Equal Energy Density Research Articles

Oscillations in the solar atmosphere: the 5-min peak as a consequence of wave reflection at the photosphere

The vertical propagation of compression waves from beneath the solar atmosphere is considered. It is shown that at the step-up in critical frequency which occurs at the photosphere, the phase difference between reflected and incident waves is strongly dependent on frequency, and is zero at about 3 mHz. This can explain why velocity power spectra deduced from photospheric spectral lines, have maxima at that frequency, period 5 min, if all modes are excited to equal velocity amplitudes, that is, to equal energy density, in the region just beneath the photosphere. Higher in the atmosphere, there is a step-down in critical frequency into the corona, the whole constituting a quasi-rectangular barrier in critical frequency. Standing-wave components can be set up, by partial reflection, at frequencies higher than the top of the barrier which is at about 4.5 mHz. The first of these has a period of about 200 s, and may be responsible for the peak observed at that period in power spectra from chromospheric spectral lines. For waves of frequency higher than 4.5 mHz, the relatively cool layer between the photosphere and corona acts as an acoustic interference filter which is most transparent at those frequencies at which standing waves are set up within it.

Enzyme Activities Associated with Carcinogen Metabolism in Liver and Nonhepatic Tissues of Rats Maintained on High Fat and Food-Restricted Diets

The influence of high fat or food-restricted diets on key enzymes associated with polycyclic aromatic hydrocarbon metabolism was assessed in liver, lung, kidney and stomach of rats. Animals had access ad libitum to the AIN-76A purified diet (control) or were given 65% of the intake of controls for 3 wk. The high fat diet was isoenergetic to the control diet by substituting corn oil for equal energy from carbohydrate and addition of cellulose to obtain equal energy density. Activities of arylhydrocarbon hydroxylase and 7-ethoxycoumarin O-deethylase were significantly increased in lungs of food-restricted rats and decreased by the high fat diet but were not altered in liver. Both diets increased arylhydrocarbon hydroxylase approximately twofold in kidney. Glucose 6-phosphate and 6-phosphogluconate dehydrogenase were lowered in lung, kidney and liver by the high fat diet. Hepatic glutathione S-transferase was increased by high fat feeding. Food restriction decreased activities of arylsulfatase and beta-glucuronidase about 40% in lung. Hepatic arylsulfatase was also decreased about 40% by this treatment. Changes in hydrolase activities in livers and lungs of animals maintained on restricted diets raises in the interesting possibility that net production of glucuronide and sulfate conjugates of carcinogens by the liver and their hydrolysis in lung is altered by food restriction.

The spatial and temporal characteristics of the conducting PRIZ spatial light modulator

The characteristics of the conducting PRIZ using single-pulse writing are found to differ from those using mulitple-pulse writing. For single-pulse writing the information storage times are long and independent of write-beam energy density up to the damage threshold. However, the spatial resolution of the devices is a function of the write-pulse energy density and saturates at about 100 μJ/cm 2. In the case of multiple-pulse writing of a static image, the optical output is a function of the write-pulse energy repetition rate, the spatial frequency of the image, and the write-beam energy density per pulse. When the single-pulse energy density equals or exceeds that required for maximum spatial resolution, a second pulse of equal energy density reduces the optical output by about seventy-five percent. This reduction is similar to dynamic image selection.

Multiple-source, multiple-frequency error of an electric field meter

Electric field meters (EFM's) are typically calibrated using single-frequency, single-source standard fields. The response to multiple sources or nonsinusoidal time dependence may be different, however. Possible errors in a multiple-source, multiple-frequency environment are analyzed for an EFM consisting of an electrically short dipole antenna with a diode load and a radio-frequency (RF) filter transmission line. Also considered are errors in the assumption of equal electric and magnetic energy densities in a multiple plane-wave environment. Typical errors of field-intensity measurements are about one to 3 dB, but in some circumstances they can exceed 10 dB.

Jump relations for shocks in an anisotropic magnetized plasma

The jump relations for shocks moving into a collision-free anisotropic magnetized plasma are investigated under the assumption of isotropy of the plasma behind the shock front. The plasma ahead of the shock is assumed to be stable against the fire-hose instability and the mirror instability. In order to facilitate comparison with the work of Bazer and Ericson on isotropic shocks our nomenclature has been adapted to theirs. It turns out that as in the case of isotropic shocks the density ratio can be at most four corresponding to γ=5/3, that the change in magnetic field is bounded and that except for the case of Alfven shocks the transverse parts of the magnetic field are collinear. It is further shown that the influence of the anisotropy is greatest for nearly equal thermal and magnetic energy densities. In the case of negative anisotropy no compressive shocks are possible with a major decrease in magnetic field if the thermal energy density much exceeds the magnetic energy density. A new kind of shock is shown to result from the analysis, the major effect of which is to destroy the anisotropy with only small changes in density, magnetic field and velocity vector. Its propagation speed is unbounded. Furthermore it has turned out that compressive, magnetic field increasing shocks have lower bounds in the density jump and magnetic field change for negative and positive anisotropy, respectively. In the collision-free case no unique entropy condition depending only on the total pressure components and densities can be given before the solution of the problem of shock structure. Therefore even expansive shocks may be admissible. The applicability of the isotropy assumption and ad-hoc-assumptions of other authors are briefly discussed.

THEORETICAL PREDICTION OF SEISMIC NOISE IN A DEEP BOREHOLE

Seismic noise attenuation as a function of depth below the earth’s surface is described in terms of surface wave modes. The energy density of the noise, which often represents a combination of modes, is computed as the arithmetic sum of the energy densities of all contributing modes. Three models are used to determine the fractional contribution of each mode. Model A stipulates that each mode contributes equally to the energy of the noise; Model B specifies that the energy fraction contributed by each mode is dependent upon the energy in those beds in which the shear velocity of the bed exceeds the phase velocity of the mode; and Model C prescribes that all modes have equal energy density at the free surface. A comparison of observations with attenuations based on the three models reveals that Model B is the best.

Interference Patterns at Boundaries in Reverberant Sound Fields

Starting with the definition of a diffuse sound field as having equal energy density at all points, the waves converging on any point being random in phase and direction, an analysis is given showing that a reflecting boundary large compared with the wavelength destroys the diffuseness of such a field by setting up an interference pattern. For a perfectly reflecting plane surface, the interference pattern can be expressed analytically as a mean square sound pressure varying as [1 + (sin2kx/2kx)] where x is the distance from the surface and k is the wave number. Similarly, the mean square particle velocity varies as 1 − sin2kx2kx + 1k2x2(sin2kx2kx − cos2kx), and the combination of these two expressions gives a mean energy density variation with distance proportional to 1 + (1/2k2x2)[(sin2kx/2kx) − cos2kx]. Thus the energy level at the surface is about 2.2 db higher than at points further away where the interference pattern is negligible. The effects of such interference patterns on transmission loss and reverberation room measurements are discussed. The patterns are not much affected by the frequency band widths habitually used in room acoustics. Experimental confirmation of the theory is given.