Related papers: Fast and reliable symplectic integration for plane…
Symplectic integrators are widely used for the study of planetary dynamics and other $N$-body problems. In a study of the outer Solar system, we demonstrate that individual symplectic integrations can yield biased errors in the semi-major…
We assess the contribution of dynamical hardening by direct three-body scattering interactions to the rate of stellar-mass black hole binary (BHB) mergers in galactic nuclei. We derive an analytic model for the single-binary encounter rate…
Most galaxies have supermassive black holes (SMBH) at their centres, surrounded by stars with binary systems also present in this environment. We use two schemes - post-Newtonian (PN) and a scalar perturbation to a background metric to…
One major objective of MESSENGER and BepiColombo spatial missions is to accurately measure Mercury's rotation and its obliquity in order to obtain constraints on internal structure of the planet. Which is the obliquity's dynamical behavior…
Symplectic methods, in particular the Wisdom-Holman map, have revolutionized our ability to model the long-term, conservative dynamics of planetary systems. However, many astrophysically important effects are dissipative. The consequences…
The optimal design of multi-target rendezvous and flyby missions is challenging due to the combination of traditional spacecraft trajectory optimization and high-dimensional combinatorial problems. This often requires large-scale global…
The numerical simulations of massive collisional stellar systems, such as globular clusters (GCs), are very time-consuming. Until now, only a few realistic million-body simulations of GCs with a small fraction of binaries (5%) have been…
Hamilton's equations of motion form a fundamental framework in various branches of physics, including astronomy, quantum mechanics, particle physics, and climate science. Classical numerical solvers are typically employed to compute the…
This series of papers is devoted to an open-ended project aimed at the solution of Hilbert's sixth problem (concerning joint axiomatization of physics and probability theory) proposed to be constructed in the framework of an all-embracing…
We present TES, a new n-body integration code for the accurate and rapid propagation of planetary systems in the presence of close encounters. TES builds upon the classic Encke method and integrates only the perturbations to Keplerian…
Most direct N-body integrations of planetary systems use a symplectic integrator with a fixed timestep. A large timestep is desirable in order to speed up the numerical simulations. However, simulations yield unphysical results if the…
We describe a parallel hybrid symplectic integrator for planetary system integration that runs on a graphics processing unit (GPU). The integrator identifies close approaches between particles and switches from symplectic to Hermite…
The "gravitational million-body problem," to model the dynamical evolution of a self-gravitating, collisional N-body system with ~10^6 particles over many relaxation times, remains a major challenge in computational astrophysics.…
Context. Integrating the motion of stars in a smoothed potential is necessary in many stellar and galactic studies. Previous works have often used numerical integrators that alternate between linear drifts and velocity kicks (such as the…
Spin-orbit coupling of planetary systems plays an important role in the dynamics and habitability of planets. However, symplectic integrators that can accurately simulate not only how orbit affects spin but also how spin affects orbit have…
We present a class of symplectic integrators adapted for the integration of perturbed Hamiltonian systems of the form $H=A+\epsilon B$. We give a constructive proof that for all integer $p$, there exists an integrator with positive steps…
While Keplerian orbits account for the majority of the astrometric motion of directly-imaged planets, perturbations due to N-body interactions allow us to directly constrain exoplanet masses in multiplanet systems. This has the potential to…
Periodic dynamical systems ubiquitously exist in science and engineering. The harmonic balance (HB) method and its variants have been the most widely-used approaches for such systems, but are either confined to low-order approximations or…
Nonadiabatic behavior of metastable systems modeled by anharmonic Hamiltonians is reproduced by the Fokker-Planck and imaginary time Schrodinger equation scheme with subsequent symplectic integration. Example solutions capture ergodicity…
The Worldvolume Hybrid Monte Carlo (WV-HMC) method [arXiv:2012.08468] is an efficient algorithm for addressing the numerical sign problem at moderate computational cost. It mitigates the sign problem while avoiding the ergodicity issues…