Related papers: Source term method for binary neutron stars initia…
We present a new numerical method for the generation of binary neutron star initial data using a method along the lines of the the Wilson-Mathews or the closely related conformal thin sandwich approach. Our method uses six different…
We explore singular second-order boundary value problems with mixed boundary conditions on a general time scale. Using the lower and upper solutions method combined with the Brouwer fixed point theorem we demonstrate the existence of a…
We present our first successful numerical results of 3D general relativistic simulations in which the Einstein equation as well as the hydrodynamic equations are fully solved. This paper is especially devoted to simulations of test problems…
As a preliminary step towards simulating binary neutron star coalescing problem, we test a post-Newtonian approach by constructing a single neutron star model. We expand the Tolman-Oppenheimer-Volkov equation of hydrostatic equilibrium by…
Two long-standing problems with the post-Newtonian approximation for isolated slowly-moving systems in general relativity are: (i) the appearance at high post-Newtonian orders of divergent Poisson integrals, casting a doubt on the soundness…
The first post-Newtonian (PN) hydrostatic equations for an irrotational fluid are solved for an incompressible binary system. The equilibrium configuration of the binary system is given by a small deformation from the irrotational…
We present the first numerical relativity simulations of the gravitational scattering of two neutron stars. Constraint-satisfying initial data for two equal-mass nonspinning sequences are constructed at fixed energy and various initial…
We discuss slowly-rotating, general relativistic, superfluid neutron stars in the Hartle-Thorne formulation. The composition of the stars is described by a simple two-fluid model which accounts for superfluid neutrons and all other…
Two main aims of this paper are to develop a numerical method to solve an inverse source problem for parabolic equations and apply it to solve a nonlinear coefficient inverse problem. The inverse source problem in this paper is the problem…
We study the initial-boundary value problem of the Navier-Stokes equations for incompressible fluids in a general domain in $\R^n$ with compact and smooth boundary, subject to the kinematic and vorticity boundary conditions on the non-flat…
Certain unresolved ambiguities surround pressure determinations for incompressible flows, both Navier-Stokes and magnetohydrodynamic. For uniform-density fluids with standard Newtonian viscous terms, taking the divergence of the equation of…
In this paper, the existence, uniqueness and dependence on initial value of solution for a singular diffusion equation with nonlinear boundary condition are discussed. It is proved that there exists a unique global smooth solution which…
A general class of solutions of Einstein's equation for a slowly rotating fluid source, with supporting internal pressure, is matched using Lichnerowicz junction conditions, to the Kerr metric up to and including first order terms in…
We construct new models of black hole-neutron star binaries in quasiequilibrium circular orbits by solving Einstein's constraint equations in the conformal thin-sandwich decomposition together with the relativistic equations of…
The very weak solution of the Poisson equation with $L^2$ boundary data is defined by the method of transposition. The finite element solution with regularized boundary data converges with order $1/2$ in convex domains but has a reduced…
We present an algorithm of finding numerical solutions of pulsar equation. The problem of finding the solutions was reduced to finding expansion coefficients of the source term of the equation in a base of orthogo- nal functions defined on…
In this article, we present an analytical direct method, based on a Numerov three-point scheme, which is sixth order accurate and has a linear execution time on the grid dimension, to solve the discrete one-dimensional Poisson equation with…
We study the tidal problem and the resulting $I$-Love-$Q$ approximate universal relations for rotating superfluid neutron stars in the Hartle-Thorne formalism. Superfluid stars are described in this work by means of a two-fluid model…
We perform a detailed analysis of radial oscillations to discuss dynamical stability in two-fluid neutron stars composed of ordinary nuclear matter and a gravitationally coupled dark matter component. Using a fully relativistic two-fluid…
We present a new numerical scheme to solve the initial value problem for black hole-neutron star binaries. This method takes advantage of the flexibility and fast convergence of a multidomain spectral representation of the initial data to…