Related papers: Application of a symplectic integrator in a non-in…
We construct an explicit reversible symplectic integrator for the planar 3-body problem with zero angular momentum. We start with a Hamiltonian of the planar 3-body problem that is globally regularised and fully symmetry reduced. This…
Multi-symplectic integrators are typically regarded as a discretization of the Hamiltonian partial differential equations. This is due to the fact that, for generic finite-dimensional Hamiltonian systems, there exists only one independent…
Accurate $N$-body simulations of multiple systems such as binaries and triples are essential for understanding the formation and evolution of interacting binaries and binary mergers, including gravitational wave sources, blue stragglers and…
We present a simple algorithm to switch between $N$-body time integrators in a reversible way. We apply it to planetary systems undergoing arbitrarily close encounters and highly eccentric orbits, but the potential applications are broader.…
Because most chemical or biological experiments are performed under conditions of controlled pressure and temperature, it is important to simulate the isobaric-isothermal ensemble at the atomic level to reveal the microscopic mechanism. By…
Harmonic inversion techniques have been shown to be a powerful tool for the semiclassical quantization and analysis of quantum spectra of both classically integrable and chaotic dynamical systems. Various computational procedures have been…
Symplectic maps can provide a straightforward and accurate way to visualize and quantify the dynamics of conservative systems with two degrees of freedom. These maps can be easily iterated from the simplest computers to obtain trajectories…
Energy methods for constructing time-stepping algorithms are of increased interest in application to nonlinear problems, since numerical stability can be inferred from the conservation of the system energy. Alternatively, symplectic…
Hamiltonian Monte Carlo is typically based on the assumption of an underlying canonical symplectic structure. Numerical integrators designed for the canonical structure are incompatible with motion generated by non-canonical dynamics. These…
Dynamic systems have a fundamental relevance in the description of physical phenomena. The search for more accurate and faster numerical integration methods for the resolution of such systems is, therefore, an important topic of research.…
With the great development of parallel computing techniques, the particle-particle (PP) model has been successfully applied in a number of plasma applications. Comparing to particle-mesh (PM) models, for example the widely used…
We study the problem of determining whether a given temporal specification can be implemented by a symmetric system, i.e., a system composed from identical components. Symmetry is an important goal in the design of distributed systems,…
Symplectic integrators separate a problem into parts that can be solved in isolation, alternately advancing these sub-problems to approximate the evolution of the complete system. Problems with a single, dominant mass can use mixed-variable…
In this paper we characterize the definiteness of the discrete symplectic system, study a nonhomogeneous discrete symplectic system, and introduce the minimal and maximal linear relations associated with these systems. Fundamental…
We develop an approach to affine symplectic invariant geometry of Lagrangian surfaces by the method of moving frames. The fundamental invariants of elliptic Lagrangian immersions in affine symplectic four-space are derived together with…
We introduce a class of general purpose linear multisymplectic integrators for Hamiltonian wave equations based on a diamond-shaped mesh. On each diamond, the PDE is discretized by a symplectic Runge--Kutta method. The scheme advances in…
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…
The existence of bi-Hamiltonian structures for the rational Harmonic Oscillator (non-central harmonic oscillator with rational ratio of frequencies) is analyzed by making use of the geometric theory of symmetries. We prove that these…
Simple semitoric systems were classified about ten years ago in terms of a collection of invariants, essentially given by a convex polygon with some marked points corresponding to focus-focus singularities. Each marked point is endowed with…
A fixed time-step variational integrator cannot preserve momentum, energy, and symplectic form simultaneously for nonintegrable systems. This barrier can be overcome by treating time as a discrete dynamic variable and deriving adaptive…