Related papers: Are long-term $N$-body simulations reliable?
The intention of this article is to illustrate the use of methods from symplectic geometry for practical purposes. Our intended audience is scientists interested in orbits of Hamiltonian systems (e.g. the three-body problem). The main…
The gravitationally-driven evolution of cold dark matter dominates the formation of structure in the Universe over a wide range of length scales. While the longest scales can be treated by perturbation theory, a fully quantitative…
We propose efficient numerical methods for nonseparable non-canonical Hamiltonian systems which are explicit, K-symplectic in the extended phase space with long time energy conservation properties. They are based on extending the original…
The large increase in exoplanet discoveries in the last two decades showed a variety of systems whose stability is not clear. In this work we chose the $\upsilon$ Andromedae system as the basis of our studies in dynamical stability. This…
This paper focuses on the parallel implementation of a direct $N$-body method~(particle-particle algorithm) and the application of multiple GPUs for galactic dynamics simulations. Application of a hybrid OpenMP-CUDA technology is considered…
The long-term relaxation of rotating, spherically symmetric globular clusters is investigated through an extension of the orbit averaged Chandrasekhar non-resonant formalism. A comparison is made with the long-term evolution of the…
Gas-poor galaxies can be modelled as composite collisionless stellar systems, with a dark matter halo and one or more stellar components, representing different stellar populations. The dynamical evolution of such composite systems is often…
Time-symmetric integration schemes share with symplectic schemes the property that their energy errors show a much better behavior than is the case for generic integration schemes. Allowing adaptive time steps typically leads to a loss of…
This paper concentrates on four key tools for performing star cluster simulations developed during the last decade which are sufficient to handle all the relevant dynamical aspects. First we discuss briefly the Hermite integration scheme…
In this paper we present our results of numerical integrations of orbits of fictive massless particle in vicinity of resonance. Our goal is to study the dependences of period (frequency) of resonance perturbations and the width of the…
The determination of the resolution of cosmological N-body simulations, i.e., the range of scales in which quantities measured in them represent accurately the continuum limit, is an important open question. We address it here using…
Nowadays, many extrasolar planetary systems possessing at least one planet on a highly eccentric orbit have been discovered. In this work, we study the possible long-term stability of such systems. We consider the general three body problem…
Cosmological N-body simulations are done on massively parallel computers. This necessitates the use of simple time integrators, and, additionally, of mesh-grid approximations of the potentials. Recently, Adamek et al. (2015);…
This technical report provides an in-depth evaluation of both established and state-of-the-art methods for simulating constrained rigid multi-body systems with hard-contact dynamics, using formulations of Nonlinear Complementarity Problems…
Chaos is present in most stellar dynamical systems and manifests itself through the exponential growth of small perturbations. Exponential divergence drives time irreversibility and increases the entropy in the system. A numerical…
We derive a new criterion for estimating characteristic dynamical timescales in N-body simulations. The criterion uses the second, third, and fourth derivatives of particle positions: acceleration, jerk, and snap. It can be used for…
Quantum simulators, in which well controlled quantum systems are used to reproduce the dynamics of less understood ones, have the potential to explore physics that is inaccessible to modeling with classical computers. However, checking the…
We use the Reversibility Error Method and the Fidelity to analyze the global effects of a small perturbation in a non-integrable system. Both methods have already been proposed and used in the literature but the aim of this paper is to…
Many binary systems of interest for gravitational-wave astronomy are orbited by a third distant body, which can considerably alter their relativistic dynamics. Precision computations are needed to understand the interplay between…
Several integration schemes exits to solve the equations of motion of the $N$-body problem. The Lie-integration method is based on the idea to solve ordinary differential equations with Lie-series. In the 1980s this method was applied for…