Related papers: Are long-term $N$-body simulations reliable?
The body of work presented here revolves around the investigation of the existence and nature of extra-solar planetary systems. The fitting of stellar radial velocity time series data is attempted by constructing a model to quantify the…
Self-consistent N-body simulations are efficient tools to study galactic dynamics. However, using them to study individual trajectories (or ensembles) in detail can be challenging. Such orbital studies are important to shed light on global…
The elliptic restricted three body problem has been well studied. However, the previous formulations of the problem have used a rotating coordinate system to keep the positions of the primary and secondary on the x-axis. This requires the…
We propose an experimental study of adaptive time-stepping methods for efficient modeling of the aggregation-fragmentation kinetics. Precise modeling of this phenomena usually requires utilization of the large systems of nonlinear ordinary…
Quantum simulators have made a remarkable progress towards exploring the dynamics of many-body systems, many of which offer a formidable challenge to both theoretical and numerical methods. While state-of-the-art quantum simulators are in…
The 2:1 mean motion resonance orbit was integrated at the restricted planar 3-body problem in absolute frame. Orbit of Jupiter was assumed circular. Initial Jupiter longitude was assumed zero. The Runge-Kutta method was used. The start of…
We present a GPU-accelerated numerical integrator specifically optimized for stability calculations of small bodies in planetary systems. Specifically, the integrator is designed for cases when large numbers of test particles (tens or…
It is widely known that numerically integrated orbits are more precise than analytical theories for celestial bodies. However, calculation of the positions of celestial bodies via numerical integration at time $t$ requires the amount of…
Cosmological $N$-body simulations are the standard tool to study the emergence of the observed large-scale structure of the Universe. Such simulations usually solve for the gravitational dynamics of matter within the Newtonian…
Extending many-body numerical techniques which are powerful in the context of simple model calculations to the realm of realistic material simulations can be a challenging task. Realistic systems often involve multiple active orbitals,…
We present the UNIT $N$-body cosmological simulations project, designed to provide precise predictions for nonlinear statistics of the galaxy distribution. We focus on characterizing statistics relevant to emission line and luminous red…
We present a new method to add long wavelength power to an evolved $N$-body simulation, making use of the Zel'dovich (1970) approximation to change positions and velocities of particles. We describe the theoretical framework of our…
Temporal surrogate models are effective for predicting chaotic dynamical systems where computational cost can be prohibitive. Several deep neural network architectures can be used for such purposes. In this work, a few commonly used…
We use a systolic N-body algorithm to evaluate the linear stability of the gravitational N-body problem for N up to 1.3 x 10^5, two orders of magnitude greater than in previous experiments. For the first time, a clear ~ln N-dependence of…
We present a detailed comparison of several integration schemes applied to the dynamic system consisting of a charged particle on the Kerr background endowed with the axisymmetric electromagnetic test field. In particular, we compare the…
A series of N-body simulations aimed to study the dynamics of small groups of galaxies are presented. The properties of small galaxy groups are very well reproduced, and those of Hickson's compact groups are well reproduced by the most…
We present the COmoving Lagrangian Acceleration (COLA) method: an N-body method for solving for Large Scale Structure (LSS) in a frame that is comoving with observers following trajectories calculated in Lagrangian Perturbation Theory…
A Kepler solver is an analytical method used to solve a two-body problem. In this paper, we propose a new correction method by slightly modifying the Kepler solver. The only change to the analytical solutions is that the obtainment of the…
We take into account the dynamics of three types of models of rotating galaxies in polar coordinates in a rotating frame. Due to non-axisymmetric potential perturbations, the angular momentum varies with time, and the kinetic energy depends…
The simulation of multi-body systems with frictional contacts is a fundamental tool for many fields, such as robotics, computer graphics, and mechanics. Hard frictional contacts are particularly troublesome to simulate because they make the…