Matrix elements, correspondence principles and line broadening

Introduction: During the early development of quantum mechanics much use was made of what Bohr referred to as “a formal analogy between the quantum theory and the classical theory”. The conceptual foundation of this “formal analogy”, which he later called the “correspondence principle”, was based on the assumption that the quantum theory contains classical mechanics as a limiting case. With the advent of modern quantum mechanics, the applications of this correspondence have until recently been neglected, perhaps due to a feeling that they were not necessary or that their range of applicability was too limited. There are unfortunately many cases where the methods of quantum mechanics are too cumbersome to be used without approximations. Recent astrophysical investigations have for instance involved transitions with principal quantum numbers of up to 250. If the approximations that have to be made become too restrictive a better policy could be to use an approximate method which can be used to solve the problem exactly. This theoretical investigation is in two parts. The first summarizes the correspondence principle methods and discusses their range of validity; by applying the correspondence principle to problems whose quantum mechanical solutions are known in special cases, we can compare the analytic expressions obtained by each method. We shall show that the two results agree over a far wider range of values than is generally realised, and that the agreement can be considerably improved by adjusting free parameters that arise naturally in the correspondence principle. The second part considers the application of classical mechanics and the correspondence principle to the broadening of spectral lines. The observation of spectral lines involving very high principal quantum numbers has led to a resurgence of approximate methods because of the difficulty of applying quantum mechanics exactly. A survey of the existing literature showed wither very formal solutions to the line broadening problem which were difficult to apply, or detailed results which had very limited validity. We shall show that our calculations agree with these accepted results in their region of validity whilst describing the line shape in the intermediate region. In Chapter II we describe the correspondence principles we invoke. In Chapter II we obtain the solution of the motion of a particle in various potentials and calculate matrix elements and other quantities in these potentials. The potentials we consider are a harmonic potential, a Morse potential, and a Coulomb potential, and we compare the results of our calculation with the quantum mechanical expression where these are known. In Chapter IV we outline the main causes of spectral line broadening. We consider the limits in which various physical approximations can be made and examine in detail the work and conclusions of Lindholm, one of the foremost workers in the field of non-quantum mechanical broadening. In Chapter V we present our theory and compare it with other in various limits, and in Chapter VI and VII we obtain line shapes which we compare with the Lindholm shapes

A Number-Theoretic Error-Correcting Code

In this paper we describe a new error-correcting code (ECC) inspired by the Naccache-Stern cryptosystem. While by far less efficient than Turbo codes, the proposed ECC happens to be more efficient than some established ECCs for certain sets of parameters. The new ECC adds an appendix to the message. The appendix is the modular product of small primes representing the message bits. The receiver recomputes the product and detects transmission errors using modular division and lattice reduction

NUMERICAL SIMULATION OF A ELASTO-VISCOPLASTIC FLUID FLOW INSIDE A CAVITY

This article addresses finite element approximations for elasto-viscoplastic flows. Numerical simulations aiming at investigating the role of elasticity for inertialess flows of viscoplastic materials within lid-driven cavity.The mechanical model is made up of the usual governing equations for incompressible fluids coupled with a Oldroyd-B type equation (de Souza Mendes, 2011) modified to incorporate the dependency both of relaxation and retardation time as the viscoplastic viscosity on the strain rate. These parameters depend on the material microstructure, which level is described by an structure parameter . This model is approximated by a multi-field Galerkin least-squares formulation (Behr et al., 1993) in terms of extra-stress tensor, the pressure field and the velocity vector. Results, focused on the determination of yield surface topology, investigate the influence of elastic and viscous governing parameters on the flow pattern

MULTI-FIELD STABILIZED FINITE ELEMENT APPROXIMATIONS FOR OLDROYD-B FLUID FLOWS

This work concerns with numerical simulations of creeping and inertial flows of viscoelastic fluids. The mechanical model consists of mass and momentum balance equations, coupled with the Oldroyd-B fluid. The model is approximated by a multi-field Galerkin least-squares (GLS) methodology in terms of extra-stress, velocity and pressure. The GLS method, introduced by Hughes et al. (1986) in the context of the Stokes problem for Newtonian fluidflows, allows the use of combinations of equal-order finite element interpolations and remains stable even for elastic- and inertiadominated fluid flows. Some steady simulations of Oldroyd-B fluids, flowing over a slot, are herein carried out. The influence of inertia and fluid viscoelasticity is taken into account ranging the Reynolds and Weissenberg numbers for relevant values of this flow. The results are in accordance to the viscoelastic literature and reassure the fine stability features of the GLS formulation

Centrifugal terms in the WKB approximation and semiclassical quantization of hydrogen

A systematic semiclassical expansion of the hydrogen problem about the classical Kepler problem is shown to yield remarkably accurate results. Ad hoc changes of the centrifugal term, such as the standard Langer modification where the factor l(l+1) is replaced by (l+1/2)^2, are avoided. The semiclassical energy levels are shown to be exact to first order in $\hbar$ with all higher order contributions vanishing. The wave functions and dipole matrix elements are also discussed.Comment: 5 pages, to appear in Phys. Rev.

INFLUENCE OF THE TYPE OF OXIDANT IN THE COMBUSTION OF NATURAL GAS INSIDE AN ALUMINUM MELTING FURNACE

ABSTRACT The fuel used as energy source for aluminum melting is of extreme importance for a better performance of the process. However, the type of oxidant can also lead to better performance, leading to a greater preservation of the equipments. Air is more abundant and cheaper, however due to the presence of nitrogen, there is undesirable NOx formation. An alternative is to employ pure oxygen. Although it is more expensive, it can lead to a cleaner and much more efficient combustion process, by significantly altering the combustion aspects inside the furnace, such as the shape of the flame and the distribution of temperature and heat flux. In the present work, numerical simulations were carried out using the commercial package FLUENT, analyzing different cases with pure oxygen and air as the oxidant for the combustion of natural gas. The results showed the possible damages caused by the process if long or too intense and concentrated flames are present. Copyright © 2006 by ASME 2 INTRODUCTION There are several industrial combustion applications which may benefit from the use of oxygen-enriched air or pure oxygen as the oxidizer during the combustion process. The resulting effects are many. Oxygen enrichment increases the flame temperature, promotes oxidation, and can lead to smaller pollutant (NOx) emissions compared with hydrocarbon-air systems, due to the absence of nitrogen. The formation of nitrogen oxides (NOx) in air-feed combustion systems represents a significant source for this pollutant within the industrial sector. With the increase in the world-wide utilization of fossil fuels, the control of NOx emissions has become an issue of global concern. Additionally, with increasing oil prices, the use of lower quality fuels will worsen the problem. Advances in computational modeling tools and the increased performance of computers have made comprehensive modeling of NOx formation and destruction a valuable tool to provide insights and understanding of the NOx reaction processes in combustion systems. This technology has the potential to enhance the application of various combustion techniques used to reduce NOx emissions from practical combustion systems Numerical modeling has became an important tool in the design and optimization of industrial equipments and also in the prediction of the emission of pollutants such as CO (carbon monoxide), SOx (sulfur oxides), and NOx. Recently, several numerical studies In the work by Frassoldati et al. [2], the attention was focused on a new procedure, based on CFD, for the determination of NOx emissions from combustion processes, which allowed the use of very detailed reaction schemes. The predictions of NOx were obtained by post-processing the flow and temperature fields, as predicted by the CFD model, and lumping together computational cells similar in terms of NOx formation. The resulting macro-cells were assumed to be a network of ideal reactors, which were simulated adopting detailed kinetic mechanisms. Nieckele et al. [3] described a numerical simulation of the 100% oxy-firing combustion process inside an industrial aluminum re-melting reverb furnace. Three different configurations were analyzed including the comparison between the staged versus non-staged combustion processes. The numerical procedure was based on the finite volume formulation and the κ−ε model of turbulence. The combustion was modeled based on the finite rate models of Arrhenius and Magnussen, and the Discrete Transfer Radiation model was employed for predicting the radiation heat transfer. The numerical predictions allowed for the determination of the flame patterns, species concentration distribution, temperature and velocity fields

Helminth resistance is mediated by differential activation of recruited monocyte-derived alveolar macrophages and arginine depletion

Macrophages are known to mediate anti-helminth responses, but it remains uncertain which subsets are involved or how macrophages actually kill helminths. Here, we show rapid monocyte recruitment to the lung after infection with the nematode parasite Nippostrongylus brasiliensis. In this inflamed tissue microenvironment, these monocytes differentiate into an alveolar macrophage (AM)-like phenotype, expressing both SiglecF and CD11c, surround invading parasitic larvae, and preferentially kill parasites in vitro. Monocyte-derived AMs (Mo-AMs) express type 2-associated markers and show a distinct remodeling of the chromatin landscape relative to tissue-derived AMs (TD-AMs). In particular, they express high amounts of arginase-1 (Arg1), which we demonstrate mediates helminth killing through L-arginine depletion. These studies indicate that recruited monocytes are selectively programmed in the pulmonary environment to express AM markers and an anti-helminth phenotype