Function Of Wavenumber Research Articles

SPECTRA OF LARGE-SCALE ATMOSPHERIC FLOW AT 300 MILLIBARS

Abstract Data at 300 mb for January-February and July-August, 1949, are used to compute spectra of atmospheric turbulence as a function of wave number along various latitude circles. Power spectra are computed for the zonal and meridional wind, and cospectra for the meridional transfer of angular momentum, dry enthalpy, and kinetic energy. Total spectra are computed daily, and for each season the mean total spectrum is divided into two parts: the spectrum of the seasonal mean flow, and the mean seasonal spectrum of the perturbations. The general characteristics of the power and cospectra are discussed. It is shown, for example, that the spectrum of the mean seasonal flow dominates at low wave numbers, while the mean spectrum of the perturbations is more important at higher wave numbers. The day-to-day variation of the total spectra is also considered. It is found that for power spectra the specific deviation is quasi-constant at all wave numbers, latitudes, and seasons. A method is presented for refining ...

Coulomb Interactions in the Uniform-Background Lattice Model

The uniform-background lattice model consists of a body-centered-cubic lattice of point charges of like sign embedded in a uniform background charge of the opposite sign. The method used by Fuchs to apply the Ewald sum formula to the case of static shear deformations is extended to apply to spatially periodic deformations. The dispersion relations (frequency as a function of wave number) are presented for propagation vectors in the [100], [110], [111], and [210] directions. Comparison is made with the dispersion relations for the same directions in a Born-von K\'arm\'an model of a body-centered cubic lattice in which only central interactions between nearest and next-nearest neighbors are considered. The values of the "Coulomb part" of the macroscopic elastic constants as calculated by Fuchs are used for this model. The problem of treating a model in which the background responds to the displacement of point charges is discussed.

The Energy Band Structure of a Linear Metal

A tight binding calculation of the one-electron energy as a function of wave number is described for a linear chain of hydrogen atoms in the ground state. The calculation is accurate to the order of exp (-2a), where a is the interatomic distance (in atomic units), all non-orthogonality and energy integrals of this order of magnitude being included in the energy expression. A closed expression for the band width is derived and compared with expressions corresponding in their approximations to those usually made in tight binding calculations for actual metals.

On the visibility of radiation at the human fovea.

1. Seeing-frequency functions (psi[S]) determined uniocularly for small (1.6'), brief images at the thoroughly dark-adapted human central fovea take the form of log-Gaussian integrals, for intensity or for exposure-time as the independent variable. They cannot be of Poisson type, since mean (tau') and standard deviation (sigma) are quite independently modifiable. 2. The properties of tau', the abscissa of inflection in the log-Gaussian integrals, and of sigma, are discussed in relation to customary determinations of spectral visibilities; agreements and certain necessary divergences are considered. 3. The values of sigma(logDeltaIlogDeltaI0), are distributed periodically, with 5 maxima in the range lambda383 to lambda712. Outside the fovea this is not the case. These maxima, and the intervening minima, are definitely correlated with "irregularities" in the values of tau' as function of lambda, with data on color threshold intensities, with data on "saturation," and quite specifically with minima and maxima in the data of lambda discrimination. They are unmistakably of analytical significance. 4. The interpretation of these properties is taken to require (consistent with the indications of other evidence) that under specified conditions the magnitude of sigma is a measure of the "size" of the population of excitable elements of neural effect, in the range of 0 to 100 per cent response-frequency as a function of wave number. This means that under the procedure used there is detectable the spectral distribution of local, specific, photosensitization. The sigma's refer to a property of the excitation process which is not affected by the action of irrelevant absorbers. 5. A preliminary test of this has been made by the use of mixed "monochromatic" lights. The total energy is empirically the significant quantity, although the separate effects of lambda's are sharply exhibited. 6. The lambda distribution of photosensitization indices, sigma(logDeltaIlogDeltaI0), is necessarily taken to have the nature of "action spectra." Careful search discloses, surprisingly enough, precise and apparently unique correspondence with the maxima and minima (and details of shape) required for the participation of: cytochrome-c reductase; the reduced forms of cytochromes-a and -c; and the often overlooked ferric-prophyrin bands of oxidized cytochrome-c. 7. For the central fovea, in which blood vessels are absent, and in which resistance to anoxia is at a maximum, the presence of an enzyme system of the sort here indicated is entirely reasonable. It is pointed out that a number of specific experiments can be based upon the general finding, whatever the causal mechanism for the sensitized lambda regions may in the end prove to be. The data cannot be reconciled to the demands of existing color primary theories, although apparently quite accurately consistent with varied observational data.