Advance P. Chem. Problems (I) Populations, Partition Functions, Particle in Box, Harmonic Oscillators, Angular Momentum and Rigid Rotor

This is a set of P. Chem. problems posed at slightly higher than the normal text book level, for students who are continuing in the study of this subject.

Alternative Formulations for Angular Momentum Operators, Cartesian and Spherical Polar Forms

The conversion between representations of angular momentum in spherical polar and cartesian form is discussed.

Unimolecular Rovibrational Bound and Resonance States for Large Angular Momentum: J=20 Calculations for HO2

We explore the calculation of unimolecular bound states and resonances for deep-well species at large angular momentum using a Chebychev filter diagonalization scheme incorporating doubling of the autocorrelation function as presented recently by Neumaier and Mandelshtam [Phys. Rev. Lett. 86, 5031 (2001)]. The method has been employed to compute the challenging J=20 bound and resonance states for the HO2 system. The methodology has firstly been tested for J=2 in comparison with previous calculations, and then extended to J=20 using a parallel computing strategy. The quantum J-specific unimolecular dissociation rates for HO2-> H+O-2 in the energy range from 2.114 to 2.596 eV have been reported for the first time, and comparisons with the results of Troe and co-workers [J. Chem. Phys. 113, 11019 (2000) Phys. Chem. Chem. Phys. 2, 631 (2000)] from statistical adiabatic channel method/classical trajectory calculations have been made. For most of the energies, the reported statistical adiabatic channel method/classical trajectory rate constants agree well with the average of the fluctuating quantum-mechanical rates. Near the dissociation threshold, quantum rates fluctuate more severely, but their average is still in agreement with the statistical adiabatic channel method/classical trajectory results.

CFD modelling of the fast pyrolysis of biomass in fluidised bed reactors, Part A: Eulerian computation of momentum transport in bubbling fluidised beds

The fluid–particle interaction inside a 150 g/h fluidised bed reactor is modelled. The biomass particle is injected into the fluidised bed and the momentum transport from the fluidising gas and fluidised sand is modelled. The Eulerian approach is used to model the bubbling behaviour of the sand, which is treated as a continuum. The particle motion inside the reactor is computed using drag laws, dependent on the local volume fraction of each phase, according to the literature. FLUENT 6.2 has been used as the modelling framework of the simulations with a completely revised drag model, in the form of user defined function (UDF), to calculate the forces exerted on the particle as well as its velocity components. 2-D and 3-D simulations are tested and compared. The study is the first part of a complete pyrolysis model in fluidised bed reactors.

Angular momentum of S0 galaxies

The aim of this thesis is to study the angular momentum of a sample of S0 galaxies. In the quest to understand whether the formation of S0 galaxies is more closely linked to that of ellipticals or that of spirals, our goal is to compare the amount of their specific angular momentum as a function of stellar mass with respect to spirals. Through kinematic comparison between these different classes of galaxies we aim to understand if a scenario of passive evolution, in which the galaxy’s gas is consumed and the star formation is quenched, can be considered as plausible mechanism to explain the transformation from spirals to S0s. In order to derive the structural and photometric parameters of galaxy sub-components we performed a bulge-disc decomposition of optical images using GALFIT. The stellar kinematic of the galaxies was measured using integral field spectroscopic data from CALIFA survey. The development of new original software, based on a Monte Carlo Markov Chain algorithm, allowed us to obtain the values of the line of sight velocity and velocity dispersion of disc and bulge components. The result that we obtained is that S0 discs have a distribution of stellar specific angular momentum that is in full agreement with that of spiral discs, so the mechanism of simple fading can be considered as one of the most important for transformation from spirals to S0s.

Design and modeling of optical fibers for spatial division multiplexing using the orbital angular momentum of light

Les besoins toujours croissants en terme de transfert de données numériques poussent au développement de nouvelles technologies pour accroître la capacité des réseaux, notamment en ce qui concerne les réseaux de fibre optique. Parmi ces nouvelles technologies, le multiplexage spatial permet de multiplier la capacité des liens optiques actuels. Nous nous intéressons particulièrement à une forme de multiplexage spatial utilisant le moment cinétique orbital de la lumière comme base orthogonale pour séparer un certain nombre de canaux. Nous présentons d’abord les notions d’électromagnétisme et de physique nécessaires à la compréhension des développements ultérieurs. Les équations de Maxwell sont dérivées afin d’expliquer les modes scalaires et vectoriels de la fibre optique. Nous présentons également d’autres propriétés modales, soit la coupure des modes, et les indices de groupe et de dispersion. La notion de moment cinétique orbital est ensuite introduite, avec plus particulièrement ses applications dans le domaine des télécommunications. Dans une seconde partie, nous proposons la carte modale comme un outil pour aider au design des fibres optiques à quelques modes. Nous développons la solution vectorielle des équations de coupure des modes pour les fibres en anneau, puis nous généralisons ces équations pour tous les profils de fibres à trois couches. Enfin, nous donnons quelques exemples d’application de la carte modale. Dans la troisième partie, nous présentons des designs de fibres pour la transmission des modes avec un moment cinétique orbital. Les outils développés dans la seconde partie sont utilisés pour effectuer ces designs. Un premier design de fibre, caractérisé par un centre creux, est étudié et démontré. Puis un second design, une famille de fibres avec un profil en anneau, est étudié. Des mesures d’indice effectif et d’indice de groupe sont effectuées sur ces fibres. Les outils et les fibres développés auront permis une meilleure compréhension de la transmission dans la fibre optique des modes ayant un moment cinétique orbital. Nous espérons que ces avancements aideront à développer prochainement des systèmes de communications performants utilisant le multiplexage spatial.

Shaken not stirred: creating exotic angular momentum states by shaking an optical lattice

We propose a method to create higher orbital states of ultracold atoms in the Mott regime of an optical lattice. This is done by periodically modulating the position of the trap minima (known as shaking) and controlling the interference term of the lasers creating the lattice. These methods are combined with techniques of shortcuts to adiabaticity. As an example of this, we show specifically how to create an anti-ferromagnetic type ordering of angular momentum states of atoms. The specific pulse sequences are designed using Lewis-Riesenfeld invariants and a fourlevel model for each well. The results are compared with numerical simulations of the full Schrodinger equation.

The viscosity parameter's dependence on the profile of the disk scale height

It is shown that, for accretion disks, the height scale is a constant whenever hydrostatic equilibrium and the subsonic turbulence regime hold in the disk. In order to have a variable height scale, processes are needed that contribute an extra term to the continuity equation. This contribution makes the viscosity parameter much greater in the outer region and much smaller in the inner region. Under these circumstances, turbulence is the presumable source of viscosity in the disk.

Beryllium abundances along the evolutionary sequence of the open cluster IC 4651-A new test for hydrodynamical stellar models

Context. Previous analyses of lithium abundances in main sequence and red giant stars have revealed the action of mixing mechanisms other than convection in stellar interiors. Beryllium abundances in stars with Li abundance determinations can offer valuable complementary information on the nature of these mechanisms. Aims. Our aim is to derive Be abundances along the whole evolutionary sequence of an open cluster. We focus on the well-studied open cluster IC 4651. These Be abundances are used with previously determined Li abundances, in the same sample stars, to investigate the mixing mechanisms in a range of stellar masses and evolutionary stages. Methods. Atmospheric parameters were adopted from a previous abundance analysis by the same authors. New Be abundances have been determined from high-resolution, high signal-to-noise UVES spectra using spectrum synthesis and model atmospheres. The careful synthetic modeling of the Be lines region is used to calculate reliable abundances in rapidly rotating stars. The observed behavior of Be and Li is compared to theoretical predictions from stellar models including rotation-induced mixing, internal gravity waves, atomic diffusion, and thermohaline mixing. Results. Beryllium is detected in all the main sequence and turn-off sample stars, both slow- and fast-rotating stars, including the Li-dip stars, but is not detected in the red giants. Confirming previous results, we find that the Li dip is also a Be dip, although the depletion of Be is more modest than for Li in the corresponding effective temperature range. For post-main-sequence stars, the Be dilution starts earlier within the Hertzsprung gap than expected from classical predictions, as does the Li dilution. A clear dispersion in the Be abundances is also observed. Theoretical stellar models including the hydrodynamical transport processes mentioned above are able to reproduce all the observed features well. These results show a good theoretical understanding of the Li and Be behavior along the color-magnitude diagram of this intermediate-age cluster for stars more massive than 1.2 M(circle dot).

Um estudo sobre o momentum angular total de estrelas com planetas

Since Michel Mayor and his student Didier Queloz s pioneer announcement, in 1995, of the existence of a planet orbiting the star 51 Peg, up to present date, 695 extrasolar planets orbiting stars of spectral type F, G, K and M have been discovered. A study on the behavior of the total angular momentum of the planetary systems known up to present date becomes relevant when we know that about 98% of the angular momentum of the solar system is associated with the planets, although they represent only 0.15 percent of the mass of the whole system. In this dissertation we study the behavior of stellar angular momentum, orbital angular momentum and total angular momentum in a sample of 282 stars harboring planets, including 40 multiple systems. We observed that planetary systems containing more than one known planet have both higher orbital angular momentum and total angular momentum compared to those who have only one planet. This analysis shows that multiplanet systems tend to have higher momenta, suggesting that the planets in such systems that contribute to the greater portion momenta have been found. Thus, planetary systems with lower values for the momenta represent the best candidates to the discovery of new planets

Aglomerado estelar M67: processos de diluição e a evolução do Momentum Angular

Galactic stellar clusters have a great variety of physical properties that make valuable probes of stellar and galactic chemical evolution. Current studies show a discrepancy between the standard evolutionary models and observations, mainly considering the level of mixing and convective dilution of light elements, as well as to the evolution of the angular momentum. In order to better settle some of these properties, we present a detailed spectroscopic analysis of 28 evolved stars, from the turn-off to the RGB, belonging to the stellar open cluster M67. The observations were performed using UVES+FLAMES at VLT/UT2. We determined stellar parameters and metallicity from LTE analysis of Fe I and Fe II lines between 420 1100 nm. The Li abundance was obtained using the line at 6707.78 ˚A, for the whole sample of stars. The Li abundances of evolved stars of M67 present a gradual decreasing when decreasing the effective temperature. The Li dilution factor for giant stars of M67 with Teff ∼ 4350K is at least 2300 times greater than that predicted by standard theory for single field giant stars. The Li abundance as a function of rotation exhibits a good correlation for evolved stars of M67, with a much smaller dispersion than the field evolved stars. The mass and the age seem to be some of the parameters that influence this connection. We discovered a Li-rich subgiant star in M67 (S1242). It is member of a spectroscopic binary system with a high eccentricity. Its Li abundance is 2.7, the highest Li content ever measured for an evolved star in M67. Two possibilities could explain this anomalous Li content: (i) preservation of the Li at the post turn off stage due to tidal effects, or (ii) an efficient dredge-up of Li, hidden below the convective zone by atomic diffusion occurring in the post turn off stage. We also study the evolution of the angular momentum for the evolved stars in M67. The results are in agreement with previous studies dedicated to evolved stars of this cluster, where stars in the same region of the CM-diagram have quite similar rotations, but with values that indicate an extra breaking along the main sequence. Finally, we analize the distributions of the average rotational velocity and of the average Li abundance as a function of age. With relation to the average Li abundances, stars in clusters and field stars present the same type of exponencial decay law t−β. Such decay is observed for ages lesser than 2 Gyr. From this age, is observed that the average Li abundance remain constant, differently of the one observed in the rotation age connection, where the average rotational velocity decreases slowly with age

Wave-vector dependence of spin and density multipole excitations in quantum dots

We have employed time-dependent local-spin density-functional theory to analyze the multipole spin and charge density excitations in GaAs-AlxGa1-xAs quantum dots. The on-plane transferred momentum degree of freedom has been taken into account, and the wave-vector dependence of the excitations is discussed. In agreement with previous experiments, we have found that the energies of these modes do not depend on the transferred wave vector, although their intensities do. Comparison with a recent resonant Raman scattering experiment [C. Schüller et al., Phys. Rev. Lett. 80, 2673 (1998)] is made. This allows us to identify the angular momentum of several of the observed modes as well as to reproduce their energies

Modeling the transport phenomena within arterial wall: porous media approach

The transport of macromolecules, such as low-density lipoprotein (LDL), and their accumulation in the layers of the arterial wall play a critical role in the creation and development of atherosclerosis. Atherosclerosis is a disease of large arteries e.g., the aorta, coronary, carotid, and other proximal arteries that involves a distinctive accumulation of LDL and other lipid-bearing materials in the arterial wall. Over time, plaque hardens and narrows the arteries. The flow of oxygen-rich blood to organs and other parts of the body is reduced. This can lead to serious problems, including heart attack, stroke, or even death. It has been proven that the accumulation of macromolecules in the arterial wall depends not only on the ease with which materials enter the wall, but also on the hindrance to the passage of materials out of the wall posed by underlying layers. Therefore, attention was drawn to the fact that the wall structure of large arteries is different than other vessels which are disease-resistant. Atherosclerosis tends to be localized in regions of curvature and branching in arteries where fluid shear stress (shear rate) and other fluid mechanical characteristics deviate from their normal spatial and temporal distribution patterns in straight vessels. On the other hand, the smooth muscle cells (SMCs) residing in the media layer of the arterial wall respond to mechanical stimuli, such as shear stress. Shear stress may affect SMC proliferation and migration from the media layer to intima. This occurs in atherosclerosis and intimal hyperplasia. The study of blood flow and other body fluids and of heat transport through the arterial wall is one of the advanced applications of porous media in recent years. The arterial wall may be modeled in both macroscopic (as a continuous porous medium) and microscopic scales (as a heterogeneous porous medium). In the present study, the governing equations of mass, heat and momentum transport have been solved for different species and interstitial fluid within the arterial wall by means of computational fluid dynamics (CFD). Simulation models are based on the finite element (FE) and finite volume (FV) methods. The wall structure has been modeled by assuming the wall layers as porous media with different properties. In order to study the heat transport through human tissues, the simulations have been carried out for a non-homogeneous model of porous media. The tissue is composed of blood vessels, cells, and an interstitium. The interstitium consists of interstitial fluid and extracellular fibers. Numerical simulations are performed in a two-dimensional (2D) model to realize the effect of the shape and configuration of the discrete phase on the convective and conductive features of heat transfer, e.g. the interstitium of biological tissues. On the other hand, the governing equations of momentum and mass transport have been solved in the heterogeneous porous media model of the media layer, which has a major role in the transport and accumulation of solutes across the arterial wall. The transport of Adenosine 5´-triphosphate (ATP) is simulated across the media layer as a benchmark to observe how SMCs affect on the species mass transport. In addition, the transport of interstitial fluid has been simulated while the deformation of the media layer (due to high blood pressure) and its constituents such as SMCs are also involved in the model. In this context, the effect of pressure variation on shear stress is investigated over SMCs induced by the interstitial flow both in 2D and three-dimensional (3D) geometries for the media layer. The influence of hypertension (high pressure) on the transport of lowdensity lipoprotein (LDL) through deformable arterial wall layers is also studied. This is due to the pressure-driven convective flow across the arterial wall. The intima and media layers are assumed as homogeneous porous media. The results of the present study reveal that ATP concentration over the surface of SMCs and within the bulk of the media layer is significantly dependent on the distribution of cells. Moreover, the shear stress magnitude and distribution over the SMC surface are affected by transmural pressure and the deformation of the media layer of the aorta wall. This work reflects the fact that the second or even subsequent layers of SMCs may bear shear stresses of the same order of magnitude as the first layer does if cells are arranged in an arbitrary manner. This study has brought new insights into the simulation of the arterial wall, as the previous simplifications have been ignored. The configurations of SMCs used here with elliptic cross sections of SMCs closely resemble the physiological conditions of cells. Moreover, the deformation of SMCs with high transmural pressure which follows the media layer compaction has been studied for the first time. On the other hand, results demonstrate that LDL concentration through the intima and media layers changes significantly as wall layers compress with transmural pressure. It was also noticed that the fraction of leaky junctions across the endothelial cells and the area fraction of fenestral pores over the internal elastic lamina affect the LDL distribution dramatically through the thoracic aorta wall. The simulation techniques introduced in this work can also trigger new ideas for simulating porous media involved in any biomedical, biomechanical, chemical, and environmental engineering applications.

Operador dipolo-dipolo na base de momento angular: um complemento ao estudo de ressonância magnética nuclear

The relationship between the magnetic dipole-dipole potential energy function and its quantum analogue is presented in this work. It is assumed the reader is familiar with the classical expression of the dipolar interaction and has basic knowledge of the quantum mechanics of angular momentum. Except for these two points only elementary steps are involved.

Wave-vector dependence of spin and density multipole excitations in quantum dots

We have employed time-dependent local-spin density-functional theory to analyze the multipole spin and charge density excitations in GaAs-AlxGa1-xAs quantum dots. The on-plane transferred momentum degree of freedom has been taken into account, and the wave-vector dependence of the excitations is discussed. In agreement with previous experiments, we have found that the energies of these modes do not depend on the transferred wave vector, although their intensities do. Comparison with a recent resonant Raman scattering experiment [C. Schüller et al., Phys. Rev. Lett. 80, 2673 (1998)] is made. This allows us to identify the angular momentum of several of the observed modes as well as to reproduce their energies