Linear Density Variation Research Articles

On the Barber dispersion relation for internal waves

We investigate the dispersive behaviour of internal waves supported by a density gradient in a fluid which has an upper boundary surface. By identifying a realistic model for the density gradient which leads to an analytically tractable internal wave eigenvalue equation we are able to verify the general applicability of, and to characterize the deviations from, the simple dispersion relation proposed recently by Barber. We also consider the effect of a linear background density variation superimposed on the localized pycnocline; this establishes a minimum frequency and wavenumber consistent with the propagation of the internal wave and leads to significant deviations from the Barber result.

Gravity effects on fluid vibration in piping systems when using the structural mechanics method

It is shown how the influence of gravity can be incorporated without difficulty in the previously developed “structural mechanics method” [1] for the analysis of uniaxial vibration of compressible fluids in piping systems. Two separate effects are treated: (a) a stiffening or weakening of each fluid column depending on its orientation in the gravity field; (b) a linear density variation along each straight member caused by the static compression of the fluid. The required modifications are introduced in the member mobility matrices only. Thus no alterations are needed in the global system assembly described in reference [1]. Rigid body and elastic body vibrations are treated in a unified manner in the present formulation. Five numerical examples demonstrate and verify the method. The gravity effect of type (a) is found to be larger at low frequencies than at high frequencies, and it is of vital importance to include this effect for systems with rigid body degrees of freedom (open systems). Type (b) is shown to be negligible in most practical situations involving only the natural gravity g=9·81 m/s 2.

On forced internal waves in a rectangular trench

The generation of internal waves in a submarine rectangular trench by normally incident surface waves has been investigated through laboratory experiments and theory. A linear model was developed for small-amplitude, simple harmonic wave motions. In this model, the fluid outside the trench is homogeneous, and the fluid in the trench is composed of two homogeneous layers of different densities separated by a transition region of linear density variation; viscous dissipation is treated based on the assumption of a laminar boundary layer. In the experiments, the stratification in the trench was created using fresh water and salt water, and a scanning laser beam and detector system was used to measure the amplitude of internal waves. The study shows that, when the frequency of the surface waves corresponds to the natural frequency of internal waves, the amplitude of internal waves becomes large compared to the amplitude of surface waves. The natural frequency of oscillation of internal waves decreases as the thickness of the density interface increases and the depth of the lower fluid decreases. Two distinct classes of internal waves were observed, namely, standing internal waves when the lower fluid was deep, and travelling internal waves when the lower fluid was shallow. The linear model predicted the response curve for internal waves quite well in all the cases investigated. It was also found that the internal waves were strongly damped when the depth of the lower fluid was small compared to the wavelength of internal waves.

Frequency domain expressions for surface and borehole gravity potential due to two- and three-dimensional mass models

Frequency domain expressions for surface and borehole gravity potential due to selected two- and three-dimensional mass models with linear variation of density are derived using conjugate complex variables formulation. The mass models include elliptical bodies, vertical and horizontal polygonal prisms, polyhedral bodies and bodies with rotational symmetry. Such analytic expressions are essential for development of interpretative theory for surface and borehole gravity data in the Fourier domain.

Power balance of negative-glow electrons.

Laser-induced fluorescence and absorption spectroscopy are used to study the mixing of populations of excited He atoms due to electron collisions in the negative glow of a dc He discharge. These measurements yield the density (${\mathit{n}}_{\mathit{e}}^{\mathit{c}}$\ensuremath{\simeq}5\ifmmode\times\else\texttimes\fi{}${10}^{11}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$) and temperature (0.1 eV\ensuremath{\le}${\mathit{k}}_{\mathit{B}}$${\mathit{T}}_{\mathit{e}}^{\mathit{c}}$\ensuremath{\le}0.2 eV) of the low-energy (or ``cold'') electrons in the negative glow. The cold electrons are trapped in a potential-energy well. In a complementary investigation, Monte Carlo simulations are used to determine the density (${\mathit{n}}_{\mathit{e}}^{\mathit{h}}$\ensuremath{\simeq}${10}^{9}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$) and temperature (${\mathit{k}}_{\mathit{B}}$${\mathit{T}}_{\mathit{e}}^{\mathit{h}}$\ensuremath{\simeq}3 eV) of the high-energy (or ``hot'') electrons in the negative glow. Results from the experiments and Monte Carlo simulations are combined to study the power balance of the cold trapped electrons. The cold-electron temperature is established by a balance between cooling from recoil during elastic collisions with neutral atoms, and heating due to Coulomb collisions with hot electrons. The linear variation of hot-electron density with discharge current density causes a linear variation in cold-electron temperature with current density. Hot electrons also excite metastable atoms to higher radiating levels to produce most of the light from the negative glow.

Contour integrals for gravity computation of horizontal 2 [formula omitted]-D bodies with variable density

Complex contour integrals for the computation of vertical gravity and its vertical derivative due to a horizontal 2 1 2 -D mass model with arbitrary cross-sectional area and variable density are developed. The gravity formulas are applicable when the field point is either inside or outside the body. For horizontal 2 1 2 -D polygonal prismatic bodies, closed-form expressions for vertical gravity with linear density variation with depth and horizontal position and the vertical gravity with uniform density are presented.

An Exploratory Study of Imperfections in Cotton Yarns

Imperfections in yams are serious flaws that greatly detract from the quality. They are classified into three categories according to their linear density variations. With a view to studying the physical nature of various imperfections, we investigated carded and combed yarns, estimating correlations between diameter and mass of various imperfections and analyzing the composition of thin and thick places and neps. We identified the major factors responsible for different categories of imperfections.

Regularized two‐dimensional Fourier gravity inversion method with application to the Silent Canyon caldera, Nevada

A modification of the 2‐D Fourier gravity inversion method includes regularization and a linear density variation with depth. Explicit downward continuation in the Fourier inversion of gravity observations from mass distributions at depth produces instability in the presence of noise and shallow mass distributions. A data‐adaptive regularization filter tapers growth of the exponential continuation function. An empirical relationship between the regularization filter parameter and a parametric model of potential field spectra results in automatic selection of the filter parameter for a given continuation depth. Inversion of synthetic data from a random noise‐contaminated basin type model produces a depth model that agrees with the synthetic structure with an rms error commensurate with the data noise. A model of the Silent Canyon caldera, buried beneath Pahute Mesa at the Nevada Test Site, results in a gravity field that agrees with the observations to within a 4 percent rms error. The caldera gravity model supports the hypothesis of a high‐density half‐space (precaldera lithology) beneath a lower density caldera infill (postcaldera volcanic activity).

Electron drift mobility in amorphous Si: H

Abstract The ‘time of flight’ technique has been employed to study the transient photoconductivity due to excess electron carriers in amorphous Si:H, over a wide range of temperature and electric field. The data are analysed in terms of the temperature/field dependence of the carrier transit time, and also in terms of the variation in pulse shape with temperature. In both cases, the behaviour suggests interactions with a tail of states extending about 0·15 eV from the band edge and showing an almost linear variation of trap density with energy over at least the range 0·085 to 0·145 eV. The capture cross-section of the centres is estimated to be of order 10−17–10−l6cm2. Interaction with states beyond the tail is comparatively weak, and is dominated by deep trapping into centres believed to be dangling bonds.

Evenness Testing of Continuous Filament Glass Yarns

The presence of substantial within-package linear density variations of continuous filament glass yarn bobbins is discussed. Methods for measuring these variations are shown, and test results on some commercial yams of current production are presented.

MODAL ANALYSIS OF AIRPHOTO LINEARS, CENTRAL IDAHO

Approximately 3,000 airphoto linears from an 8,300 km2 area of central Idaho are plotted, classified for azimuthal orientation, counted for frequency, and measured for length. Dominant linear orientations, weighted for length, are compared to equivalent central tendency measures for joints, dikes, and foliation. Variations in linear density are also compared to differing lithologies. Statistical analysis reveals the following: (1) the dominant lineation mode is statistically independent of the dominant foliation mode; (2) no statistically significant difference exists between the dominant lineation mode and the average directional mode of dikes; (3) no statistically significant difference exists between the dominant lineation mode and the average directional mode of joints; (4) linear frequency is statistically independent of lithology. Visual comparison of raised relief maps with the isopleth map of directionally dominant linears reveals a pronounced correspondence between those areas exhibiting strong s...

Convective response of a mass of water near 4 °C to a constant cooling rate applied on its boundaries

The transient natural convection of a mass of water confined within a closed cavity with wall temperature decreasing at a steady rate is considered. For situations where a linear density-temperature relationship can be assumed, a quasi-steady state following an initial transient may be reached, provided that the cooling rate applied to the wall is held constant long enough. Steady-state flow characteristics in the case of a specific geometry are functions of a single parameter, the Rayleigh number, in which a dimensionless temperature, based on the cooling rate, is used. For the particular case of water cooled through 4 °C, the temperature at which maximum density occurs, a linear variation of density with respect to temperature is no more acceptable. However, it can be assumed that a linear relationship between the water thermal-expansion coefficient and the temperature is valid in the neighbourhood of 4 °C. With such an assumption it is still possible to characterize the cooling process that follows the initial transient by a single parameter. Detailed numerical results are presented for the particular case of a square cavity. Existing experimental and numerical results for the case of a horizontal circular pipe are also discussed.

Proton backscatter as a means of mass normalization in PIXE scanning of human hair

Variations in linear density along a given hair can cause changes in X-ray intensity which do not reflect elemental concentration changes. Hairs from different subjects vary by a factor ∼5 in linear density, so that very different X-ray intensities need not necessarily reflect different concentrations. We investigate the usefulness of the backscattered proton intensity as a means of determining the mass undergoing PIXE analysis. Specimen damage can be avoided in the BS measurement via low currents without loss of statistcs. A correlation is found between BS intensity and mass, but a laser diffraction measurement of the hair diameter provides an equally satisfactory mass determination.

SIMULATION ON THE YARN IRREGULARITY AND BREAK USING THE STEADY-STATE SINGLE FILAMENT MELT SPINNING THEORY

Simulation on the yarn irregularity and break was performed by using the steady-state single filament melt spinning theory described in a previous report (Part 1).Following results are obtained; (1) Linear density variation of as-spun yarn depends upon both the calculated value of 1/V (dV/dx) as response and the extent of disturbance of cooling air at the maximum point of this value, (2) Spinning instability which is caused by the twitching beneath the orifice increases with the increase of spinning temperature and is simulated by introducing the calculated value of the stress beneath the orifice as response, (3) Simulation of unevenness properties of as-spun yarns among the nozzles is performed by calculating the dependency of out-put values, for example, σ95 on any spinning conditions. When dependency is large, unevenness is simulated to be severe, (4) Brittle rupture of yarn is estimated by the value of the yarn stress after perfect cooling.

Small‐scale irregularities of electron density in the F region from ƒN resonances observed by a rocket‐borne relaxation sounding experiment

The plasma resonance phenomena observed near the plasma frequency ƒN through active experiments of relaxation sounding have been experimentally investigated within the range 100‐500 km in the ionosphere by means of the three rocket launches of the EIDI payloads (Experiment on the Impedance of a Dipole in the Ionosphere). The design of the EIDI relaxation sounders has been improved with respect to that of previous topside sounding experiments (Alouette and ISIS programs) in that it records both the envelope and the waveform of the resonance signals in a large dynamic range. This allows the study of spectral features of the plasma resonance phenomena. The data of EIDI 3 are first used to point out the accuracy and the reliability of relaxation sounding experiments for the measurement of the ionospheric electron density; the electron density profile obtained is typical of a midlatitude, winter, nighttime ionosphere. Secondly, the spectral features of the ƒN resonance signals are investigated. Their comparison with those predicted by the theory of oblique echoes for the ƒN resonances leads to a disagreement, although the waves received are shown to be the electrostatic slow ones used in this theory. However, a correlation processing between the Fourier spectra of the ƒN resonance signals observed in sequence allows us to point out the existence of small‐scale irregularities of the electron density. This result is inconsistent with the theoretical hypothesis of a linear density variation versus altitude. By taking these irregularities into account, the features of the resonance signals can then be qualitatively explained. The properties deduced from the data regarding the size and the amplitude of the density irregularities are in agreement with those obtained under comparable ionospheric conditions through another kind of experiment for measuring the irregularities (Retarding Potential Analyzer on the OGO 6 satellite). Moreover, the unexplained phenomena of beat frequency oscillations observed on the Alouette and ISIS ƒN resonance data are tentatively interpreted in a similar way through the existence of sinusoidal irregularities of the electron density. Finally, it is pointed out that the relaxation sounding experiment on‐board the GEOS satellite has been designed to provide an effective measurement of the electron density irregularities in the magnetosphere.

Fully developed laminar free convection flow between two parallel vertical walls—I

Based on the non-linear variation of the density with temperature—(NDT) in the buoyancy term, the free convection flow and heat transfer between two parallel vertical walls is analysed. When the wall temperature ratio m or the free convection parameter K is moderately large the fluid velocities and temperatures for the NDT case exceed the corresponding values of the linear density variation (LDT) and this increase is more pronounced in the presence of the heat sources. As a special case we discuss the problem for the case of quadratic-density temperature-variation (QDT) when the heat sources are present.

Determination of semimicroscopic linear density variations in porous materials by X-ray absorption measurements in the electron microprobe

In electron microprobe investigations of porous materials there are no simple relations between porosity and the signals normally applied (emitted X-rays and backscattered electrons). The absorption of X-rays by a body of constant composition, however, is a simple and well established function of the mass density and thus of the porosity. It is demonstrated how measurements can be performed in a simple way in the electron microprobe where a certain spatial resolution can be obtained by using the electron beam to produce a point-shaped X-ray source. Optimal conditions for the measurements are found and practical arrangements described. The method is suitable for instance for measuring radial density variations in cylindrical, spherical, or similar bodies, the measurements being performed on a plate cut along a centre plane.

43—LINEAR-DENSITY VARIATIONS IN FILAMENTS FROM DRAW-TEXTURED PARTIALLY ORIENTED YARNS

The linear-density variations of filaments from simultaneously draw-textured partially oriented yarns are described and compared with the previously reported variations in filaments from draw-textured undrawn yarns and in conventionally false-twist-textured filaments. The possible connexion between this variation and the appearance of dyed fabric is discussed, together with other possible influences on dyed appearance.

Linear polarization and flux density variations in the radio galaxy 3C120

Linear polarization and flux density variations in the radio galaxy 3C120

Surface wave propagation on an inhomogeneous semiconductor plasma

The propagation of surface waves on an inhomogeneous semiconductor plasma for linear density variation along a radial direction is investigated. A dispersion relation is derived by taking a quasistatic approximation for collisionless plasma and is plotted for various values of inhomogeneity parameter alpha . The inhomogeneity of the plasma greatly affects the propagating mode. It has been found that the axial surface wave mode is very much affected by the variation of alpha . High values of alpha lead to the propagation of backward waves in the plasma column.