Hydrostatic equilibrium

About: Hydrostatic equilibrium is a research topic. Over the lifetime, 2451 publications have been published within this topic receiving 62172 citations.

Thermomagnetic effect with two temperature theory for photothermal process under hydrostatic initial stress

Abstract: A novel technique is used to investigate the influence of magnetic field for a two dimensional deformations on a two temperature problem at the free surface of a semi-infinite medium. The investigation is carried out under the effects of both mechanical force and hydrostatic initial stress during a photothermal excitation theory. The equations of elastic waves, heat conduction equation, quasi-static electric field, carrier density, two temperature coefficient, ratios, and constitutive relationships for the thermo-magnetic-electric medium are obtained using the Harmonic Wave Method (HWM) technique. The effects of thermoelastic, thermoelectric and two temperature parameters of the applied force on the displacement component, force stress, carrier density and temperature distribution has been depicted graphically.

Shock initiated instabilities in underwater cylindrical structures

Abstract: An experimental investigation to understand the mechanisms of dynamic buckling instability in cylindrical structures due to underwater explosive loadings is conducted. In particular, the effects of initial hydrostatic pressure coupled with a dynamic pressure pulse on the stability of metallic cylindrical shells are evaluated. The experiments are conducted at varying initial hydrostatic pressures, below the critical buckling pressure, to estimate the threshold after which dynamic buckling will initiate. The transient underwater full-field deformations of the structures during shock wave loading are captured using high-speed stereo photography coupled with modified 3-D Digital Image Correlation (DIC) technique. Experimental results show that increasing initial hydrostatic pressure decreases the natural vibration frequency of the structure indicating loss in structural stiffness. DIC measurements reveal that the initial structural excitations primarily consist of axisymmetric vibrations due to symmetrical shock wave loading in the experiments. Following their decay after a few longitudinal reverberations, the primary mode of vibration evolves which continues throughout later in time. At the initial hydrostatic pressures below the threshold value, these vibrations are stable in nature. The analytical solutions for the vibration frequency and the transient response of cylindrical shell are discussed in the article by accounting for both (1) the added mass effect of the surrounding water and (2) the effect of initial stress on the shell imposed by the hydrostatic pressure. The analytical solutions match reasonably well with the experimental vibration frequencies. Later, the transient response of a cylindrical shell subjected to a general underwater pressure wave loading is derived which leads to the analytical prediction of dynamic stability.

Polishing system including a hydrostatic fluid bearing support

Abstract: A polishing system such as a chemical mechanical belt polisher includes a hydrostatic fluid bearing that supports polishing pads and incorporates one or more of the following novel aspects. One aspect uses compliant surfaces surrounding fluid inlets in an array of inlets to extend areas of elevated support pressure around the inlets. Another aspect modulates or reverses fluid flow in the bearing to reduce deviations in the time averaged support pressure and to induce vibrations in the polishing pads to improve polishing performance. Another aspect provides a hydrostatic bearing with a cavity having a lateral extent greater than that of an object being polished. The depth and bottom contour of cavity can be adjusted to provide nearly uniform support pressure across an area that is surrounded by a retaining ring support. Changing fluid pressure to the retaining ring support adjusts the fluid film thickness of the bearing. Yet another aspect of the invention provides a hydrostatic bearing with spiral or partial cardiod drain grooves. This bearing has a non-uniform support pressure profile but provides a uniform average pressure to a wafer that is rotated relative to the center of the bearing. Another aspect of the invention provides a hydrostatic bearing with constant fluid pressure at inlets but a support pressure profile that is adjustable by changing the relative heights of fluid inlets to alter local fluid film thicknesses in the hydrostatic bearing.

Length of day variations due to zonal tides for an inelastic earth in non-hydrostatic equilibrium

Abstract: We present a refined theoretical model for length-of-day (lod) variations induced by the zonal part of the tide-generating potential. The model is computed from a numerical integration, from the Earth's centre up to the surface, of the equation of motion, the rheological equation of state and Poisson's equation. The Earth is modelled as a three-layered body, with an inelastic inner core, an inviscid fluid core and an inelastic mantle sustaining convection, which,induces deviations from hydrostatic equilibrium. The model also incorporates ocean corrections deduced from dynamic ocean models. It is shown that the non-hydrostatic structure inside the Earth has an effect of less than 0.1 per cent on the transfer functions, while the different modellings of mantle inelasticity (different combinations of possible values for the inelastic parameters) can lead to a wide range of results. Finally, we show that the precision of the geodetic observations of UT1 and the precision of the oceanic and atmospheric corrections are not yet sufficient to obtain information about mantle inelasticity from the comparison between theoretical models and geodetic observations.

Neutron star properties and the equation of state for the core

Abstract: Context. Few unified equations of state for neutron star matter, in which core and crust are described using the same nuclear model, are available. However the use of non-unified equations of state with simplified matching between the crust and core has been shown to introduce uncertainties in the radius determination, which can be larger than the expected precision of the next generation of X-ray satellites. Aims. We aim to eliminate the dependence of the radius and mass of neutron stars on the detailed model for the crust and on the crust-core matching procedure. Methods. We solved the approximate equations of the hydrostatic equilibrium for the crust of neutron stars and obtained a precise formula for the radius that only depends on the core mass and radius, the baryon chemical potential at the core-crust interface, and at the crust surface. For a fully accreted crust one needs, additionally, the value of the total deep crustal heating per one accreted nucleon.Results. For typical neutron star masses, the approximate approach allows us to determine the neutron star radius with an error ~0.1% (~10 m, equivalent to a 1% inaccuracy in the crust thickness). The formalism applies to neutron stars with a catalyzed or a fully accreted crust. The difference in the neutron star radius between the two models is proportional to the total energy release due to deep crustal heating.Conclusions. For a given model of dense matter describing the neutron star core, the radius of a neutron star can be accurately determined independent of the crust model with a precision much better than the ~5% precision expected from the next generation of X-ray satellites. This allows us to circumvent the problem of the radius uncertainty that may arise when non-unified equations of state for the crust and core are used.