Related papers: A Variable Polytrope Index Applied to Planet and M…
Although it is well known that a massive planet opens a gap in a proto-planetary gaseous disk, there is no analytic description of the surface density profile in and near the gap. The simplest approach, which is based upon the balance…
Vibrational entropy plays a central role in determining phase stability and temperature dependent behavior in materials, yet its calculation from first-principles phonon methods remains computationally demanding. In this work, we combine…
A new discontinuous Galerkin finite element method for the Stokes equations is developed in the primary velocity-pressure formulation. This method employs discontinuous polynomials for both velocity and pressure on general…
The increasing precision of planetary mass and radius observations is bringing major questions about the structure and formation of planets--such as the nature of the radius valley and origin of super-Mercuries--within reach, demanding the…
It is well known that alternative theories to the Standard Model allow -- and sometimes require -- fundamental constants, such as the fine-structure constant, $\alpha$, to vary in spacetime. We demonstrate that one way to investigate these…
The goal of this paper is to develop and analyze some fully discrete finite element methods for a displacement-pressure model modeling swelling dynamics of polymer gels under mechanical constraints. In the model, the swelling dynamics is…
This is a review of particle-theory models of inflation, and of their predictions for the primordial density perturbation that is thought to be the origin of structure in the Universe. It contains mini-reviews of the relevant observational…
In this paper, we extend our study of mass transport in multicomponent isothermal fluids to the incompressible case. For a mixture, incompressibility is defined as the independence of average volume on pressure, and a weighted sum of the…
Precipitation of fine particles into the base material of a metal is a potent strengthening mechanism. This is numerically analyzed within a continuum framework based on a higher order strain gradient plasticity theory and by use of an…
The prospects for finding transiting exoplanets in the range of a few to 20 Earth masses is growing rapidly with both ground-based and spaced-based efforts. We describe a publicly available computer code to compute and quantify the…
The basic ideas of a homotopy-based multiple-variable method is proposed and applied to investigate the nonlinear interactions of periodic traveling waves. Mathematically, this method does not depend upon any small physical parameters at…
Many theories of modified gravity, including the well studied Horndeski models, are characterized by a screening mechanism that ensures that standard gravity is recovered near astrophysical bodies. In a recently introduced class of…
We estimate the minimal mass of selfgravitating polytropic disks using the famous Sobolev inequality. This bound resembles the well known mass formula for Lane-Emden stars. For ideal gas with the polytropic index n = 3 the minimal mass is…
In this work we study class I interior solutions supported by anisotropic polytropes. The generalized Lane--Emden equation compatible with the embedding condition is obtained and solved for a different set of parameters in both the…
Exoplanet surveys have revealed a wide diversity of planetary systems, requiring integrated models of planet formation to explain their origin. Planet population synthesis (PPS) modelling is a key tool for linking theory with the…
In the past, measures of ``Earth-likeness'' of exoplanets have been qualitative, considered an abiotic Earth, or required discretionary choices of what parameters make a planet Earth-like. With the advent of high-resolution exoplanet…
The inflationary expansion of our early-time universe is considered in terms of the van der Waals equation, as equation of state for the cosmic fluid, where a bulk viscosity contribution is assumed to be present. The corresponding…
Particle based methods such as the Discrete Element Method and the Lattice Spring Method may be used for describing the behaviour of isotropic linear elastic materials. However, the common bond models employed to describe the interaction…
In lattice models local pressure on a surface is derived from the change in the free energy of the system due to the exclusion of a certain boundary site, while the total force on the surface can be obtained by a similar exclusion of all…
We model a compact relativistic body with anisotropic pressures in the presence of an electric field. The equation of state is barotropic with a linear relationship between the radial pressure and the energy density. Simple exact models of…