Hydrostatic equilibrium

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

Solar Structure in terms of Gauss' Hypergeometric Function

Abstract: Hydrostatic equilibrium and energy conservation determine the conditions in the gravitationally stabilized solar fusion reactor. We assume a matter density distribution varying non-linearly through the central region of the Sun. The analytic solutions of the differential equations of mass conservation, hydrostatic equilibrium, and energy conservation, together with the equation of state of the perfect gas and a nuclear energy generation rate ∈ = ∈0ρ n T nT m ,are given in terms of Gauss' hypergeometric function. This model for the structure of the Sun gives the run of density, mass, pressure, temperature, and nuclear energy generation through the central region of the Sun. Because of the assumption of a matter density distribution, the conditions of hydrostatic equilibrium and energy conservation are separated from the mode of energy transport in the Sun.

Geophysically Realistic, Ellipsoidal, Analytically Tractable (GREAT) coordinates for atmospheric and oceanic modelling

Abstract: Suitable models of Earth's geopotential field provide foundations for developing geopotential coordinate systems for modelling Earth's atmosphere and oceans. Earth's geopotential surfaces are traditionally represented as spheres. However, the suitability of this spherical representation for state-of-the-science models is debatable: the geopotentials are more accurately approximated by ellipsoids. A new, ellipsoidal, geopotential approximation is proposed. It is not based on confocal or similar ellipses (as used in previous studies) but is nevertheless relatively simple and analytically tractable. It properly represents the underlying physics, and gives geophysically realistic horizontal and vertical variation of apparent gravity. Exploiting this geopotential approximation, an orthogonal, ellipsoidal, geopotential coordinate system for atmospheric and oceanic modelling is developed analytically and in a self-consistent manner. By construction, the horizontal coordinate surfaces coincide with geopotential surfaces. This ensures that there is no component of apparent gravity in any direction tangential to coordinate surfaces. Accurate representation of intrinsic horizontal and vertical force balances, such as geostrophic and hydrostatic balance, is thereby facilitated. The proposed coordinate system has the potential not only to improve the quality of terrestrial model forecasts in the future, but to be used to model the atmospheres and oceans of mildly oblate planetary bodies, and also for space weather simulation.

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.

Quark stars with isotropic matter in Hořava gravity and Einstein–æther theory

Abstract: We study non-rotating and isotropic strange quark stars in Lorentz-violating theories of gravity, and in particular in Hořava gravity and Einstein-aether theory. For quark matter we adopt both linear and non-linear equations of state, corresponding to the MIT bag model and color flavor locked state, respectively. The new structure equations describing hydrostatic equilibrium generalize the usual Tolman–Oppenheimer–Volkoff (TOV) equations of Einstein’s general relativity. A dimensionless parameter $$ u $$ measures the deviation from the standard TOV equations, which are recovered in the limit $$ u \rightarrow 0$$. We compute the mass, the radius as well as the compactness of the stars, and we show graphically the impact of the parameter $$ u $$ on the mass-to-radius profiles for different equations of state describing quark matter. The energy conditions and stability criteria are also considered, and they are all found to be fulfilled.