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Hydrostatic equilibrium
About: Hydrostatic equilibrium is a research topic. Over the lifetime, 2451 publications have been published within this topic receiving 62172 citations.
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01 Jan 1997
TL;DR: In this article, two end-member models of Mars' present interior structure are presented: the first model is optimized to satisfy the geochemical data derived from the SNC meteorites in terms of the bulk chondritic ratio Fe/Si- 1.71, while the second model was optimized to satisfying the most probable maximum value C- 0.366 x Mprp of the polar moment of inertia factor.
Abstract: Two end-member models of Mars' present interior structure are presented: the first model is optimized to satisfy the geochemical data derived from the SNC meteorites in terms of the bulk chondritic ratio Fe/Si- 1.71, while the second model is optimized to satisfy the most probable maximum value C- 0.366 x Mprpof the polar moment of inertia factor. Hydrostatic equilibrium and stationary heat transfer are assumed, and the basic differential equations for the mechanical and thermal structure are solved numerically together with an isothermal Murnaghan-Birch type equation of state truncated in Eulerian strain at forth order. We obtain the radial distribution of mass, hydrostatic pressure, gravity, temperature, and heat flow density along with the corresponding density stratification, viscosity profiles, and the global seismic velocity structure of model Mars. The first model being consistent with the geochemical requirement produces C- 0.357 x Mprp , whereas the second model commensurate with the geophysical constraint gives Fe/Si- 1.35. The calculated central pressure is about 40 GPa in both models, and the central temperature is in the 2000 to 2200 K range. The model calculations suggest a Fe-Ni-FeS core a little less than one half of the planetary radius in size surrounded by a silicate mantle subdivided into lower spinel and upper olivine layers and overlain by a 100- to 250-km thick basaltic crust and a surface heatflow density of 25 to 30 mW m -2. In both models the pressure in the mantle is not sucient for the spinel to perovskite transition to occur. The present thermal lithosphere is estimated to be about 500 km thick and to be subdivided into a 300- km-thick outermost rheological lithosphere and an underlying thermal boundary layer of mantle convection. Given the core sulfur content of 14 wt% as derived from SNC meteorites, the Martian core is found to be entirely molten, implying the nonoperation of a self-sustained dynamo due to the absence of sufficiently vigorous convection.
14 citations
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TL;DR: In this paper, the authors obtained an expression for the active gravitational mass of a relativistic heat conducting fluid, just after its departure from hydrostaticequilibrium, on a time scale of the order of relaxation time.
Abstract: We obtain an expression for the activegravitational mass of a relativistic heat conductingfluid, just after its departure from hydrostaticequilibrium, on a time scale of the order of relaxationtime. It is shown that an increase of acharacteristic parameter leads to larger (smaller)values of active gravitational mass of collapsing(expanding) spheres, enhancing thereby the instabilityof the system.
14 citations
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TL;DR: In this article, the design of internal pressure cell-specimen capsule arrangements has been improved to allow X ray and ultrasonic measurements to hydrostatic pressures in excess of 6 GPa.
Abstract: Over the last decade, high-pressure-temperature experiments in mineral physics generally have employed either diamond anvil, shock wave, or conventional pressure generation methods. In the latter category, one would include standard hydrostatic fluid vessels, piston-cylinder devices, “belt” and “girdle” apparatus, and multianvil units. Recent emphasis in the use of such systems has centered on improvements in volume, pressure, and temperature capabilities, as well as the achievement of more hydrostatic pressure environments. Because the pressure generation level of conventional equipment is rather limited, in comparison to diamond anvil and shock wave methods, focus has been placed on the usage of working volume in terms of material synthesis and the measurement of physical properties. In this regard, the design of internal pressure cell-specimen capsule arrangements has been improved to allow X ray and ultrasonic measurements to hydrostatic pressures in excess of 6 GPa. Mineral data derived from such measurements should provide the bases for more accurate representations of the equation of state in the lower mantle and core by virtue of the inclusion of higher-order elastic properties.
14 citations
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TL;DR: In this article, a non-hydrostatic numerical model with the three-dimensional Navier-Stokes equations on structured grids was constructed and discussed, based upon a staggered finite difference Crank-Nicholson scheme on a Cartesian grid.
Abstract: A new non-hydrostatic numerical model with the three-dimensional Navier-Stokes equations on structured grids was constructed and discussed. The algorithm is based upon a staggered finite difference Crank-Nicholson scheme on a Cartesian grid. The eddy viscosity coefficient was calculated by the efficient k-e turbulence model. A new surface-layer non-hydrostatic treatment and a local cell bottom treatment were introduced so that the three-dimensional model is fully non-hydrostatic and is free of any hydrostatic assumption. The developed model is second-order accuracy in both time and space when semi-implicit coefficient is set to 0.5. The validity of the present solution algorithm was demonstrated from its application to the three-dimension channel flow and the wave propagation over a submerged bar problems.
14 citations
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TL;DR: In this article, the existence and stability of the out-of-plane equilibrium points of a third body of infinitesimal mass when the equations of motion are written in the three dimensional form under the set up of the Robe's circular restricted three-body problem, in which the hydrostatic equilibrium figure of the first primary is an oblate spheroid and the second one is a triaxial rigid body under the full buoyancy force of the fluid.
Abstract: This paper examines the existence and stability of the out-of-plane equilibrium points of a third body of infinitesimal mass when the equations of motion are written in the three dimensional form under the set up of the Robe’s circular restricted three-body problem, in which the hydrostatic equilibrium figure of the first primary is an oblate spheroid and the second one is a triaxial rigid body under the full buoyancy force of the fluid. The existence of the out of orbital plane equilibrium points lying on the xz-plane is noticed. These points are however unstable in the linear sense.
14 citations