Thermodynamics from a scaling Hamiltonian

There are problems with defining the thermodynamic limit of systems with long-range interactions; as a result, the thermodynamic behavior of these types of systems is anomalous. In the present work, we review some concepts from both extensive and nonextensive thermodynamic perspectives. We use a model, whose Hamiltonian takes into account spins ferromagnetically coupled in a chain via a power law that decays at large interparticle distance $r$ as $1/r^{\alpha}$ for $\alpha\geq0$. Here, we review old nonextensive scaling. In addition, we propose a new Hamiltonian scaled by $2\frac{(N/2)^{1-\alpha}-1}{1-\alpha}$ that explicitly includes symmetry of the lattice and dependence on the size, $N$, of the system. The new approach enabled us to improve upon previous results. A numerical test is conducted through Monte Carlo simulations. In the model, periodic boundary conditions are adopted to eliminate surface effects.Comment: 12 pages, 2 figures, submitted for publication to Phys. Rev.

Bayesian inference in spherical linear models: robustness and conjugate analysis

AbstractThe early work of Zellner on the multivariate Student-t linear model has been extended to Bayesian inference for linear models with dependent non-normal error terms, particularly through various papers by Osiewalski, Steel and coworkers. This article provides a full Bayesian analysis for a spherical linear model. The density generator of the spherical distribution is here allowed to depend both on the precision parameter φ and on the regression coefficients β. Another distinctive aspect of this paper is that proper priors for the precision parameter are discussed.The normal-chi-squared family of prior distributions is extended to a new class, which allows the posterior analysis to be carried out analytically. On the other hand, a direct joint modelling of the data vector and of the parameters leads to conjugate distributions for the regression and the precision parameters, both individually and jointly. It is shown that some model specifications lead to Bayes estimators that do not depend on the choice of the density generator, in agreement with previous results obtained in the literature under different assumptions. Finally, the distribution theory developed to tackle the main problem is useful on its own right

Varied nanostructures from a single multifunctional molecular material

The control of the morphology of nanostructures formed from a single component molecular material incorporating electron accepting and donating moieties is shown, from both solution and gel states. The compound comprises one tetrathiafulvalene (TTF) and two pyrene units which act as the [small pi]-electron rich and deficient units, respectively, and which are united by amide-containing linkers whose additional role is to aide aggregation by hydrogen bonding. This role was demonstrated by IR and NMR spectroscopy. The gels were deposited onto surfaces and the solvent allowed to evaporate, leaving films formed by meshes of fibres with different morphologies in accord with the different solvents used to form the materials. Doping of these xerogels with iodine vapour afforded conducting films whose characteristics were probed with current sensing atomic force microscopy (CS-AFM), providing current maps and I-V curves which show how dramatically the processing solvent can influence the electronic properties of these xerogel-derived materials

Adventures of a tidally induced bar

Using N-body simulations, we study the properties of a bar induced in a discy dwarf galaxy as a result of tidal interaction with the Milky Way. The bar forms at the first pericentre passage and survives until the end of the evolution at 10 Gyr. Fourier decomposition of the bar reveals that only even modes are significant and preserve a hierarchy so that the bar mode is always the strongest. They show a characteristic profile with a maximum, similar to simulated bars forming in isolated galaxies and observed bars in real galaxies. We adopt the maximum of the bar mode as a measure of the bar strength and we estimate the bar length by comparing the density profiles along the bar and perpendicular to it. The bar strength and the bar length decrease with time, mainly at pericentres, as a result of tidal torques acting at those times and not to secular evolution. The pattern speed of the bar varies significantly on a time-scale of 1 Gyr and is controlled by the orientation of the tidal torque from the Milky Way. The bar is never tidally locked, but we discover a hint of a 5/2 orbital resonance between the third and fourth pericentre passage. The speed of the bar decreases in the long run so that the bar changes from initially rather fast to slow in the later stages. The boxy/peanut shape is present for some time and its occurrence is preceded by a short period of buckling instability

Un modelo Poissoniano para predecir la matriculación de vehículos en países europeos

En este artículo presentamos una modelización para la matriculación de vehículos en países de Europa mediante un proceso de Poisson Doblemente Estocástico con media aleatoria Normal truncada. Apoyándonos en trabajos previos acerca de este proceso, se amplía el estudio de características de éste. Asímismo, se hace una predicción de este proceso para los años 2000 y 2001

A simple numerical experiment of Green's function expansion in the Fast Multipole Method

In this paper the theoretical foundation of the fast multipole method applied to problems involving electromagnetic scattering is briefly presented, the truncation of the Green’s function expansion is revisited, and the well established truncation criteria, in terms of the relative accuracy of the solutions of the electric field integral equation, is revised from a numerical experiment. Finally, from this numerical procedure an interesting result for the number L of poles is reported