Related papers: JANUS: A bit-wise reversible integrator for N-body…

Recently a new class of numerical integration methods -- ``mixed variable symplectic integrators'' -- has been introduced for studying long-term evolution in the conservative gravitational few-body problem. These integrators are an order of…

We present a novel computational framework for simulating suspensions of rigid spherical Janus particles in Stokes flow. We show that long-range Janus particle interactions for a wide array of applications may be resolved using fast,…

We review the implementation of individual particle time-stepping for N-body dynamics. We present a class of integrators derived from second order Hamiltonian splitting. In contrast to the usual implementation of individual time-stepping,…

In this paper Janus black holes in AdS3 are considered. These are static solutions of an Einstein-scalar system with broken translation symmetry along the horizon. These solutions are dual to interface conformal field theories at finite…

Symplectic integrators are the tool of choice for many researchers studying dynamical systems because of their good long-term energy conservation properties. For systems with a dominant central mass, symplectic integrators are also highly…

Molecular Dynamics method is based on solution of Newtonian differential equations of motion. A new very accurate and efficient time-reversible explicit integrator was derived on the basis of second order Tailor expansion of force. There is…

When fitting N-body models to astronomical data - including transit times, radial velocity, and astrometric positions at observed times - the derivatives of the model outputs with respect to the initial conditions can help with model…

We apply one of the exactly symplectic integrators, that we call HB15, of \cite{HB15}, along with the Kepler problem solver of \cite{WH15}, to solve planetary system $N$-body problems. We compare the method to Wisdom-Holman methods (WH) in…

In this paper we describe a new algorithm for the long-term numerical integration of the two-body problem, in which two particles interact under a Newtonian gravitational potential. Although analytical solutions exist in the unperturbed and…

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…

We present and compare different numerical schemes for the integration of the variational equations of autonomous Hamiltonian systems whose kinetic energy is quadratic in the generalized momenta and whose potential is a function of the…

This paper describes the architecture, the development and the implementation of Janus II, a new generation application-driven number cruncher optimized for Monte Carlo simulations of spin systems (mainly spin glasses). This domain of…

We developed a Keplerian-based Hamiltonian splitting for solving the gravitational $N$-body problem. This splitting allows us to approximate the solution of a general $N$-body problem by a composition of multiple, independently evolved…

Time-reversible symplectic methods, which are precisely compatible with Liouville's phase-volume-conservation theorem, are often recommended for computational simulations of Hamiltonian mechanics. Lack of energy drift is an apparent…

Nonlinear N-body integrable Hamiltonian systems, where N is an arbitrary number, attract the attention of mathematical physicists for the last several decades, following the discovery of some number of these systems. This paper presents a…

Reliable studies of the long-term dynamics of planetary systems require numerical integrators that are accurate and fast. The challenge is often formidable because the chaotic nature of many systems requires relative numerical error bounds…

We present a new mixed variable symplectic (MVS) integrator for planetary systems, that fully resolve close encounters. The method is based on a time regularisation that allows keeping the stability properties of the symplectic integrators,…

We present a system of $N$-coupled Li\'enard type nonlinear oscillators which is completely integrable and possesses explicit $N$ time-independent and $N$ time-dependent integrals. In a special case, it becomes maximally superintegrable and…

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);…

The integration of the equations of motion in gravitational dynamical systems -- either in our Solar System or for extra-solar planetary system -- being non integrable in the global case, is usually performed by means of numerical…