Showing papers on "Hydrostatic equilibrium published in 2000"

Shear strain in carbon nanotubes under hydrostatic pressure

Abstract: We investigated the hydrostatic and shear strain components introduced in the graphite hexagons by applying hydrostatic pressure to single-walled carbon nanotubes. The vibrational modes are expected to show different pressure derivatives depending on the polarization of the eigenvector with respect to the nanotube axis, but independent of chirality. A comparison with tight-binding calculations allows us to estimate the Gr\"uneisen parameter (1.24) and the shear phonon deformation potentials (0.41); they compare favorably with experimental results on nanotubes.

Anisotropic charged fluid spheres in D space–time dimensions

Abstract: The equations describing the hydrostatic equilibrium (mass continuity and Tolman–Oppenheimer–Volkoff) of a static anisotropic general relativistic fluid sphere are obtained in D (D⩾4) space–time dimensions in the presence of a cosmological constant. The formalism thus developed is used to study homogeneous anisotropic constant density charged fluid spheres and homogeneous anisotropic charged spheres with a neutral isotropic core in higher dimensions. For these configurations and with a particular choice of the proper charge density a complete solution of the coupled Einstein–Maxwell equations is obtained.

The effect of hydrostatic pressure on the electronic and optical properties of InP

Abstract: Based on the empirical pseudo-potential method, the electronic and optical properties of the InP compound in the zinc-blende structure at ambient and under hydrostatic pressure are reported. The first-order pressure coefficients of the main band gaps (at Γ, X, and L) are given. The agreement between our calculated hydrostatic deformation potential and the available experimental data is better than 5%, whereas for the crossover pressure from direct to indirect band gap is about 10% less. The valence bandwidth increases with increasing pressure reflecting the decreased ionicity in the material of interest. Besides the electronic properties, the effect of pressure on the dielectric function is also analysed.

Time Variations In Gravity And Inferences On The Earth's Structure And Dynamics

Abstract: This paper reviews how the study of the surface gravity changes is able to provide useful information on the Earth's structure and global dynamics. The spectral range which is observable with superconducting gravimeters is broad and goes from the seismic frequency band to periods longer than one year. We first investigate the seismic and sub-seismic bands with a special attention paid to the gravity detection of core modes in the liquid core and to the Slichter mode of translation of the solid inner core. In the tidal bands, we show how accurate measurements allow us to infer constraints on various phenomena such as mantle (an-)elasticity, as well as ocean and atmospheric loading. The observation of the Free Core Nutation resonance in the diurnal frequency band is reviewed and indirectly suggests an increase in the ellipticity of the core-mantle boundary with respect to its hydrostatic value. A similar resonance is also theoretically predicted in the diurnal band for the rotation of the solid inner core (Free Inner Core Nutation) but we show that its detection is much more difficult because of the small amplitude and lack of a nearby tidal frequency. Oceanic and atmospheric loading mechanisms induce gravity changes over a wide spectral range and we present some recent progress in this field. Finally, because superconducting gravimeters have high calibration stability and small long-term instrumental drift, they can easily measure longperiod gravity variations due to polar motion and hydrogeology.

Composite Polytrope Models of Molecular Clouds. I. Theory

Abstract: We construct spherical, hydrostatic models of dense molecular cores and Bok globules consisting of two distinct, spatially separate gas components: a central, isothermal region surrounded by a negative-index, polytropic envelope. The clouds are supported against their own self-gravity by a combination of thermal, mean magnetic, and turbulent wave pressure. The latter two are included by allowing for locally adiabatic, nonisentropic pressure components. Such models are meant to represent, in a schematic manner, the velocity and density structure of cores and globules, as inferred from molecular line and dust continuum observations. In addition, our picture reflects the theoretical expectation that MHD wave motions, which are important at scales 0.1 pc in typical low-mass star-forming regions, are damped at smaller scales, giving rise to a finite-sized, thermally dominated core region. We show that if the pressure components are isentropic, then the pressure drop from the center to the edge of the composite polytropes we consider is limited to 197, the square of the value for the Bonnor-Ebert sphere. If the pressure components are nonisentropic, it is possible to have arbitrarily large pressure drops, in agreement with the recent work of McKee & Holliman. However, we find that even for nonisentropic pressure components, the ratio of the mean to surface pressure in the composite polytropes we consider is less than 4. We show by explicit construction that it is possible to have dense cores comparable to the Jeans mass embedded in stable clouds of much larger mass. In a subsequent paper, we show that composite polytropes on the verge of gravitational instability can reproduce the observed velocity and density structure of cores and globules under a variety of physical conditions.

Hydrostatic Equilibrium of a Perfect Fluid Sphere with Exterior Higher-Dimensional Schwarzschild Spacetime

Abstract: We discuss the question of how the number of dimensions of space and time can influence the equilibrium configurations of stars. We find that dimensionality does increase the effect of mass but not the contribution of the pressure, which is the same in any dimension. In the presence of a (positive) cosmological constant the condition of hydrostatic equilibrium imposes a lower limit on mass and matter density. We show how this limit depends on the number of dimensions and suggest that Λ>0 is more effective in 4D than in higher dimensions. We obtain a general limit for the degree of compactification (gravitational potential on the boundary) of perfect fluid stars in D dimensions. We argue that the effects of gravity are stronger in 4D than in any other number of dimensions. The generality of the results is also discussed.

The CO Fundamental Vibration-Rotation Lines in the Solar Spectrum. II. Non-LTE Transfer Modeling in Static and Dynamic Atmospheres

Abstract: We present a numerical method for solving radiative transfer in molecular vibration-rotation bands that allows for departures from local thermodynamic equilibrium (LTE) while accurately including a large number of lines. The method is applied to the formation of the CO fundamental vibration-rotation bands in several plane-parallel hydrostatic models and in a sequence of 20 snapshots from a radiation-hydrodynamics simulation of chromospheric dynamics. Calculations for the hydrostatic models performed with different values of the collisional coupling between different vibrational states confirm earlier results in the literature showing that the CO lines have LTE source functions in the solar atmosphere, so emergent CO intensities reflect actual temperatures therein. Only if the canonical collisional strengths are too large by more than 2 orders of magnitude would it be possible to explain the low temperatures derived from CO line core intensities at the solar limb by scattering in an atmosphere with much higher temperatures, consistent with the values derived from UV line and continuum and Ca II resonance line diagnostics. An interesting feature in the wavelength structure of the CO vibration-rotation bands is pointed out, in which pairs of lines can be found in different bands but of similar strength and wavelength. In principle such pairs provide a diagnostic for departures from LTE in the CO lines. CO line core intensity variations computed from the sequence of dynamical snapshots, which represent a typical episode in the chromospheric dynamics simulation, have an amplitude that is 2.5 times higher than observed. It is shown that this large amplitude is due in part to the up and down shift of the CO line formation region during the evolution of the atmosphere and is related to the assumption of instantaneous chemical equilibrium that was assumed to calculate CO concentrations. This suggests that the CO concentration is not in equilibrium, may be lower than would be expected on the basis of chemical equilibrium at the time-averaged mean temperature of the atmosphere, and may have reduced variations compared to instantaneous chemical equilibrium values at the local temperatures.

Winds from Luminous Late-Type Stars. I. The Effects of Nonlinear Alfvén Waves

Abstract: We present the results of magnetohydrodynamic (MHD) modeling of winds from luminous late-type stars using a 2.5-dimensional, nonlinear MHD computer code. We assume that the wind is generated within an initially hydrostatic atmosphere and is driven by torsional Alfven waves generated at the stellar surface. Two cases of atmospheric topology are considered: case I has longitudinally uniform density distribution and isotropic radial magnetic field over the stellar surface, and case II has an isotropic, radial magnetic field with a transverse density gradient, which we refer to as an "atmospheric hole." We use the same set of boundary conditions for both models.The calculations are designed to model a cool luminous star, for which we assume an initial hydrostatic pressure scale height of 0.072 R*, an Alfven wave speed of 92 km s-1 at the surface, and a wave period of 76 days, which roughly corresponds with the convective turnover time. For case I the calculations produce a wind with terminal velocity of ~22 km s-1 and a mass loss rate comparable to the expected value of 10-6 M☉ yr-1. For case II we predict a two-component wind: a fast (25 km s-1) and relatively dense wind outside of the atmospheric hole and a slow (15 km s-1), rarefied wind inside of the hole.

The solar oblateness and its relationship with the structure of the tachocline and of the Sun's subsurface

Abstract: The solar oblateness " was computed with a dynami- cal up-to-date solar model of mass and density, combined with a recent rotational model established from the helioseismic data, and including the effects of differential rotation with depth. To determine the theoretical value of the oblateness " of the Sun, we integrated the extended differential equation governing the fluids in hydrostatic equilibrium and the Poisson equation for the gravitational potential. From this analysis, we deduced the profiles of ", as a function of the radius and of the latitude, from the core to the surface, for a Sun splitted into a series of con- centric shells. As each shell is affected by a potential distortion, mainly due to the rotation, and as the rotation rate depends on the radius and on the latitude, each shell of the Sun is affected by a different oblateness. As a result of the integration of this function, we found " =8 :77:10 6 , that we compared to the oblateness of a rigidly rotating sphere. To interprete the difference in oblateness " of the studied layers within the Sun, we linked the profiles to the solar interior structures, specially to the tachocline and to the subsurface, that help us to understand why and how these regions are mainly governed by shear. In particular, we propose for these two layers a double structure, one where the magnetic field would be stored and one of shear. Finally, we compared our results of radial integrated oblate- ness with the latitudinal variation of the semidiameter from solar astrolabe observations.

The Effect of Hydrostatic Weighting on the Vertical Temperature Structure of the Solar Corona.

Abstract: We investigate the effect of hydrostatic scale heights λ(T) in coronal loops on the determination of the vertical temperature structure T(h) of the solar corona. Every method that determines an average temperature at a particular line of sight from optically thin emission (e.g., in EUV or soft X-ray wavelengths) of a mutlitemperature plasma is subject to the emission measure-weighted contributions dEM(T)/dT from different temperatures. Because most of the coronal structures (along open or closed field lines) are close to hydrostatic equilibrium, the hydrostatic temperature scale height introduces a height-dependent weighting function that causes a systematic bias in the determination of the temperature structure T(h) as function of altitude h. The net effect is that the averaged temperature seems to increase with altitude, dT(h)/dh > 0, even if every coronal loop (of a multitemperature ensemble) is isothermal in itself. We simulate this effect with differential emission measure distributions observed by SERTS for an instrument with a broadband temperature filter such as Yohkoh/Soft X-Ray Telescope and find that the apparent temperature increase due to hydrostatic weighting is of order ΔT ≈ T0h/r☉. We suggest that this effect largely explains the systematic temperature increase in the upper corona reported in recent studies (e.g., by Sturrock et al., Wheatland et al., or Priest et al.), rather than being an intrinsic signature of a coronal heating mechanism.

Deformation of Earth's inner core by electromagnetic forces

Abstract: A recent study of Karato (1999) suggests that deformation induced in the inner core by electromagnetic (Lorentz) forces may account for the development of seismic anisotropy. The viability of this proposal depends on whether Lorentz forces can sustain persistent flow within the inner core. We explore this question by establishing the conditions for static equilibrium when Lorentz forces are present. We find that the requirements for thermodynamic and hydrostatic equilibrium are incompatible at the surface of the inner core. However, the resulting deformation redistributes mass in the interior so as to minimize steady flow. Numerical calculations show that the flow becomes vanishingly weak and is confined to the top of the inner core. Strains in the interior are small and the alignment of crystals is insufficient to explain the anisotropy inferred from seismological observations.

FUSE Observations of the Stellar Winds of Two O7 Supergiants in the Magellanic Clouds

Abstract: We compare the stellar wind features in far-UV spectra of Sk -67 111, an O7 Ib(f) star in the LMC, with Sk 80, an O7 Iaf+ star in the SMC. The most striking differences are that Sk 80 has a substantially lower terminal velocity, much weaker O VI absorption, and stronger S IV emission. We have used line-blanketed, hydrodynamic, non-LTE atmospheric models to explore the origin of these differences. The far-UV spectra require systematically lower stellar temperatures than previous determinations for O7 supergiants derived from plane-parallel, hydrostatic models of photospheric line profiles. At these temperatures, the O VI in Sk -67 111 must be due primarily to shocks in the wind.

Lifting by Convergence Lines

Abstract: The lifting depth of a convergence line in an unstratified boundary layer beneath a stably stratified atmosphere is examined with both analytical and numerical models. Cases are considered with and without flow in the layer above the convergence line. Three different stability profiles above the boundary layer are also considered: an inversion, continuous stratification, and a combination of the two. For the case in which there is no flow above the convergence line, analytical solutions are obtained for the lifting depth for the three different stability profiles. Simulations of the flow with a nonlinear, nonhydrostatic model show good agreement with these analytical predictions. The presence of flow in the upper layer increases the complexity of the problem due to the presence of gravity waves in the steady-state solution. For an atmosphere with just an inversion, the analytical model predicts that, for hydrostatic flow, the depth of lifting is independent of the upper-level flow; while for nonh...

Normal Modes of a Global Nonhydrostatic Atmospheric Model

Abstract: Anticipating use of a very high resolution global atmospheric model for numerical weather prediction in the future without a traditional hydrostatic assumption, this article describes a unified method to obtain the normal modes of a nonhydrostatic, compressible, and baroclinic global atmospheric model. A system of linearized equations is set up with respect to an atmosphere at rest. An eigenvalue–eigenfunction problem is formulated, consisting of horizontal and vertical structure equations with suitable boundary conditions. The wave frequency and the separation parameter, referred to as “equivalent height,” appear in both the horizontal and vertical equations. Hence, these two equations must be solved as a coupled problem. Numerical results are presented for an isothermal atmosphere. Since the solutions of the horizontal structure equation can only be obtained numerically, the coupled problem is solved by an iteration method. In the primitive-equation (hydrostatic) models, there are two kinds of ...

Non‐linear inversion for the hydrostatic structure of the solar interior

Abstract: We present the results of a non-linear inverse analysis for the hydrostatic, spherically symmetric component of the solar internal structure using the observed p-mode frequencies. The iterative non-linear inversion technique used here is based on the succesive Born approximation description of solar p-modes developed by Roxburgh & Vorontsov. This description can give a high resolution of regions of rapid variation of seismic parameters with depth (e.g., the base of the convection zone), and accounts accurately for the strong influence of gravity perturbations on low-degree modes which penetrate deep into the solar core. The inversion procedure is non-linear; the eigenfrequency equation obtained from the Born approximation is solved by iteration. The particular target of our inverse analysis is to achieve the highest possible resolution of the region near the base of the solar convection zone, searching for possible signatures of penetrative convection, element diffusion and/or strong magnetic fields. The results of the global inversion obtained with solar p-mode frequencies provided by the recent high-quality observational data (GONG, SOI/MDI, GOLF) are presented and discussed.

A constrained parametric inversion for velocity analysis based on CFP technology

Abstract: A method of velocity analysis based on the common focusing point (CFP) method is presented. The two important aspects of the method are the use of the CFP domain and the use of a new parameterization—a vertical velocity gradient to describe the lateral velocity variation within a layer. The layer velocity is defined with only two parameters: an average velocity (υ0)and a vertical velocity gradient (β). Layer velocity parameterization using υ0 and β assumes that the lithology of the layer is constant and that the overburden and fluid pressure increase linearly with depth. This type of parameterization is suitable for areas with gross changes in lithology (clastic‐carbonate‐salt) and for rock in hydrostatic equilibrium. A layer‐based model is required for these areas. The salt dome data example presented belongs to this type of area, so the layer‐based model with the defined parameterization produced a very good subsurface velocity model. The method is based on the principle of equal traveltime between the ...

A new look at the pseudo-incompressible solution to Lamb's problem of hydrostatic adjustment

Abstract: The pseudo-incompressible solution to Lamb’s problem of the hydrostatic adjustment of the atmosphere is revisited using a generalized formulation that allows time variation of the base state. It is found that the generalized pseudo-incompressible equations do reproduce the compressible solution of the nonlinear hydrostatic adjustment in the limit of small heating.

Effects due to compressional and compositional density stratification on load-induced Maxwell viscoelastic perturbations

Abstract: SUMMARY Calculations of viscoelastic perturbations of an incompressible £uid earth initially in hydrostatic equilibrium have been conventionally based on models consisting of isocompositional layers. A special case is the incompressible, isocompositional half-space, for which the initial density distribution is spatially uniform. One of the de¢ciencies of this model is that it ignores the increase of the initial density with depth in the earth’s interior due to compressional and compositional strati¢cation. The presentstudy is concernedwith load-induced Maxwellviscoelastic perturbations of a half-space with a compressional and compositional initial density gradient. Analytic solutions to this problem are deduced for the limiting cases of purely compressional strati¢cation (earth model P) and purely compositional strati¢cation (earth model C). The comparison of the solutions for these earth models with that for the special case of no density strati¢cation (earth model R) shows that eiects due to the initial density gradient become important for perturbations whose lateral scale length exceeds about 10 3 km. Using axisymmetric models of the Pleistocene Fennoscandian and Canadian ice sheets and considering the vertical surface displacements near the load axes, the maximum diierences are found to be about 10 m (Fennoscandia) or 35 m (Canada) at the beginning of relaxation for earth models P and R and about 50 m (Fennoscandia) or 150 m (Canada) at intermediate times of relaxation for earth models C and R.

Analysis of the hydrostatic approximation in oceanography with compression term

Abstract: The hydrostatic approximation of the incompressible 3D stationary Navier-Stokes equations is widely used in oceanography and other applied sciences. It appears through a limit process due to the anisotropy of the domain in use, an ocean, and it is usually studied as such. We consider in this paper an equivalent formulation to this hydrostatic approximation that includes Coriolis force and an additional pressure term that comes from taking into account the pressure in the state equation for the density. It therefore models a slight dependence of the density upon compression terms. We study this model as an independent mathematical object and prove an existence theorem by means of a mixed variational formulation. The proof uses a family of finite element spaces to discretize the problem coupled with a limit process that yields the solution. We finish this paper with an existence and uniqueness result for the evolutionary linear problem associated to this model. This problem includes the same additional pressure term and Coriolis force.

Linear dynamics of hydrostatic adjustment to horizontally homogeneous heating

Abstract: The process of hydrostatic adjustment to horizontally homogeneous heating in a stably stratifiedatmosphere of arbitrary thermal structure is investigated in the limit of small perturbations. Alinear differential equation is derived for the vertical pressure distribution in the final balancedstate. Solutions of this equation are compared with the time dependent solution which is foundby numerically integrating the equations in time. During the process of hydrostatic adjustmentacoustic-buoyancy oscillations are generated. The amplitudes of these oscillations become sogreat that static instability is generated at heights above 100 km, depending on where and howabruptly the heat is added. As a crude representation of the unstable breakdown and dampingof these waves, Rayleigh damping is introduced. If the associated damping coefficient in theupper atmosphere is sufficiently large (greater than the Brunt Vaisala frequency), the oscillationsvanish. Below a height of about 50 km the steady state predicted by the above mentioneddifferential equation is reached approximately in 10 min. DOI: 10.1034/j.1600-0870.2000.00063.x

Continuously variable hydrostatic-mechanical split transmission regulates hydrostatic unit speed so coupling elements to be closed are stationary or synchronised

Abstract: The transmission has a first hydrostatic unit (A) of variable vol. and a second hydrostatic unit (B) of constant or variable vol. with a summing planetary gear for summing the power at the transmission input separated into a hydrostatic and a mechanical power branch with one or more selection ranges. A control and regulating device compares the revolution rates of at least two rotating transmission elements. The speed of the second hydrostatic unit is regulated to the accurate native speed required when the vehicle is stationary so that coupling (K1) elements to be closed are stationary or rotating in synchronism.

Small-amplitude coastally trapped disturbances and the reduced-gravity shallow-water approximation

Abstract: Solutions are obtained for linear hydrostatic disturbances propagating parallel to the face of an uninterrupted topographic step in an infinitely deep, stably stratified fluid on an β-plane. These waves are vertically trapped because their frequencies are smaller than the Coriolis parameter and the height of the topographic step is finite. These waves are referred to as step-trapped Kelvin waves, because they are dynamically similar to internal Kelvin waves throughout the layer of fluid below the top of the topographic step. These waves appear to provide an idealized, semi-analytic model for the coastally trapped disturbances observed to propagate parallel to mountainous coastlines in several parts of the world. Computations are performed for a basic state with uniform static stability and for a three-layer basic state in which the two lowest layers represent the marine boundary layer and a strong capping inversion. One might suppose that the linear dynamics of hydrostatic disturbances in the three-layer basic state could be well approximated by a reduced-gravity shallow-water model, but this is not the case. In particular, the reduced-gravity shallow-water model does not provide reliable estimates for the phase speed of linear step-trapped Kelvin waves. This defect suggests that detailed quantitative comparisons between marine boundary-layer flows and the reduced-gravity shallow-water system may not have any intrinsic physical significance. Nevertheless, these results do not preclude the possibility of constructing useful qualitative analogies between marine boundary-layer flows and the reduced-gravity shallow-water model.

Hydraulic Theory and Particle‐Driven Gravity Currents

Abstract: Hydraulic theory, as it has been applied to compositionally driven gravity flows, involves the single simplifying assumption that the pressure in the fluid is hydrostatic [1]. This assumption provides, as a consequence, a depth independent horizontal velocity field. This approach has led to a greatly increased understanding of many of the phenomena associated with these complex flows, including issues surrounding internal hydraulic jumps and energy loss [2]. Recently, investigations into flow and deposition of particles from particle-driven gravity currents have been carried out using an approach that employs the hydraulic theory that had proved so successful in the case of homogeneous flows [3]-[7]. Unfortunately, as we show here, there is a fundamental contradiction in adopting this simplifying assumption when particles drive the flow. This contradiction is essentially that one cannot have a hydrostatic pressure that arises from the presence of particles while at the same time maintaining a depth-independent horizontal velocity field, as was assumed in references [3]-[7].

Differential hydrostatic transmission system

Abstract: A hydrostatic transmission system for driving a rotatable member includes a differential having an output coupled with the rotatable member, a first hydrostatic drive having an output coupled to a first input of the differential, and a second hydrostatic drive having an output coupled to a second input of the differential. The output of the first hydrostatic drive is rotatable in a first selected direction and at a first selected speed. The output of the second hydrostatic drive is rotatable in a second selected direction and at a second selected speed. A rotational speed and direction of the output of the differential is related to the algebraic sum of the rotational speeds and directions of the outputs of the hydrostatic drives. In one embodiment, the speeds of the first and second drives are maintained above a minimum stable threshold, while operating the rotatable drive at very low or zero speed, by selecting the first direction to be opposite the second direction.

FROM: Large-scale Earth Structure from Analyses of Free Oscillation Splitting and Coupling

Abstract: Since departures from spherical symmetry are small (particularly in the deep Earth), it is useful to consider an approximate Earth model which is spherically symmetric, non-rotating, and elastically isotropic. Departures from this state (anelasticity, anisotropy, rotation and three-dimensional structure) are supposed sufficiently small that they can be treated by perturbation theory. The model is assumed to be initially quiescent and in a state of hydrostatic equilibrium. The equations governing the small oscillations of such a body are given by:

Solar System Dynamics: Tides, Rotation, and Shape

Abstract: What fates impose, that men must needs abide; It boots not to resist both wind and tide. William Shakespeare, Henry VI (3), IV, iii Introduction So far we have considered all objects as being point masses with no physical dimensions. Since this is evidently not the case for real bodies, we must now consider the effects of the application of universal gravitation to the matter that forms the bodies of the solar system. A tide is raised on one body by another because of the effect of the gravitational gradient or the variation of the gravitational force across the body. For example, if we consider the tide raised on a planet by an orbiting satellite, the force experienced by the side of the planet facing the satellite is stronger than that experienced by the far side of the planet. Since none of the bodies that make up the solar system is perfectly rigid, there will be a distortion that gives rise to a tidal bulge . The magnitude of the tidal bulge on a body is determined in part by its internal density distribution and thus, in principle, a measurement of the tidal amplitude could lead to a determination of the internal structure. Such measurements are not possible for any of the planets in the solar system other than the Earth.