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.

Solution of the relativistic Schrödinger equation for the δ ′ -Function potential in one dimension using cutoff regularization

We study the relativistic version of the Schrödinger equation for a point particle in one dimension with the potential of the first derivative of the delta function. The momentum cutoff regularization is used to study the bound state and scattering states. The initial calculations show that the reciprocal of the bare coupling constant is ultraviolet divergent, and the resultant expression cannot be renormalized in the usual sense, where the divergent terms can just be omitted. Therefore, a general procedure has been developed to derive different physical properties of the system. The procedure is used first in the nonrelativistic case for the purpose of clarification and comparisons. For the relativistic case, the results show that this system behaves exactly like the delta function potential, which means that this system also shares features with quantum filed theories, like being asymptotically free. In addition, in the massless limit, it undergoes dimensional transmutation, and it possesses an infrared conformal fixed point. The comparison of the solution with the relativistic delta function potential solution shows evidence of universality.

Modern solar maximum forced late twentieth century Greenland cooling

The abrupt Northern Hemispheric warming at the end of the twentieth century has been attributed to an enhanced greenhouse effect. Yet Greenland and surrounding subpolar North Atlantic remained anomalously cold in 1970s to early 1990s. Here we reconstructed robust Greenland temperature records (North Greenland Ice Core Project and Greenland Ice Sheet Project 2) over the past 2100 years using argon and nitrogen isotopes in air trapped within ice cores and show that this cold anomaly was part of a recursive pattern of antiphase Greenland temperature responses to solar variability with a possible multidecadal lag. We hypothesize that high solar activity during the modern solar maximum (approximately 1950s–1980s) resulted in a cooling over Greenland and surrounding subpolar North Atlantic through the slowdown of Atlantic Meridional Overturning Circulation with atmospheric feedback processes.

Challenges in Collating Spirometry Reference Data for South-Asian Children: An Observational Study.

METHODS Spirometry datasets from South-Asian children were collated from four centres in India and five within the UK. Records with transcription errors, missing values for height or spirometry, and implausible values were excluded(n = 110). RESULTS Following exclusions, cross-sectional data were available from 8,124 children (56.3% male; 5-17 years). When compared with GLI-predicted values from White Europeans, forced expired volume in 1s (FEV1) and forced vital capacity (FVC) in South-Asian children were on average 15% lower, ranging from 4-19% between centres. By contrast, proportional reductions in FEV1 and FVC within all but two datasets meant that the FEV1/FVC ratio remained independent of ethnicity. The 'GLI-Other' equation fitted data from North India reasonably well while 'GLI-Black' equations provided a better approximation for South-Asian data than the 'GLI-White' equation. However, marked discrepancies in the mean lung function z-scores between centres especially when examined according to socio-economic conditions precluded derivation of a single South-Asian GLI-adjustment. CONCLUSION Until improved and more robust prediction equations can be derived, we recommend the use of 'GLI-Black' equations for interpreting most South-Asian data, although 'GLI-Other' may be more appropriate for North Indian data. Prospective data collection using standardised protocols to explore potential sources of variation due to socio-economic circumstances, secular changes in growth/predictors of lung function and ethnicities within the South-Asian classification are urgently required.

The Gronwall form of the Schrodinger Equation for Helium

The 1937 paper of Gronwall which concerns an alternative form for the Schrodinger Equation of the 2-electron Helium problem is re-derived in a (hopefully) transparent (possibly pedestrian) manner.

Frobenius Solution for Legendre's Equation, Rodrigue's Formula and Normalization

The Frobenius solution to Legendre/s equation is developed in detail as is Rodrigue's formula, which is employed to normalize Legendre polynomials.

Continued Fraction Solutions to Hermite's, Legendre's and Laguerre's Differential Equation

The continued fraction method for solving differential equations is illustrated using three famous differential equations used in quantum chemistry.