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At least 37 records · Page 2

Information theory and the earth's density distribution

The present paper argues for using the information theory approach as an inference technique in solid earth geophysics. A spherically symmetric density distribution is derived as an example of the method. A simple model of the earth plus knowledge of its mass and moment of inertia leads to a density distribution. Future directions for the information theory approach in solid earth geophysics as well as its strengths and weaknesses are discussed.

Rubincam, D. P.↗

Study of density distribution in a near-critical simple fluid (19-IML-1)

This experiment uses visual observation, interferometry, and light scattering techniques to observe and analyze the density distribution in SF6 above and below the critical temperature. Below the critical temperature, the fluid system is split up into two coexisting phases, liquid and vapor. The spatial separation of these phases on earth, liquid below and vapor above, is not an intrinsic property of the fluid system; it is merely an effect of the action of the gravity field. At a fixed temperature, the density of each of the coexisting phases is in principle fixed. However, near T sub c where the fluid is strongly compressible, gravity induced hydrostatic forces will result in a gradual decrease in density with increasing height in the sample container. This hydrostatic density profile is even more pronounced in the one phase fluid at temperatures slightly above T sub c. The experiment is set up to study the intrinsic density distributions and equilibration rates of a critical sample in a small container. Interferometry will be used to determine local density and thickness of surface and interface layers. The light scattering data will reveal the size of the density fluctuations on a microscopic scale.

Michels, Teun↗

Large-scale coronal temperature and density distributions, 1984-1992

We characterize the temperature and the density structure of the corona utilizing spectrophotometric observations at different heights but at the same latitude during the descending phase of cycle 21 through the ascending phase of cycle 22. The data include ground-based intensity observations of the green (Fe XIV 5303) and red (Fe X 6374) coronal forbidden lines, photospheric magnetographs from the National Solar Observatory, Kitt Peak, and synoptic maps of white-light K-coronal polarized brightness from the High Altitude Observatory. A determination of plasma temperature, T, can be estimated from the intensity ratio Fe X/Fe XIV (where T is inversely proportional to the ratio), since both emission lines come from ionized states of Fe, and the ratio is only weakly dependent on density. Distributions of the electron temperature from the line ratio and the polarized brightness which yields electron density of the corona during the descending and the ascending phases of solar cycles 21 and 22 are presented. These data refer to structures of the corona which are relatively large scale, having a temporal coherence of at least two or more synoptic rotation periods, such as the streamer belts, the individual helmet streamers, and the larger coronal holes.

Guhathakurta, M.↗

The density distribution of refractory elements away from the Galactic plane

The density distributions of the three refractory elements Ti II, Ca II, and Fe II away from the Galactic plane are compared with the distribution of hydrogen and dust by examining plots of N s in b versus z. It is found that Ti II and Ca II are considerably more extended in z than the H I and dust and that Fe II has an intermediate extension. Although the results are strongly influenced by sample bias, the indicated exponential scale heights for the data sample are h(Ti II) not less than 2 kpc, h(Ca II) = 1 kpc, h(Fe II) = 0.5 kpc, H(H I) = 0.3 kpc, and h(E/B-V) = 0.1 kpc. Furthermore, it is demonstrated that Ti II and Ca II are much more smoothly distributed in space than the hydrogen or dust. The large scale heights for Ti II and Ca II and their smooth distributions are most easily understood as the effect of a mixture along the line of sight of two H I phases namely, a diffuse cloud phase, in which nearly all of the Ti and Ca are tied up in dust, and an intercloud medium, where refractory elements are less depleted. It is found that Ti II and Ca II mostly trace the smoothly distributed intercloud medium. The smoothness of the distributions of Ti II and Ca II makes them candidates for use as distance indicators.

Edgar, Richard J.↗

On the statistical theory of self-gravitating collisionless dark matter flow: Scale and redshift variation of velocity and density distributions

The statistics of velocity and density fields are crucial for cosmic structure formation and evolution. Here, this paper extends our previous work on the two-point second-order statistics for the velocity field [Phys. Fluids 35, 077105 (2023)] to one-point probability distributions for both density and velocity fields. The scale and redshift variation of density and velocity distributions are studied by a halo-based non-projection approach. First, all particles are divided into halo and out-of-halo particles so that the redshift variation can be studied via generalized kurtosis of distributions for halo and out-of-halo particles, respectively. Second, without projecting particle fields onto a structured grid, the scale variation is analyzed by identifying all particle pairs on different scales $r$. We demonstrate that: (i) Delaunay tessellation can be used to reconstruct the density field. The density correlation, spectrum, and dispersion functions were obtained, modeled, and compared with the N-body simulation; (ii) the velocity distributions are symmetric on both small and large scales and are non-symmetric with a negative skewness on intermediate scales due to the inverse energy cascade on small scales with a constant rate $\varepsilon_u$; (iii) On small scales, the even order moments of pairwise velocity $\Delta u_L$ follow a two-thirds law $\propto{(-\varepsilon_ur)}^{2/3}$, while the odd order moments follow a linear scaling $\langle(\Delta u_L)^{2n+1}\rangle=(2n+1)\langle(\Delta u_L)^{2n}\rangle\langle\Delta u_L\rangle\propto{r}$; (iv) The scale variation of the velocity distributions was studied for longitudinal velocities $u_L$ or $u_L^{'}$, pairwise velocity (velocity difference) $\Delta u_L$=$u_L^{'}$-$u_L$ and velocity sum $\Sigma u_L$=$u^{'}_L$+$u_L$. Fully developed velocity fields are never Gaussian on any scale, despite that they can initially be Gaussian; (v) On small scales, $u_L$ and $\Sigma u_L$ can be modeled by a $X$ distribution to maximize the entropy of the system. The distribution of $\Delta u_L$ can be different; (vi) On large scales, $\Delta u_L$ and $\Sigma u_L$ can be modeled by a logistic or a $X$ distribution, while $u_L$ has a different distribution; (vii) the redshift variation of the velocity distributions follows the evolution of the $X$ distribution involving a shape parameter $\alpha(z)$ decreasing with time.

79 ASTRONOMY AND ASTROPHYSICS↗

Stress due to electric charge density distribution in a dielectric slab

The spatial distribution of electric field due to an imposed electric charge density profile in an infinite slab of dielectric material is derived analytically by integrating Gauss’s law. Various charge density distributions are considered, including exponential and power-law forms. Here, the Maxwell stress tensor is used to compute a notional static stress in the material due to the charge density and its electric field. Characteristics of the electric field and stress distributions are computed for example cases in polyethylene, showing that field magnitudes exceeding the dielectric strength would be required in order to achieve a stress exceeding the ultimate tensile strength.

42 ENGINEERING↗

First-flight escape from spheres with R(-2) density distribution

Energy-independent first-flight transport kernels are evaluated for a spherical region with an R(-2) density distribution. The uncollided angular-flux distribution is obtained and integrated for a source distribution that is proportional to the density to give the uncollided emitted particle flux and current density. These are useful for the calculation of mass, energy, and momentum carried away by fast particles born in the medium. The data are relevant to estimate escape from weakly bound atmospheres such as comet comae, dilute circumstellar envelopes, and some unconfined laboratory plasmas.

Huebner, W. F.↗