Related papers: The quasi-incompressible planet: some analytics
In the article the formulas for the modeling of conservative fields in piecewise infinite plate with a thin inclusion found. The accuracy of the found formulas is of order equal to the thickness of the outer layer. The problem for higher…
Fractional calculus is an effective tool in incorporating the effects of non-locality and memory into physical models. In this regard, successful applications exist rang- ing from signal processing to anomalous diffusion and quantum…
Quasi-equilibrium models of rapidly rotating triaxially deformed stars are computed in general relativistic gravity, assuming a conformally flat spatial geometry (Isenberg-Wilson-Mathews formulation) and a polytropic equation of state.…
In the standard model of terrestrial planet formation, planets are formed through giant impacts of planetary embryos after the dispersal of the protoplanetary gas disc. Traditionally, $N$-body simulations have been used to investigate this…
Context. Semi-grey atmospheric models (with one opacity for the visible and one opacity for the infrared) are useful to understand the global structure of irradiated atmospheres, their dynamics and the interior structure and evolution of…
We present a class of exact solutions of Einstein's gravitational field equations describing spherically symmetric and static anisotropic stellar type configurations. The solutions are obtained by assuming a particular form of the…
In a 2D conservative Hamiltonian system there is a formal integral $\Phi$ besides the energy H. This is not convergent near a stable periodic orbit, but it is convergent near an unstable periodic orbit. We explain this difference and we…
Many exoplanets are discovered in binary star systems in internal or in circumbinary orbits. Whether the planet can be habitable or not depends on the possibility to maintain liquid water on its surface, and therefore on the luminosity of…
Static structure models, which map mass-radius constraints to bulk planet composition, are frequently used to categorise exoplanets due to their computational efficiency and the high-level insight they offer into planetary properties.…
Equilibria of binary neutron stars in close circular orbits are computed numerically in a waveless formulation: The full Einstein-relativistic-Euler system is solved on an initial hypersurface to obtain an asymptotically flat form of the…
A fundamental assumption in the so-called "global polytropic model" is hydrostatic equilibrium for a system of planets or statellites. By solving the Lane-Emden differential equation for such a system in the complex plane, we find…
The condition for pressure isotropy is reduced to a recurrence equation with variable, rational coefficients of order three. We prove that this difference equation can be solved in general. Consequently we can find an exact solution to the…
The core of a terrestrial-type planet consists of a spherical shell of rapidly rotating, electrically conducting, fluid. Such a body supports two distinct classes of quasi-geostrophic eigenmodes: fast, primarily hydrodynamic, inertial modes…
New exact interior solutions to the Einstein field equations for anisotropic spheres are found. We utilise a procedure that necessitates a choice for the energy density and the radial pressure. This class contains the constant density model…
We present some analytical solutions to the Einstein equations, describing radiating collapsing spheres in the diffusion approximation. Solutions allow for modeling physical reasonable situations. The temperature is calculated for each…
Because the distant retrograde orbits dynamics inherently depends on special functions, approximate analytical solutions in the literature are commonly constrained to providing rough approximations of the qualitative behavior. We rely on…
The structure of a star composed of locally non-electroneutral incompressible three-component matter is considered within the framework of general relativity. For thermodynamic quantities like the pressure, the solution can be represented…
Complex scalar fields charged under a global U(1) symmetry can admit non-topological soliton configurations called Q-balls which are stable against decay into individual particles or smaller Q-balls. These Q-balls are interesting objects…
Relying on rays, we search for submodules of a module V over a supertropical semiring on which a given anisotropic quadratic form is quasilinear. Rays are classes of a certain equivalence relation on V, that carry a notion of convexity,…
Let $K$ be a locally compact non-discrete field of characteristic $p>2$ and $Q$ be a non-degenerate isotropic binary quadratic form with coefficients in $K$. We obtain asymptotic estimates for the number of solutions in the two-fold product…