Related papers: Collision detection for N-body Kepler systems
An N-component continuous-time dynamic system is considered whose components evolve autonomously all the time except for in discrete asynchronous instances of pairwise interactions. Examples include chaotically colliding billiard balls and…
We investigate a one-dimensional system of $N$ particles, initially distributed with random positions and velocities, interacting through binary collisions. The collision rule is such that there is a time after which the $N$ particles do…
Collision detection plays an important role in simulation, control, and learning for robotic systems. However, no existing method is differentiable with respect to the configurations of the objects, greatly limiting the sort of algorithms…
We present a proof of concept for a new algorithm which can be used to detect exoplanets in high contrast images. The algorithm properly combines mutliple observations acquired during different nights, taking into account the orbital motion…
This paper presents a real-time solution for collision detection between objects based on the physics properties. Traditional approaches on collision detection often rely on the geometric relationships that computing the intersections…
We study the orbital architecture of multi-planet systems detected by the Kepler transit mission using N-body simulations, focusing on the orbital spacing between adjacent planets in systems showing four or more transiting planets. We find…
Simulations of many rigid bodies colliding with each other sometimes yield particularly interesting results if the colliding objects differ significantly in size and are non-spherical. The most expensive part within such a simulation code…
We investigated the underlying architecture of planetary systems by deriving the distribution of planet multiplicity (number of planets) and the distribution of orbital inclinations based on the sample of planet candidates discovered by the…
Robustly handling collisions between individual particles in a large particle-based simulation has been a challenging problem. We introduce particle merging-and-splitting, a simple scheme for robustly handling collisions between particles…
In the past two decades, since the discovery of the figure-8 orbit by Chenciner and Montgomery, the variational method has became one of the most popular tools for constructing new solutions of the $N$-body problem and its extended…
Direct-summation N-body algorithms compute the gravitational interaction between stars in an exact way and have a computational complexity of O(N^2). Performance can be greatly enhanced via the use of special-purpose accelerator boards like…
Ncorpi$\mathcal{O}$N is a $N$-body software developed for the time-efficient integration of collisional and fragmenting systems of planetesimals or moonlets orbiting a central mass. It features a fragmentation model, based on crater scaling…
In the last decade, thanks to the development of sophisticated numerical codes, major breakthroughs have been achieved in our understanding of the formation of asteroid families by catastrophic disruption of large parent bodies. In this…
We present N-body simulations of planetary accretion beginning with 1 km radius planetesimals in orbit about a 1 solar mass star at 0.4 AU. The initial disk of planetesimals contains too many bodies for any current N-body code to integrate;…
Over the course of the recent decades, $N$-body simulations have become a standard tool for quantifying the gravitational perturbations that ensue in planet-forming disks. Within the context of such simulations, massive non-central bodies…
The gravitational $N$-body problem is a nearly universal problem in astrophysics which, despite its deceptive simplicity, still presents a significant computational challenge. For collisional systems such as dense star clusters, the need to…
Population studies of Kepler's multi-planet systems have revealed a surprising degree of structure in their underlying architectures. Information from a detected transiting planet can be combined with a population model to make predictions…
Terrestrial planet formation theory is at a bottleneck, with the growing realization that pairwise collisions are treated far too simply. Here, and in our companion paper (Cambioni et al. 2019) that introduces the training methodology, we…
Astrophysical Challenges which demand the solution of the one million (or more) gravitating body problem are briefly discussed for the fields of cosmology, galactic nuclei and globular star clusters. Results from the classical three-body…
Many topics in planetary studies demand an estimate of the collision probability of two objects moving on nearly Keplerian orbits. In the classic works of \"Opik (1951) and Wetherill (1967), the collision probability was derived by…