic fluid

We investigate the liquid-vapor interface of the restricted primitive model (RPM) for an ionic fluid using a density-functional approximation based on correlation functions of the homogeneous fluid as obtained from the mean-spherical approximation (MSA). In the limit of a homogeneous fluid our approach yields the well-known MSA (energy) equation of state. The ionic interfacial density profiles, which for the RPM are identical for both species, have a shape similar to those of simple atomic fluids in that the decay towards the bulk values is more rapid on the vapor side than on the liquid side. This is the opposite asymmetry of the decay to that found in earlier calculations for the RPM based on a square-gradient theory. The width of the interface is, for a wide range of temperatures, approximately four times the second moment correlation length of the liquid phase. We discuss the magnitude and temperature dependence of the surface tension, and argue that for temperatures near the triple point the ratio of the dimensionless surface tension and critical temperature is much smaller for the RPM than for simple atomic fluids.Comment: 6 postscript figures, submitted to Phys. Rev.

Density Fluctuations in an Electrolyte from Generalized Debye-Hueckel Theory

Near-critical thermodynamics in the hard-sphere (1,1) electrolyte is well described, at a classical level, by Debye-Hueckel (DH) theory with (+,-) ion pairing and dipolar-pair-ionic-fluid coupling. But DH-based theories do not address density fluctuations. Here density correlations are obtained by functional differentiation of DH theory generalized to {\it non}-uniform densities of various species. The correlation length $\xi$ diverges universally at low density $\rho$ as $(T\rho)^{-1/4}$ (correcting GMSA theory). When $\rho=\rho_c$ one has $\xi\approx\xi_0^+/t^{1/2}$ as $t\equiv(T-T_c)/T_c\to 0+$ where the amplitudes $\xi_0^+$ compare informatively with experimental data.Comment: 5 pages, REVTeX, 1 ps figure included with epsf. Minor changes, references added. Accepted for publication in Phys. Rev. Let

Ginzburg Criterion for Coulombic Criticality

To understand the range of close-to-classical critical behavior seen in various electrolytes, generalized Debye-Hueckel theories (that yield density correlation functions) are applied to the restricted primitive model of equisized hard spheres. The results yield a Landau-Ginzburg free-energy functional for which the Ginzburg criterion can be explicitly evaluated. The predicted scale of crossover from classical to Ising character is found to be similar in magnitude to that derived for simple fluids in comparable fashion. The consequences in relation to experiments are discussed briefly.Comment: 4 pages, revtex, 2 tables (latex2.09 required due to revtex's incompatibility with latex2e tables