ANALYTICAL MODELS OF EXOPLANETARY ATMOSPHERES. I. ATMOSPHERIC DYNAMICS VIA THE SHALLOW WATER SYSTEM

Within the context of exoplanetary atmospheres, we present a comprehensive linear analysis of forced, damped, magnetized shallow water systems, exploring the effects of dimensionality, geometry (Cartesian, pseudo-spherical, and spherical), rotation, magnetic tension, and hydrodynamic and magnetic sources of friction. Across a broad range of conditions, we find that the key governing equation for atmospheres and quantum harmonic oscillators are identical, even when forcing (stellar irradiation), sources of friction (molecular viscosity, Rayleigh drag, and magnetic drag), and magnetic tension are included. The global atmospheric structure is largely controlled by a single key parameter that involves the Rossby and Prandtl numbers. This near-universality breaks down when either molecular viscosity or magnetic drag acts non-uniformly across latitude or a poloidal magnetic field is present, suggesting that these effects will introduce qualitative changes to the familiar chevron-shaped feature witnessed in simulations of atmospheric circulation. We also find that hydrodynamic and magnetic sources of friction have dissimilar phase signatures and affect the flow in fundamentally different ways, implying that using Rayleigh drag to mimic magnetic drag is inaccurate. We exhaustively lay down the theoretical formalism (dispersion relations, governing equations, and time-dependent wave solutions) for a broad suite of models. In all situations, we derive the steady state of an atmosphere, which is relevant to interpreting infrared phase and eclipse maps of exoplanetary atmospheres. We elucidate a pinching effect that confines the atmospheric structure to be near the equator. Our suite of analytical models may be used to develop decisively physical intuition and as a reference point for three-dimensional magnetohydrodynamic simulations of atmospheric circulation.

Harmonic Oscillator in a 1D or 2D Cavity with General Perfectly Reflecting Walls

We investigate the simple harmonic oscillator in a 1-d box, and the 2-d isotropic harmonic oscillator problem in a circular cavity with perfectly reflecting boundary conditions. The energy spectrum has been calculated as a function of the self-adjoint extension parameter. For sufficiently negative values of the self-adjoint extension parameter, there are bound states localized at the wall of the box or the cavity that resonate with the standard bound states of the simple harmonic oscillator or the isotropic oscillator. A free particle in a circular cavity has been studied for the sake of comparison. This work represents an application of the recent generalization of the Heisenberg uncertainty relation related to the theory of self-adjoint extensions in a finite volume.

Sideband-Ratio and Harmonic Response of Sub-Millimeter Wave Mixers measured with a Martin Puplett Interferometer

Heterodyne receivers at millimeter and submillimeter wavelength are widely used for radiometric spectral line observations for atmospheric remote sensing or radio astronomy. The quantitative analysis of such observations requires an accurate knowledge of the mixers's sideband ratio. In addition, its potential sensitivity to spurious harmonics needs to be well understood. In this paper, we discuss a measurement technique for these receiver characteristics, which is based on a scanning Martin Puplett Interferometer used in conjunction with a wide band digital autocorrelation spectrometer for the analysis of the intermediate frequency band. We present measurement results of different double sideband and sideband separating mixers, which were developed for the proposed 340GHz multi-beam limb sounder STEAMR.

Root system of singular perturbations of the harmonic oscillator type operators

We analyze perturbations of the harmonic oscillator type operators in a Hilbert space H, i.e. of the self-adjoint operator with simple positive eigenvalues μ k satisfying μ k+1 − μ k ≥ Δ > 0. Perturbations are considered in the sense of quadratic forms. Under a local subordination assumption, the eigenvalues of the perturbed operator become eventually simple and the root system contains a Riesz basis.

Absolute polarity determination of teeth cementum by phase sensitive second harmonic generation microscopy

The absolute sign of local polarity in relation to the biological growth direction has been investigated for teeth cementum using phase sensitive second harmonic generation microscopy (PS-SHGM) and a crystal of 2-cyclooctylamino-5-nitropyridine (COANP) as a nonlinear optic (NLO) reference material. A second harmonic generation (SHG) response was found in two directions of cementum: radial (acellular extrinsic fibers that are oriented more or less perpendicular to the root surface) and circumferential (cellular intrinsic fibers that are oriented more or less parallel to the surface). A mono-polar state was demonstrated for acellular extrinsic cementum. However, along the different parts of cementum in circumferential direction, two corresponding domains were observed featuring an opposite sign of polarity indicative for a bi-polar microscopic state of cellular intrinsic cementum. The phase information showed that the orientation of radial collagen fibrils of cementum is regularly organized with the donor (D) groups pointing to the surface. Circumferential collagen molecules feature orientational disorder and are oriented up and down in random manner showing acceptor or donor groups at the surface of cementum. Considering that the cementum continues to grow in thickness throughout life, we can conclude that the cementum is growing circumferentially in two opposite directions and radially in one direction. A Markov chain type model for polarity formation in the direction of growth predicts D-groups preferably appearing at the fiber front.