Chronometric geodesy applies general relativity to study the problem of the shape of celestial bodies including the earth, and their gravitational field. The present paper discusses the relativistic problem of construction of a background geometric manifold that is used for describing a reference ellipsoid, geoid, the normal gravity field of the earth and for calculating geoid’s undulation (hei...

The problem of potential flow of a second-order fluid around an ellipsoid is solved, following general expressions in Lamb (1993), and the flow and stress fields are computed. The flow fields are determined by the harmonic potential but the stress fields depend on viscosity and the parameters of the second-order fluid. The stress fields on the surface of a tri-axial ellipsoid depend strongly on...

Constraints are often represented as ellipsoids. One of the main advantages of such constrains is that, in contrast to boxes, over which optimization of even quadratic functions is NP-hard, optimization of a quadratic function over an ellipsoid is feasible. Sometimes, the area described by constrains is too large, so it is reasonable to bisect this area (one or several times) and solve the opti...

The self gravitating ellipsoid has been the subject of study by many physicists and mathematicians. Newton first started the subject in the attempt to determine the eccentricity of the earth, which he modelled using a rigidly rotating ellipsoid made of a fluid of uniform density and subject only to its own gravity. Later on McLaurin generalized and refined his calculation of the eccentricity. I...

In this problem, one of the primaries of mass m1 is a Roche Ellipsoid filled with a homogeneous incompressible fluid of density ρ1. The smaller primary of mass m2 is a point mass outside the Ellipsoid. The third and the fourth bodies (of mass m3 and m4 respectively) are small solid spheres of density ρ3 and ρ4 respectively inside the Ellipsoid, with the assumption that the mass and the radius o...

the third order term in the density functional is required for study of an inhomogeneous fluid. this term can be chosen such that, the thermodynamic potential gives the correct bulk pressure. the density porofile of a hard sphere fluid near hard wall which is an inhomogeneous fluid is obtained and it is shown that, if the third order term is ignored, although an exact bulk direct correlation fu...

The liquid crystal phase transitions for a classical uid mixture of hard ellip-soids with aspect ratios 10 : 1 and 1 : 10, and equal volume, has been studied at two compositions using Onsager theories and by computer simulation. The original Onsager form of the Helmholtz free energy contains the second virial coeecient, but the eeect of higher virial coeecients may be taken into account indirec...

Analytic expressions were derived for the compressibility factor and residual internal energy of the square-well plus Sutherland fluid. In this derivation, we used the second order Barker-Henderson perturbation theory based on the macroscopic compressibility approximation together with an analytical expression for radial distribution function of the reference hard sphere fluid. These properties...