Related papers: Implementing Few-Body Algorithmic Regularization w…
We describe a novel N-body code designed for simulations of the central regions of galaxies containing massive black holes. The code incorporates Mikkola's 'algorithmic' chain regularization scheme including post-Newtonian terms up to PN2.5…
In this paper we describe a new algorithm for the long-term numerical integration of the two-body problem, in which two particles interact under a Newtonian gravitational potential. Although analytical solutions exist in the unperturbed and…
We first discuss two-body and chain regularization methods for direct N-body simulations on HARP-2 and GRAPE-6. The former is used for accurate integration of perturbed binaries and hierarchies, whereas the latter deals with strong…
The post-Newtonian approximation is still the most widely used approach to obtaining explicit solutions in general relativity, especially for the relativistic two-body problem with arbitrary mass ratio. Within many of its applications, it…
We describe efforts over the last six years to implement regularization methods suitable for studying one or more interacting black holes by direct N-body simulations. Three different methods have been adapted to large-N systems: (i)…
We present the open source few-body gravity integration toolkit {\tt SpaceHub}. {\tt SpaceHub} offers a variety of algorithmic methods, including the unique algorithms AR-Radau, AR-Sym6, AR-ABITS and AR-chain$^+$ which we show out-perform…
We report on the first fully consistent conventional cluster simulation which includes terms up to post^{5/2} Newtonian in the potential of the massive body. Numerical problems for treating extremely energetic binaries orbiting a single…
We present a new time-stepping criterion for N-body simulations that is based on the true dynamical time of a particle. This allows us to follow the orbits of particles correctly in all environments since it has better adaptivity than…
Detailed numerical analyses of the orbital motion of a test particle around a spinning primary are performed. They aim to investigate the possibility of using the post-Keplerian (pK) corrections to the orbiter's periods (draconitic,…
In this paper we describe optimal reduction for the system of two bodies in $\mathbb{R}^3$ whose Hamiltonian is invariant under rotations and translations. In doing this, we introduce parametrizations and charts which help giving explicit…
We examine the Newman-Janis algorithm's application to an exact regular static solution sustained by a minimally coupled scalar field with a non-standard kinetic term. Although coordinate complexification leads to a regular Kerr-like black…
An accurate and efficient method dealing with the few-body dynamics is important for simulating collisional N-body systems like star clusters and to follow the formation and evolution of compact binaries. We describe such a method which…
The application of renormalization group methods to microscopic nuclear many-body calculations is discussed. We present the solution of the renormalization group equations in the particle-hole channels for neutron matter and the application…
This paper presents a fortran program to solve diverse few-body problems with the stochastic variational method. Depending on the available computational resources the program is applicable for $N=2-3-4-5-6-...$-body systems with $L=0$…
A systolic algorithm rhythmically computes and passes data through a network of processors. We investigate the performance of systolic algorithms for implementing the gravitational N-body problem on distributed-memory computers. Systolic…
The regularization of a new problem, namely the three-body problem, using 'similar' coordinate system is proposed. For this purpose we use the relation of 'similarity', which has been introduced as an equivalence relation in a previous…
We revisit the dynamics of the post-Newtonian (PN) two-body problem for two inspiraling compact bodies. Starting from a matter-only reduced Hamiltonian, we present an adapted framework based on the Lie series approach, enabling the…
In this study, an $N$-body simulation code was developed for self-gravitating systems with a limited first-order post-Newtonian approximation. The code was applied to a special case in which the system consists of one massive object and…
We present the Kustaanheimo-Stiefel (KS) regularization of the elliptic restricted three-body problem (ER3BP) at the secondary body $P_2$, and discuss its use to study a category of transits through its Hill's sphere (fast close…
We present a new approach to describe the dynamics of an isolated, gravitationally bound astronomical $N$-body system in the weak field and slow-motion approximation of the general theory of relativity. Celestial bodies are described using…