Showing papers on "Hydrostatic equilibrium published in 1969"
TL;DR: In this paper, a penumbra model in hydrostatic equilibrium is presented, which accounts for the continuum observations as well as the observations of Fraunhofer lines in the Penumbra.
Abstract: A penumbra model in hydrostatic equilibrium is presented. The model accounts for the continuum observations as well as the observations of Fraunhofer lines in the penumbra. The uncertainty in the model in deeper layers is discussed. It is shown that the penumbra is probably not in strict radiative equilibrium.
43 citations
TL;DR: In this paper, an operational formalism for obtaining elementary solutions for point impulse sources is developed for finding elementary solutions to point-source point-invariant sources in terms of convergent series solutions for small time and asymptotic series solution for large time.
Abstract: Linear equations for the motions of inviscid ideal gas atmospheres are considered, a brief description of the climatology of the relevant propagation parameters being given An operational formalism is developed for obtaining elementary solutions for point impulse sources The propagation of a pulse according to the Boussinesq gravity wave model is analyzed in terms of convergent series solutions for small time and in terms of asymptotic series solutions for large time Elementary propagators for the gravity wave mode and buoyancy oscillation mode are defined by contour integrals about the singularities of the propagator operator The theory is extended to the propagation of a pulse in a stratified compressible atmosphere All motion is then confined within an acoustic front expanding radially with the speed of sound Series solution in powers of the distance behind the front is described Sufficiently far behind the front, the motion is given by an acoustic oscillation, buoyancy oscillation, and gravity wave mode Consideration of the analogous problem, except for a hydrostatic atmosphere on a rotating plane, indicates when and where the assumptions of hydrostatic balance and absence of rotation are tenable With rotation, a potential vorticity mode describing time-independent motion also occurs, or, if the variation of the earth's vorticity is included in the model, Rossby waves occur Addition of a lower boundary is discussed with emphasis on the horizontal propagation of the Lamb wave mode Impulsive addition of heat excites a Lamb pressure wave pulse strongly modulated by buoyancy oscillations
42 citations
TL;DR: In this article, a finite amplitude gravity wave in a rotating and homogeneous ideal fluid is considered and a theoretical analysis is made by modifying the nonlinear solution for the nonrotating case, and it assumes that the rotational effects are small.
Abstract: Solutions are found for a finite amplitude gravity wave in a rotating and homogeneous ideal fluid. Pressure is assumed to be hydrostatic, and gradients in one horizontal direction are set equal to zero. A theoretical analysis is made by modifying the nonlinear solution for the nonrotating case. This modification is according to a linear solution for waves in a rotating coordinate system, and it assumes that the rotational effects are small. The analytical solutions are compared with numerical solutions for the complete equations. Results are used to determine the delay in jump formation and the reduction in jump intensity due to rotation. In general, the study shows that both effects are exponentially dependent on the product of the length scale and rate of rotation, and they are inversely proportional to the square of the amplitude of the wave. It is concluded that the dispersion effects of rotation are unimportant in atmospheric situations where hydraulic jump analogies have been proposed.
28 citations
01 Jan 1969
TL;DR: In this article, a model of the primitive solar nebula was constructed and the distribution of angular momentum per unit mass in the initial model was that appropriate to a fragment of a collapsing interstellar gas cloud.
Abstract: Models of the primitive solar nebula have been constructed. A model is required to be in centrifugal equilibrium radially in the plane of the disk and in hydrostatic equilibrium perpendicular to the plane of the disk. The distribution of angular momentum per unit mass in the initial model is that appropriate to a fragment of a collapsing interstellar gas cloud.
16 citations
TL;DR: The effect of pressure on the atomic positional parameter u for Sb and Bi has been determined at room temperature by single crystal X-ray diffraction under hydrostatic pressures to 3 kbar as discussed by the authors.
14 citations
TL;DR: In this article, an investigation is made of some general properties of motions of a compressible fluid under the influence of a gravitational field, and the mathematical model based on these hypotheses is the linear theory of rotating stratified non- dissipative flow.
Abstract: : An investigation is made of some general properties of motions of a compressible fluid under the influence of a gravitational field. Motions (or time scales) for the dissipative effects of viscosity and heat condition are not important, and the motions are small deviations from a basic state of rigidly rotating hydrostatic equilibrium. It is assumed that the gravitational field is externally given, and is not itself affected by the motion. The mathematical model based on these hypotheses is the linear theory of rotating stratified non- dissipative flow.
14 citations
TL;DR: In this article, a boundary condition derived from the external potential theory which neither assumes nor discounts the presence of equilibrium conditions in the Earth's interior has been proposed to solve de Sitter's hydrostatic equations.
Abstract: Summary If de Sitter’s hydrostatic equations are developed independent of the external potential theory, the hydrostatic geopotential coefficient Jh occurs explicitly on the right-hand side of these equations. Since this Jh has to be treated as an unknown in the solution of the problem, it becomes rather difficult to solve these hydrostatic equations independently, regardless of which of the dynamical parameters associated with the Earth is taken as the initial datum. The solution of these equations is possible, however, with the help of a boundary condition derived from the external potential theory which neither assumes nor discounts the presence of equilibrium conditions in the Earth’s interior. If a general solution is constructed on these lines, the three particular solutions, usually quoted in literature, stem from it in the wake of the appropriate assumptions. Of course, out of these the only meaningful solution is that corresponding to the polar moment of inertia as the initial datum. It is essential that the solution be constructed in this way in order to demonstrate clearly the correct structure of the problem of hydrostatic equilibrium. The anomalous gravity field of the Earth referred to the hydrostatic figure is compared with that referred to the international reference ellipsoid.
14 citations
01 Jan 1969
11 citations
9 citations
TL;DR: In this paper, a model of the solar photosphere incorporating a simple two-stream representation of granulation is found to give a small but significant improvement in the continuous radiation field over a homogeneous model.
Abstract: A model of the solar photosphere incorporating a simple two-stream representation of granulation is found to give a small but significant improvement in the continuous radiation field over a homogeneous model. It is common to assume that the pressure does not vary with horizontal position; however, this assumption cannot be valid if the material is in hydrostatic equilibrium, so horizontal pressure differences between the hot and cold columns are allowed. This has a major effect on the structure, and one of the consequences is that temperature fluctuations at equal optical depths are greater than those at equal geometric depths.
9 citations
TL;DR: In this article, a general Monte Carlo relaxation method was formulated for the computation of physically self-consistent model stellar atmospheres, where the local physical state was obtained by solving simultaneously the equations of statistical equilibrium for the atomic and ionic level populations, the kinetic energy balance equation for the electron gas to obtain the electron temperature, and the equation of radiative transfer.
Abstract: A general Monte Carlo relaxation method has been formulated for the computation of physically self-consistent model stellar atmospheres. The local physical state is obtained by solving simultaneously the equations of statistical equilibrium for the atomic and ionic level populations, the kinetic energy balance equation for the electron gas to obtain the electron temperature, and the equation of radiative transfer. Anisotropic Thomson scattering is included in the equation of transfer and radiation pressure effects are included in the hydrostatic equation. The constraints of hydrostatic and radiative equilibrium are enforced. Local thermodynamic equilibrium (L.T.E.) is assumed as a boundary condition deep in the atmosphere. Elsewhere in the atmosphere L.T.E. is not assumed.
TL;DR: In this article, the critical mass of neutron stars is obtained by integrating the general relativistic equations for hydrostatic equilibrium using the equation of state, which is valid for low and moderate densities.
Abstract: The equation of state of the neutron gas is calculated by a variational method, using the HamadaJohnson potential for the two-nucleon interaction. The energy-density relation determined in this way is valid for low and moderate densities. This result is extrapolated to higher densities and is joined smoothly to the relativistic energy-density relation for free particles. The critical mass of neutron stars is obtained by integrating the general relativistic equations for hydrostatic equilibrium using the equation of state. The critical mass is found to be less than 0.7 of the mass of the Sun.
Patent•
22 Dec 1969TL;DR: In this paper, a combine harvester having a multiple-speed range mechanical transmission combined with a hydrostatic transmission and providing valve means for the hydraulic transmission which valve means is connected to the mechanical transmission so that pressure fluid is supplied to the hydrostatic transmissions resulting in acceleration/deceleration of the harvesters commensurate with the particular speed range selected.
Abstract: A combine harvester having a multiple-speed range mechanical transmission combined with a hydrostatic transmission and in providing valve means for the hydrostatic transmission which valve means is connected to the mechanical transmission so that pressure fluid is supplied to the hydrostatic transmission resulting in acceleration/deceleration of the harvester commensurate with the particular speed range selected.
TL;DR: In this paper, the effect of internal hydrostatic or lateral pressure on the deformations of an infinitely long, thin, cylindrical isotropic shell subjected to equal concentrated loads equally spaced around a circular cross section is investigated.
Abstract: The effect of internal hydrostatic or lateral pressure on the deformations of an infinitely long, thin, cylindrical isotropic shell subjected to equal concentrated loads equally spaced around a circular cross section is investigated. An exact solution of Fliigge's equations for buckling of cylindrical shells, considered herein as equations for small deformations superimposed on large deformations, is obtained. Calculations are shown primarily for the case of two loads, for which the effect of internal pressure is found to be most pronounced.
TL;DR: In this article, a very economical method is proposed for solution of the hydrostatic equilibrium equations of neutron stars using Brueckner's equation of state, and the importance of the effect of correlation can be demonstrated.
Abstract: A very economical method is proposed for solution of the hydrostatic equilibrium equations of neutron stars. As a simple example the model of homogeneous internal distribution is constructed. UtilizingBrueckner’s equation of state the importance of the effect of correlation can be demonstrated.
01 Jan 1969
TL;DR: In this paper, a detailed account of techniques in the hydrostatic region can be found in the books by Bridgman1 and by Hamann2 for laboratory use and by Comings3 for industrial scale applications.
Abstract: This chapter is concerned with apparatus which can be used for determining physical parameters up to pressures normally reached in truly hydrostatic conditions, the upper limit being approximately 30 kb at room temperature. Apparatus for pressures greater than 30 kb will be considered in subsequent chapters. Detailed accounts of techniques in the hydrostatic region can be found in the books by Bridgman1 and by Hamann2 for laboratory use and by Comings3 for industrial scale applications. Here a description will be given of the fundamental properties of cylinders and pistons and of sealing and methods for entering probes in the general sense which includes many recent innovations not included in these books.