Related papers: An efficient integrator for stellar dynamics in ef…
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…
A new algorithm is introduced to integrate the equations of rotational motion. The algorithm is derived within a leapfrog framework and the quantities involved into the integration are mid-step angular momenta and on-step orientational…
A new method is proposed to numerically integrate a dynamical system on a manifold such that the trajectory stably remains on the manifold and preserves first integrals of the system. The idea is that given an initial point in the manifold…
Two specialized algorithms for the numerical integration of the equations of motion of a Brownian walker obeying detailed balance are introduced. The algorithms become symplectic in the appropriate limits, and reproduce the equilibrium…
Stellar dynamics is almost unreasonably well suited for an implementation in terms of special-purpose hardware. Unlike the case of molecular dynamics, stellar dynamics deals exclusively with a long-range force, gravity, which leads to a…
Action-angle coordinates are an essential tool for understanding the properties of the six dimensional phase space involved in orbits of stars in galactic potentials. A new method, which does not require specific knowledge of a generating…
We develop a method for constraining the potential of the Milky Way using stellar streams with a known progenitor. The method expresses the stream in angle-action coordinates and integrates the orbits of the stars backwards in time to…
A parallel implementation of coupled spin-lattice dynamics in the LAMMPS molecular dynamics package is presented. The equations of motion for both spin only and coupled spin-lattice dynamics are first reviewed, including a detailed account…
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…
We discuss how dynamical fermion computations may be made yet cheaper by using symplectic integrators that conserve energy much more accurately without decreasing the integration step size. We first explain why symplectic integrators…
We present a new implicit asymptotic preserving time integration scheme for charged-particle orbit computation in arbitrary electromagnetic fields. The scheme is built on the Crank-Nicolson integrator and continues to recover full-orbit…
Symplectic schemes are powerful methods for numerically integrating Hamiltonian systems, and their long-term accuracy and fidelity have been proved both theoretically and numerically. However direct applications of standard symplectic…
Symplectic integrators evolve dynamical systems according to modified Hamiltonians whose error terms are also well-defined Hamiltonians. The error of the algorithm is the sum of each error Hamiltonian's perturbation on the exact solution.…
We present a new hybrid Smoothed Particle Hydrodynamics (SPH)/N-body method for modelling the collisional stellar dynamics of young clusters in a live gas background. By deriving the equations of motion from Lagrangian mechanics we obtain a…
For conventional smoothed particle hydrodynamics (SPH), obtaining the static solution of a problem is time-consuming. To address this drawback, we propose an efficient dynamic relaxation method by adding large artificial-viscosity-based…
We introduce a novel numerical method to integrate partial differential equations representing the Hamiltonian dynamics of field theories. It is a multi-symplectic integrator that locally conserves the stress-energy tensor with an excellent…
We study symplectic numerical integration of mechanical systems with a Hamiltonian specified in non-canonical coordinates and its application to guiding-center motion of charged plasma particles in magnetic confinement devices. The…
Modified Hamiltonian Monte Carlo (MHMC) methods combine the ideas behind two popular sampling approaches: Hamiltonian Monte Carlo (HMC) and importance sampling. As in the HMC case, the bulk of the computational cost of MHMC algorithms lies…
We show how the Hamiltonian Monte Carlo algorithm can sometimes be speeded up by "splitting" the Hamiltonian in a way that allows much of the movement around the state space to be done at low computational cost. One context where this is…
The symplectic Wisdom-Holman map revolutionized long-term integrations of planetary systems. There is freedom in such methods of how to split the Hamiltonian and which coordinate system to employ, and several options have been proposed in…