The cumulus-capped boundary layer. II: Interface fluxes

This paper considers the relationship between the mean temperature and humidity profiles and the fluxes of heat and moisture at cloud base and the base of the inversion in the cumulus-capped boundary layer. The relationships derived are based on an approximate form of the scalar-flux budget and the scaling properties of the turbulent kinetic energy (TKE) budget. The scalar-flux budget gives a relationship between the change in the virtual potential temperature across either the cloud base transition zone or the inversion and the flux at the base of the layer. The scaling properties of the TKE budget lead to a relationship between the heat and moisture fluxes and the mean subsaturation through the liquid-water flux. The 'jump relation' for the virtual potential temperature at cloud base shows the close connection between the cumulus mass flux in the cumulus-capped boundary layer and the entrainment velocity in the dry-convective boundary layer. Gravity waves are shown to be an important feature of the inversion.

The Klein-Gordon equation in a domain with time-dependent boundary

We solve a Dirichlet boundary value problem for the Klein–Gordon equation posed in a time-dependent domain. Our approach is based on a general transform method for solving boundary value problems for linear and integrable nonlinear PDE in two variables. Our results consist of the inversion formula for a generalized Fourier transform, and of the application of this generalized transform to the solution of the boundary value problem.

The method of least squares used to invert an orbit problem

Six parameters uniquely describe the orbit of a body about the Sun. Given these parameters, it is possible to make predictions of the body's position by solving its equation of motion. The parameters cannot be directly measured, so they must be inferred indirectly by an inversion method which uses measurements of other quantities in combination with the equation of motion. Inverse techniques are valuable tools in many applications where only noisy, incomplete, and indirect observations are available for estimating parameter values. The methodology of the approach is introduced and the Kepler problem is used as a real-world example. (C) 2003 American Association of Physics Teachers.

Notations and conventions in molecular spectroscopy: part 1. General spectroscopic notation

The field of Molecular Spectroscopy was surveyed in order to determine a set of conventions and symbols which are in common use in the spectroscopic literature. This document, which is Part I in a series, establishes the notations and conventions used for general spectroscopic notations and deals with quantum mechanics, quantum numbers (vibrational states, angular momentum and energy levels), spectroscopic transitions, and miscellaneous notations (e.g. spectroscopic terms). Further parts will follow, dealing inter alia with symmetry notation, permutation and permutation-inversion symmetry notation, vibration-rotation spectroscopy and electronic spectroscopy.

Notations and conventions in molecular spectroscopy: part 2. Symmetry notation

The field of Molecular Spectroscopy was surveyed in order to determine a set of conventions and symbols which are in common use in the spectroscopic literature. This document, which is Part 2 in a series, establishes the notations and conventions used for the description of symmetry in rigid molecules, using the Schoenflies notation. It deals firstly with the symmetry operators of the molecular point groups (also drawing attention to the difference between symmetry operators and elements). The conventions and notations of the molecular point groups are then established, followed by those of the representations of these groups as used in molecular spectroscopy. Further parts will follow, dealing inter alia with permutation and permutation-inversion symmetry notation, vibration-rotation spectroscopy and electronic spectroscopy.

Microwave spectrum of 2-aminopyridine

The microwave spectra of 2-aminopyridine-NH2, -ND2, and of both of the two possible -NHD molecules have been observed and assigned in the 0+ vibrational state of the amino group inversion vibration; the assignment for three of the molecules in the 0− state is also made. From intensity measurements the 0+-0− splitting is estimated to be 135 ± 25 cm−1 for the -NH2 molecule and 95 ± 30 cm−1 for the -ND2 molecule. The rotational constants are interpreted in terms of a structure in which the amino group is bent about 32° out of the molecular plane, the c coordinates of the two amino H atoms being 0.21 and 0.28 Å. Stark effect measurements give a dipole moment of about 0.9 D which is almost entirely in the b axis, and which changes quite significantly between the 0+ and 0− states.

Quantitative analysis of remote gas temperatures and concentrations from their infrared emission spectra

Techniques for obtaining quantitative values of the temperatures and concentrations of remote hot gaseous effluents from their measured passive emission spectra have been examined in laboratory experiments and on field trials. These emission spectra were obtained using an adapted FTIR spectrometer with 0.25 cm-1 spectral resolution. The CO2 and H2O vapour content in the plume from a 55 m smoke stack and the temperature of these gases were obtained by comparing the measured emission spectra with those modelled using the HITRAN atmospheric transmission database. The spatial distributions of CO2, CO and unburnt CH4 in a laboratory methane flame were reconstructed tomographically using a matrix inversion technique.