Related papers: New methods for large dynamical range problems in …
This paper describes a fourth-order integration algorithm for the gravitational N-body problem based on discrete Lagrangian mechanics. When used with shared timesteps, the algorithm is momentum conserving and symplectic. We generalize the…
We present a new symplectic integrator designed for collisional gravitational $N$-body problems which makes use of Kepler solvers. The integrator is also reversible and conserves 9 integrals of motion of the $N$-body problem to machine…
State-of-the-art planet formation models are now capable of accounting for the full spectrum of known planet types. This comes at the cost of increasing complexity of the models, which calls into question whether established links between…
Symplectic integrators are a foundation to the study of dynamical $N$-body phenomena, at scales ranging from from planetary to cosmological. These integrators preserve the Poincar\'e invariants of Hamiltonian dynamics. The $N$-body…
Relativistic dynamics of a charged particle in time-dependent electromagnetic fields has theoretical significance and a wide range of applications. It is often multi-scale and requires accurate long-term numerical simulations using…
We extend the results of planetary formation synthesis by computing the long-term evolution of synthetic systems from the clearing of the gas disk into the dynamical evolution phase. We use the symplectic integrator SyMBA to numerically…
Many astrophysical simulations involve extreme dynamic range of timescales around 'special points' in the domain (e.g. black holes, stars, planets, disks, galaxies, shocks, mixing interfaces), where processes on small scales couple strongly…
The Kepler planet candidates are an interesting testbed for planet formation scenarios. We present results from N-body simulations of multi-planetary systems that resemble those observed by Kepler. We add both smooth (Type I/II) and…
This white paper discusses a repurposed mission for the Kepler spacecraft that focusses on solving outstanding problems in planet formation and evolution by targeting the study of the hot Jupiter population of young stars. This mission can…
Formation models in which terrestrial bodies grow via the pairwise accretion of planetesimals have been reasonably successful at reproducing the general properties of the solar system, including small body populations. However, planetesimal…
We describe a hybrid algorithm to calculate the formation of planets from an initial ensemble of planetesimals. The algorithm uses a coagulation code to treat the growth of planetesimals into oligarchs and explicit N-body calculations to…
Computational efficiency demands discretised, hierarchically organised, and individually adaptive time-step sizes (known as the block-step scheme) for the time integration of N-body models. However, most existing N-body codes adapt…
The sample of host stars with multiple transiting planets has illuminated the orbital architectures of exoplanetary systems. These architectures may be shaped mostly by formation conditions, be continually sculpted by ongoing dynamical…
A new approach is developed to integrate numerically the equations of motion for systems of interacting rigid polyatomic molecules. With the aid of a leapfrog framework, we directly involve principal angular velocities into the integration,…
We describe an updated version of our hybrid N-body-coagulation code for planet formation. In addition to the features of our 2006-2008 code, our treatment now includes algorithms for the 1D evolution of the viscous disk, the accretion of…
The existence of planets born in environments highly perturbed by a stellar companion represents a major challenge to the paradigm of planet formation. In numerical simulations, the presence of a close binary companion stirs up the relative…
Doppler planet searches revealed that many giant planets orbit close to their host star or in highly eccentric orbits. These and subsequent observations inspired new theories of planet formation that invoke gravitation interactions in…
We present new almost time-reversible integrators for solution of planetary systems consisting of "planets" and a dominant mass ("star"). The algorithms can be considered adaptive generalizations of the Wisdom--Holman method, in which all…
Exoplanets are often found with short periods or high eccentricities, and multiple-planet systems are often in resonance. They require dynamical theories that describe more extreme motions than those of the relatively placid planetary…
A pure two-body problem has seven integrals including the Kepler energy, the Laplace vector, and the angular momentum vector. However, only five of them are independent. When the five independent integrals are preserved, the two other…