Related papers: Approximate Analytical Solutions to the Relativist…

An approximate analytical solution of the Thomas-Fermi equation for neutral atoms is obtained, using the Ritz variational method, which reproduces accurately the numerical solution, in the range $0\leq x\leq50$, and its derivative at $x=0$.…

This article is the continued version of the analytical blowup solutions for 2-dimensional Euler-Poisson equations in "M.W. Yuen, Analytical Blowup Solutions to the 2-dimensional Isothermal Euler-Poisson Equations of Gaseous Stars, J. Math.…

With insight from examples and physical arguments, the Tolman-Ehrenfest criterion of thermal equilibrium for test fluids in static spacetimes is extended to local thermal equilibrium in conformally static geometries. The temperature of the…

We consider the solution of the fully kinetic (including electrons) Vlasov-Amp\`ere system in a one-dimensional physical space and two-dimensional velocity space (1D-2V) for an arbitrary number of species with a time-implicit Eulerian…

General solutions of relativistic wave equations are studied in terms of the functions on the Lorentz group. A close relationship between hyperspherical functions and matrix elements of irreducible representations of the Lorentz group is…

Motivated by recent work on approximation of diffusion equations by deterministic interacting particle systems, we develop a nonlocal approximation for a range of linear and nonlinear diffusion equations and prove convergence of the method…

In the framework of non-riemannian geometry, we derive exact static vacuum solutions of the field equations obtained from the full equivalent version of the Einstein-Hilbert action when torsion degrees of freedom are taken into account. By…

A new formalism, called "tensor optimized Fermi sphere (TOFS) method", is developed to treat the nuclear matter using a bare interaction among nucleons. In this method, the correlated nuclear matter wave function is taken to be a power…

Methods to solve the relativistic hydrodynamic equations are a key computational kernel in a large number of astrophysics simulations and are crucial to understanding the electromagnetic signals that originate from the merger of…

In this work, we apply the parametric Nikiforov-Uvarov method to obtain eigen solutions and total normalized wave function of Schr\"odinger equation express in terms of Jacobi polynomial using Coulomb plus Screened Exponential Hyperbolic…

We use the Klein-Gordon equation in a curved spacetime to construct the relativistic analog of the Schr\"odinger-Newton problem, where a scalar particle lives in a gravitational potential well generated by its own probability distribution.…

The Einstein-Vlasov-Maxwell (EVM) system can be viewed as a relativistic generalization of the Vlasov-Poisson (VP) system. As it is proved below, one of nice property obeys by the first system is that the strong energy condition holds and…

We construct analytic solutions to the generalized Grad-Shafranov equation, which incorporates both toroidal and poloidal flows. This is achieved by adopting a general linearizing ansatz for the free-function terms of the equation and…

In this comment we discuss the application of homotopy perturbation method to a nonlinear differential mass equation that solves the Tolman-Oppenheimer-Volkoff equation for an isotropic and spherically symmetric system. We show that one…

We present an analytic solution of the Riemann problem for the equations of relativistic hydrodynamics with the ultra-relativistic equation of state and non-zero tangential velocities. A 3-dimensional numerical code solving such equations…

We present exact solutions to the Einstein-Maxwell system of equations in spherically symmetric gravitational fields with a specified form of the electric field intensity. The condition of pressure isotropy yields a difference equation with…

The Teleparallel Theory is an alternative theory of gravity equivalent to General Relativity (GR) and with non-vanishing torsion $T$. Some extensions of this theory, the so-called $f(T)$ models, have been subject of many recent works. The…

We study the role of the equilibrium equation in bootstrapped Newtonian gravity (BNG) by including terms inspired by the post-Newtonian expansion of the Tolman-Oppenheimer-Volkov (TOV) equation. We then compare (approximate) BNG solutions…

A recent time-of-flight (TOF) expansion experiment with polarized fermionic erbium atoms measured a Fermi surface deformation from a sphere to an ellipsoid due to dipole-dipole interaction, thus confirming previous theoretical predictions.…

Lane Emden differential equation of the polytropic gas sphere could be used to construct simple models of stellar structures, star clusters and many configurations in astrophysics. This differential equation suffers from the singularity at…