Related papers: Source term method for binary neutron stars initia…
In this work we consider the primal mixed variational formulation of the Poisson equation with a line source. The analysis and approximation of this problem is non-standard as the line source causes the solutions to be singular. We start by…
We describe the theory and implementation of a three-dimensional fluid dynamics code which we have developed for calculating the surface geometry and circulation currents in the secondaries of interacting binary systems. The main method is…
We propose a new numerical method to calculate irrotational binary systems composed of compressible gaseous stars in Newtonian gravity. Assuming irrotationality, i.e. vanishing of the vorticity vector everywhere in the star in the inertial…
In this paper we present a novel fast method to solve Poisson equation in an arbitrary two dimensional region with Neumann boundary condition. The basic idea is to solve the original Poisson problem by a two-step procedure: the first one…
This thesis details an effort to generate astrophysically interesting solutions to the two-body problem in General Relativity. The thesis consists of two main parts. The first part presents an analytical variational principle for describing…
Most numerical models of binary stars - in particular neutron stars in compact binaries - assume the companions to be either corotational or irrotational. Either one of these assumptions leads to a significant simplification in the…
We propose a new numerical method to compute quasi-equilibrium sequences of general relativistic irrotational binary neutron star systems. It is a good approximation to assume that (1) the binary star system is irrotational, i.e. the…
We present a numerical method to compute quasiequilibrium configurations of close binary neutron stars in the pre-coalescing stage. A hydrodynamical treatment is performed under the assumption that the flow is either rigidly rotating or…
We develop a numerical hydrodynamics code using a pseudo-Newtonian formulation that uses the weak field approximation for the geometry, and a generalized source term for the Poisson equation that takes into account relativistic effects. The…
We introduce a new numerical scheme for solving the initial value problem for quasiequilibrium binary neutron stars allowing for arbitrary spins. The coupled Einstein field equations and equations of relativistic hydrodynamics are solved in…
This work proposes a fast iterative method for local steric Poisson--Boltzmann (PB) theories, in which the electrostatic potential is governed by the Poisson's equation and ionic concentrations satisfy equilibrium conditions. To present the…
A three-dimensional (3D) Poisson solver with longitudinal periodic and transverse open boundary conditions can have important applications in beam physics of particle accelerators. In this paper, we present a fast efficient method to solve…
The Poisson--Boltzmann equation is widely used to model electrostatics in molecular systems. Available software packages solve it using finite difference, finite element, and boundary element methods, where the latter is attractive due to…
We derive new boundary conditions and implementation procedures for nonlinear initial boundary value problems (IBVPs) with non-zero boundary data that lead to bounded solutions. The new boundary procedure is applied to nonlinear IBVPs in…
Next-generation gravitational-wave detectors are expected to constrain the properties of extreme density matter via observations of static and dynamical tides in binary neutron star inspirals. The required modelling is straightforward in…
We present a method that gives highly accurate electrostatic potentials for systems where we have periodic boundary conditions in two spatial directions but free boundary conditions in the third direction. These boundary conditions are…
Quasi-equilibrium sequences of binary neutron stars are constructed for a variety of equations of state in general relativity. Einstein's constraint equations in the Isenberg-Wilson-Mathews approximation are solved together with the…
In general neutron stars in binaries are spinning. Recently, a new quasi-equilibrium approximation that includes a rotational velocity piece for each star has been proposed to describe binary neutron stars with arbitrary rotation states in…
We present a formalism to obtain equilibrium configurations of uniformly rotating fluid in the second post-Newtonian approximation of general relativity. In our formalism, we need to solve 29 Poisson equations, but their source terms…
In general neutron stars in binaries are spinning. Due to the existence of millisecond pulsars we know that these spins can be substantial. We argue that spins with periods on the order a few dozen milliseconds could influence the late…