Hydrodynamics with spin angular momentum from systematic coarse graining: a tutorial example

The derivation of time evolution equations for slow collective variables starting from a micro- scopic model system is demonstrated for the tutorial example of the classical, two-dimensional XY model. Projection operator techniques are used within a nonequilibrium thermodynamics framework together with molecular simulations in order to establish the building blocks of the hydrodynamics equations: Poisson brackets that determine the deterministic drift, the driving forces from the macroscopic free energy and the friction matrix. The approach is rather general and can be applied for deriving the equations of slow variables for a broad variety of systems.

Angular momentum and energy-momentum densities as gauge currents

If we replace the general spacetime group of diffeomorphisms by transformations taking place in the tangent space, general relativity can be interpreted as a gauge theory, and in particular as a gauge theory for the Lorentz group. In this context, it is shown that the angular momentum and the energy-momentum tensors of a general matter field can be obtained from the invariance of the corresponding action integral under transformations taking place, not in spacetime, but in the tangent space, in which case they can be considered as gauge currents.

Energy and angular momentum of the gravitational field in the teleparallel geometry

The Hamiltonian formulation of the teleparallel equivalent of general relativity is considered. Definitions of energy, momentum and angular momentum of the gravitational field arise from the integral form of the constraint equations of the theory. In particular, the gravitational energy-momentum is given by the integral of scalar densities over a three-dimensional spacelike hypersurface. The definition for the gravitational energy is investigated in the context of the Kerr black hole. In the evaluation of the energy contained within the external event horizon of the Kerr black hole, we obtain a value strikingly close to the irreducible mass of the latter. The gravitational angular momentum is evaluated for the gravitational field of a thin, slowly rotating mass shell. © 2002 The American Physical Society.

Accretion of Mass and Angular Momentum onto The Discs of Spiral Galaxies

In this Thesis, we study the accretion of mass and angular momentum onto the disc of spiral galaxies from a global and a local perspective and comparing theory predictions with several observational data. First, we propose a method to measure the specific mass and radial growth rates of stellar discs, based on their star formation rate density profiles and we apply it to a sample of nearby spiral galaxies. We find a positive radial growth rate for almost all galaxies in our sample. Our galaxies grow in size, on average, at one third of the rate at which they grow in mass. Our results are in agreement with theoretical expectations if known scaling relations of disc galaxies are not evolving with time. We also propose a novel method to reconstruct accretion profiles and the local angular momentum of the accreting material from the observed structural and chemical properties of spiral galaxies. Applied to the Milky Way and to one external galaxy, our analysis indicates that accretion occurs at relatively large radii and has a local deficit of angular momentum with respect to the disc. Finally, we show how structure and kinematics of hot gaseous coronae, which are believed to be the source of mass and angular momentum of massive spiral galaxies, can be reconstructed from their angular momentum and entropy distributions. We find that isothermal models with cosmologically motivated angular momentum distributions are compatible with several independent observational constraints. We also consider more complex baroclinic equilibria: we describe a new parametrization for these states, a new self-similar family of solution and a method for reconstructing structure and kinematics from the joint angular momentum/entropy distribution.

Legendre Polynomials and Angular Momentum

An introduction to Legendre polynomials as precursor to studying angular momentum in quantum chemistry,

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.

Momentum transfer effects in the transport of adsorbate at a nano-patterned surface

Adsorbate molecules scattered in the repulsive field of a surface feature in the form of a semi-cylindrical stripe may be considered as a simple model for a nano-patterned surface. The extent of scattering was conveniently expressed as the tangential momentum accommodation coefficient. An analytical result was obtained using a simple local specular reflection hypothesis in contrast to the more complicated situation of an array of atoms discussed elsewhere, in which screening and secondary reflection may occur (Nicholson and Bhatia 2005). It was also demonstrated that a simple 2D representation leads to the same result for the tangential momentum accommodation coefficient.

Hydrogen(electron-deuteron) studies of the deuteron at high squared momentum transfer

A high resolution study of the quasielastic 2 H(e, e'p)n reaction was performed in Hall A at the Thomas Jefferson Accelerator Facility in Newport News, Virginia. The measurements were performed at a central momentum transfer of : q: ∼ 2400 MeV/c, and at a central energy transfer of ω ∼ 1500 MeV, a four momentum transfer Q2 = 3.5 (GeV/c)2, covering missing momenta from 0 to 0.5 GeV/c. The majority of the measurements were performed at Φ = 180° and a small set of measurements were done at Φ = 0°. The Hall A High Resolution Spectrometers (HRS) were used to detect coincident electrons and protons, respectively. Absolute 2H(e, e'p) n cross sections were obtained as a function of the recoiling neutron scattering angle with respect to [special characters omitted]. The experimental results were compared to a Plane Wave Impulse Approximation (PWIA) model and to a calculation that includes Final State Interaction (FSI) effects. Experimental 2H(e, e'p)n cross sections were determined with an estimated systematic uncertainty of 7%. The general features of the measured cross sections are reproduced by Glauber based calculations that take the motion of the bound nucleons into account (GEA). Final State Interactions (FSI) contributions were found to depend strongly on the angle of the recoiling neutron with respect to the momentum transfer and on the missing momentum. We found a systematic deviation of the theoretical prediction of about 30%. At small &thetas; nq (&thetas;nq < 60°) the theory overpredicts the cross section while at large &thetas; nq (&thetas;nq > 80°) the theory underestimates the cross sections. We observed an enhancement of the cross section, due to FSI, of about 240%, as compared to PWIA, for a missing momentum of 0.4 GeV/c at an angle of 75°. For missing momentum of 0.5 GeV/c the enhancement of the cross section due to the same FSI effects, was about 270%. This is in agreement with GEA. Standard Glauber calculations predict this large contribution to occur at an angle of 90°. Our results show that GEA better describes the 2H(e, e'p)n reaction.

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.

Issues in stratosphere-troposphere coupling

An overview is given of current issues concerning the coupling between the stratosphere and troposphere. The tropopause region, more generally the upper troposphere/lower stratosphere, is the region of direct contact where exchange of material takes place. Dynamical coupling through angular momentum transfer by waves occurs nonlocally, and provides a generally negative torque on the stratosphere which drives an equator-to-pole circulation (i.e., towards the Earth’s axis of rotation). This wave-driven circulation is the principal mechanism for intraseasonal and interannual variability in the extratropical stratosphere. Although such variability is generally dynamical in origin, there are important chemical and radiative feedbacks. The location of the tropopause has implications for radiative forcing of climate, through its effect on the distribution of relatively short-lived greenhouse gases (ozone and water vapour). Some outstanding puzzles in our current understanding are identified. Attention is focused on possible climate sensitivities, and how these may be tested and constrained. Results from the Canadian Middle Atmosphere Model (CMAM), a fully interactive radiative-chemical-dynamical general circulation model, are used to illustrate some of the points.