Shared information in stationary states at criticality

We consider bipartitions of one-dimensional extended systems whose probability distribution functions describe stationary states of stochastic models. We define estimators of the information shared between the two subsystems. If the correlation length is finite, the estimators stay finite for large system sizes. If the correlation length diverges, so do the estimators. The definition of the estimators is inspired by information theory. We look at several models and compare the behaviors of the estimators in the finite-size scaling limit. Analytical and numerical methods as well as Monte Carlo simulations are used. We show how the finite-size scaling functions change for various phase transitions, including the case where one has conformal invariance.

Restoring the azimuthal symmetry of lateral distributions of charged particles in the range of the KASCADE-Grande experiment

The reconstruction of Extensive Air Showers (EAS) observed by particle detectors at the ground is based on the characteristics of observables like the lateral particle density and the arrival times. The lateral densities, inferred for different EAS components from detector data, are usually parameterised by applying various lateral distribution functions (LDFs). The LDFs are used in turn for evaluating quantities like the total number of particles or the density at particular radial distances. Typical expressions for LDFs anticipate azimuthal symmetry of the density around the shower axis. The deviations of the lateral particle density from this assumption arising from various reasons are smoothed out in the case of compact arrays like KASCADE, but not in the case of arrays like Grande, which only sample a smaller part of the azimuthal variation. KASCADE-Grande, an extension of the former KASCADE experiment, is a multi-component Extensive Air Shower (EAS) experiment located at the Karlsruhe Institute of Technology (Campus North), Germany. The lateral distributions of charged particles are deduced from the basic information provided by the Grande scintillators - the energy deposits - first in the observation plane, then in the intrinsic shower plane. In all steps azimuthal dependences should be taken into account. As the energy deposit in the scintillators is dependent on the angles of incidence of the particles, azimuthal dependences are already involved in the first step: the conversion from the energy deposits to the charged particle density. This is done by using the Lateral Energy Correction Function (LECF) that evaluates the mean energy deposited by a charged particle taking into account the contribution of other particles (e.g. photons) to the energy deposit. By using a very fast procedure for the evaluation of the energy deposited by various particles we prepared realistic LECFs depending on the angle of incidence of the shower and on the radial and azimuthal coordinates of the location of the detector. Mapping the lateral density from the observation plane onto the intrinsic shower plane does not remove the azimuthal dependences arising from geometric and attenuation effects, in particular for inclined showers. Realistic procedures for applying correction factors are developed. Specific examples of the bias due to neglecting the azimuthal asymmetries in the conversion from the energy deposit in the Grande detectors to the lateral density of charged particles in the intrinsic shower plane are given. (C) 2011 Elsevier B.V. All rights reserved.

The Mobility of Chondroitin Sulfate in Articular and Artificial Cartilage Characterized by (13)C Magic-Angle Spinning NMR Spectroscopy

We have studied the molecular dynamics of one of the major macromolecules in articular cartilage, chondroitin sulfate. Applying (13)C high-resolution magic-angle spinning NMR techniques, the NMR signals of all rigid macromolecules in cartilage can be suppressed, allowing the exclusive detection of the highly mobile chondroitin sulfate. The technique is also used to detect the chondroitin sulfate in artificial tissue-engineered cartilage. The tissue-engineered material that is based on matrix producing chondrocytes cultured in a collagen gel should provide properties as close as possible to those of the natural cartilage. Nuclear relaxation times of the chondroitin sulfate were determined for both tissues. Although T(1) relaxation times are rather similar, the T(2) relaxation in tissue-engineered cartilage is significantly shorter. This suggests that the motions of chondroitin sulfate in data:rat and artificial cartilage different. The nuclear relaxation times of chondroitin sulfate in natural and tissue-engineered cartilage were modeled using a broad distribution function for the motional correlation times. Although the description of the microscopic molecular dynamics of the chondroitin sulfate in natural and artificial cartilage required the identical broad distribution functions for the correlation times of motion, significant differences in the correlation times of motion that are extracted from the model indicate that the artificial tissue does not fully meet the standards of the natural ideal. This could also be confirmed by macroscopic biomechanical elasticity measurements. Nevertheless, these results suggest that NMR is a useful tool for the investigation of the quality of artificially engineered tissue. (C) 2010 Wiley Periodicals, Inc. Biopolymers 93: 520-532, 2010.

Size and power properties of some tests in the Birnbaum-Saunders regression model

The Birnbaum-Saunders distribution has been used quite effectively to model times to failure for materials subject to fatigue and for modeling lifetime data. In this paper we obtain asymptotic expansions, up to order n(-1/2) and under a sequence of Pitman alternatives, for the non-null distribution functions of the likelihood ratio, Wald, score and gradient test statistics in the Birnbaum-Saunders regression model. The asymptotic distributions of all four statistics are obtained for testing a subset of regression parameters and for testing the shape parameter. Monte Carlo simulation is presented in order to compare the finite-sample performance of these tests. We also present two empirical applications. (C) 2010 Elsevier B.V. All rights reserved.

Reliability Nonparametric Bayesian Estimation in Parallel Systems

Relevant results for (sub-)distribution functions related to parallel systems are discussed. The reverse hazard rate is defined using the product integral. Consequently, the restriction of absolute continuity for the involved distributions can be relaxed. The only restriction is that the sets of discontinuity points of the parallel distributions have to be disjointed. Nonparametric Bayesian estimators of all survival (sub-)distribution functions are derived. Dual to the series systems that use minimum life times as observations, the parallel systems record the maximum life times. Dirichlet multivariate processes forming a class of prior distributions are considered for the nonparametric Bayesian estimation of the component distribution functions, and the system reliability. For illustration, two striking numerical examples are presented.

Local power of some tests in exponential family nonlinear models

In this paper we obtain asymptotic expansions up to order n(-1/2) for the nonnull distribution functions of the likelihood ratio, Wald, score and gradient test statistics in exponential family nonlinear models (Cordeiro and Paula, 1989), under a sequence of Pitman alternatives. The asymptotic distributions of all four statistics are obtained for testing a subset of regression parameters and for testing the dispersion parameter, thus generalising the results given in Cordeiro et al. (1994) and Ferrari et al. (1997). We also present Monte Carlo simulations in order to compare the finite-sample performance of these tests. (C) 2010 Elsevier B.V. All rights reserved.

The impact of high latitudes on the optical design of solar systems

Irradiation distribution functions based on the yearly collectible energy have been derived for two locations; Sydney, Australia which represents a mid-latitude site and Stockholm, Sweden, which represents a high latitude site. The strong skewing of collectible energy toward summer solstice at high latitudes dictates optimal collector tilt angles considerably below the polar mount. The lack of winter radiation at high latitudes indicates that the optimal acceptance angle for a stationary EW-aligned concentrator decreases as latitude increases. Furthermore concentrator design should be highly asymmetric at high latitudes.

Monte Carlo investigations of intermolecular interactions in water-amide mixtures

Monte Carlo simulations of water-amides (amide=fonnamide-FOR, methylfonnamide-NMF and dimethylformamide-DMF) solutions have been carried out in the NpT ensemble at 308 K and 1 atm. The structure and excess enthalpy of the mixtures as a function of the composition have been investigated. The TIP4P model was used for simulating water and six-site models previously optimized in this laboratory were used for simulating the liquid amides. The intermolecular interaction energy was calculated using the classical 6-12 Lennard-Jones potential plus a Coulomb term. The interaction energy between solute and solvent has been partitioned what leads to a better understanding of the behavior of the enthalpy of mixture obtained for the three solutions experimentally. Radial distribution functions for the water-amides correlations permit to explore the intermolecular interactions between the molecules. The results show that three, two and one hydrogen bonds between the water and the amide molecules are formed in the FOR, NMF and DMF-water solutions, respectively. These H-bonds are, respectively, stronger for DMF-water, NMF-water and FOR-water. In the NMF-water solution, the interaction between the methyl group of the NMF and the oxygen of the water plays a role in the stabilization of the aqueous solution quite similar to that of an H-bond in the FOR-water solution. (c) 2005 Elsevier B.V. All rights reserved.

Monte Carlo thermodynamic and structural properties of the TIP4P water model: dependence on the computational conditions

Classical Monte Carlo simulations were carried out on the NPT ensemble at 25°C and 1 atm, aiming to investigate the ability of the TIP4P water model [Jorgensen, Chandrasekhar, Madura, Impey and Klein; J. Chem. Phys., 79 (1983) 926] to reproduce the newest structural picture of liquid water. The results were compared with recent neutron diffraction data [Soper; Bruni and Ricci; J. Chem. Phys., 106 (1997) 247]. The influence of the computational conditions on the thermodynamic and structural results obtained with this model was also analyzed. The findings were compared with the original ones from Jorgensen et al [above-cited reference plus Mol. Phys., 56 (1985) 1381]. It is notice that the thermodynamic results are dependent on the boundary conditions used, whereas the usual radial distribution functions g(O/O(r)) and g(O/H(r)) do not depend on them.

The Wigner function associated with the Rogers-Szego polynomials

A Wigner function associated with the Rogers-Szego polynomials is proposed and its properties are discussed. It is shown that from such a Wigner function it is possible to obtain well-behaved probability distribution functions for both angle and action variables, defined on the compact support -pi less than or equal to theta < pi, and for m greater than or equal to 0, respectively. The width of the angle probability density is governed by the free parameter q characterizing the polynomials.

Quantitative aspects of entanglement in the driven Jaynes-Cummings model

Adopting the framework of the Jaynes-Cummings model with an external quantum field, we obtain exact analytical expressions of the normally ordered moments for any kind of cavity and driving fields. Such analytical results are expressed in the integral form, with their integrands having a commom term that describes the product of the Glauber-Sudarshan quasiprobability distribution functions for each field, and a kernel responsible for the entanglement. Considering a specific initial state of the tripartite system, the normally ordered moments are then applied to investigate not only the squeezing effect and the nonlocal correlation measure based on the total variance of a pair of Einstein-Podolsky-Rosen type operators for continuous variable systems, but also the Shchukin-Vogel criterion. This kind of numerical investigation constitutes the first quantitative characterization of the entanglement properties for the driven Jaynes-Cummings model.

QUASIDISTRIBUTIONS and COHERENT STATES FOR FINITE-DIMENSIONAL QUANTUM SYSTEMS

In recent years, an approach to discrete quantum phase spaces which comprehends all the main quasiprobability distributions known has been developed. It is the research that started with the pioneering work of Galetti and Piza, where the idea of operator bases constructed of discrete Fourier transforms of unitary displacement operators was first introduced. Subsequently, the discrete coherent states were introduced, and finally, the s-parametrized distributions, that include the Wigner, Husimi, and Glauber-Sudarshan distribution functions as particular cases. In the present work, we adapt its formulation to encompass some additional discrete symmetries, achieving an elegant yet physically sound formalism.

Uncertainties in the prediction of spatial variability of soil CO2 emissions and related properties

A emissão de CO2 do solo apresenta alta variabilidade espacial, devido à grande dependência espacial observada nas propriedades do solo que a influenciam. Neste estudo, objetivou-se: caracterizar e relacionar a variabilidade espacial da respiração do solo e propriedades relacionadas; avaliar a acurácia dos resultados fornecidos pelo método da krigagem ordinária e simulação sequencial gaussiana; e avaliar a incerteza na predição da variabilidade espacial da emissão de CO2 do solo e demais propriedades utilizando a simulação sequencial gaussiana. O estudo foi conduzido em uma malha amostral irregular com 141 pontos, instalada sobre a cultura de cana-de-açúcar. Nesses pontos foram avaliados a emissão de CO2 do solo, a temperatura do solo, a porosidade livre de água, o teor de matéria orgânica e a densidade do solo. Todas as variáveis apresentaram estrutura de dependência espacial. A emissão de CO2 do solo mostrou correlações positivas com a matéria orgânica (r = 0,25, p < 0,05) e a porosidade livre de água (r = 0,27, p <0,01) e negativa com a densidade do solo (r = -0,41, p < 0,01). No entanto, quando os valores estimados espacialmente (N=8833) são considerados, a porosidade livre de água passa a ser a principal variável responsável pelas características espaciais da respiração do solo, apresentando correlação de 0,26 (p < 0,01). As simulações individuais propiciaram, para todas as variáveis analisadas, melhor reprodução das funções de distribuição acumuladas e dos variogramas, em comparação à krigagem e estimativa E-type. As maiores incertezas na predição da emissão de CO2 estiveram associadas às regiões da área estudada com maiores valores observados e estimados, produzindo estimativas, ao longo do período estudado, de 0,18 a 1,85 t CO2 ha-1, dependendo dos diferentes cenários simulados. O conhecimento das incertezas gerado por meio dos diferentes cenários de estimativa pode ser incluído em inventários de gases do efeito estufa, resultando em estimativas mais conservadoras do potencial de emissão desses gases.

C-H center dot center dot center dot O and N-H center dot center dot center dot O hydrogen bonds in liquid amides investigated by Monte Carlo simulation

Monte Carlo simulations of liquid formamide, N-methylformamide (MF), and N,N-dimethylformamide (DMF) have been performed in the isothermal and isobaric ensemble at 298 K and 1 atm, aiming to investigate the C-H ... O and N-H ... O hydrogen bonds. The interaction energy was calculated using the classical 6-12 Lennard-Jones pairwise potential plus a Coulomb term on a rigid six-site molecular model with the potential parameters being optimized in this work. Theoretical values obtained for heat of vaporization and liquid densities are in good agreement with the experimental data. The radial distribution function [RDF, g(r)] obtained compare well with R-X diffraction data available. The RDF and molecular mechanics (MM2) minimization show that the C-H ... O interaction has a significant role in the structure of the three liquids. These results are supported by ab initio calculations. This Interaction is particularly important in the structure of MF. The intensity of the N-H ... O hydrogen bond is greater in the MF than formamide. This could explain some anomalous properties verified in MF. (C) 1997 John Wiley & Sons, Inc.

Characterization of the porosity developed in a new titania-alumina catalyst support prepared by the sol gel route

Titanium oxide (TiO2) is a good candidate for support of hydrotreating catalysts but has the disadvantage of presenting a low surface area and a poor thermal stability when compared with Al2O3. A mixed TiO2-Al2O3 support was proposed as an alternative that is expected to be free from these drawbacks. The variation during firing of the nanoporous texture of supports composed of TiO2-Al2O3, TiO2 and Al2O3 was studied by small angle X-ray scattering (SAXS). The supports were prepared by the sol-gel route using Ti and Al isopropoxides. We have particularly analyzed the effects of acid and basic hydrolysis on the nanostructural features of catalyst supports fired at different temperatures. The nanopore radius distribution functions were determined from SAXS results assuming a simple model of spherical nanopores embedded in a homogeneous solid matrix. The modal pore radius in both pure TiO2 and pure Al2O3 supports grows from 1.3 to 2.2 nm as the firing temperature increases from 673 to 973 K. on the other hand, the modal pore radius in the mixed TiO2-Al2O3 support remains below 1.2 nm over the same range of firing temperatures. These results demonstrate the good thermal stability of the nanoporous texture of mixed TiO2-Al2O3 supports.