Related papers: Collision detection for N-body Kepler systems
We consider a belt of small bodies around a star, captured in one of the external or 1:1 mean-motion resonances with a massive perturber. The objects in the belt collide with each other. Combining methods of celestial mechanics and…
The dynamics of planetesimals plays an important role in planet formation, because their velocity distribution sets the growth rate to larger bodies. When planetesimals form in protoplanetary discs, their orbits are nearly circular and…
We study a particle system naturally associated to the $2$-dimensional Keller-Segel equation. It consists of $N$ Brownian particles in the plane, interacting through a binary attraction in $\theta/(Nr)$, where $r$ stands for the distance…
This paper deals with the problem of simulating dense dispersed systems composed by large numbers of particles undergoing ballistic aggregation. The most classical approaches for dealing with such problems are represented by the so-called…
The general consensus in the N-body community is that statistical results of an ensemble of collisional N-body simulations are accurate, even though individual simulations are not. A way to test this hypothesis is to make a direct…
This paper examines several methods of tracing galaxies in N-body simulations and their effects on the derived galaxy statistics, especially measurements of velocity bias. Using two simulations with identical initial conditions, one…
Particle collisions are the primary mechanism of inter-particle momentum and energy exchange for dense particle-laden flow. Accurate approximation of this collision operator in four-way coupled Euler-Lagrange approaches remains challenging…
The interval approach to computation of dynamics of celestial bodies in the planetary problem has been considered. It is based on the refusal from idealization of infinitely high resolving capacity of measuring tools, and forms an…
We develop an Euler-type particle method for the simulation of a McKean--Vlasov equation arising from a mean-field model with positive feedback from hitting a boundary. Under assumptions on the parameters which ensure differentiable…
Given that secular perturbations in a binary system not only excite high orbital eccentricities but also alter the planetary orbital inclination, the classical Keplerian orbital model is no longer applicable for orbital retrieval. The…
Simulating the evolution of the gravitational N-body problem becomes extremely computationally expensive as N increases since the problem complexity scales quadratically with the number of bodies. We study the use of Artificial Neural…
We construct an advanced model for interacting multiple stellar systems in which we compute all trajectories with a numerical N-body integrator, namely the Bulirsch--Stoer from the SWIFT package. We can then derive various observables:…
Gravitational scattering of small bodies (planetesimals) by a planet remains a fundamental problem in celestial mechanics. It is traditionally modeled within the circular restricted three-body problem (CR3BP), where individual particle…
Group-level behaviour of particles undergoing a velocity jump process with hard-sphere interactions is investigated. We derive $N$-particle transport equations that include the possibility of collisions between particles and apply different…
The "gravitational million-body problem," to model the dynamical evolution of a self-gravitating, collisional N-body system with ~10^6 particles over many relaxation times, remains a major challenge in computational astrophysics.…
We perform N-body simulations of young triple systems consisting of two low-mass companions orbiting around a significantly more massive primary. We find that, when the orbits of the companions are coplanar and not too widely separated, the…
One of the fundamental aspects of statistical behaviour in many-body systems is exponential divergence of neighbouring orbits, which is often discussed in terms of Liapounov exponents. Here we study this topic for the classical…
Short-period super-Earths and mini-Neptunes encircle more than $\sim50\%$ of Sun-like stars and are relatively amenable to direct observational characterization. Despite this, environments in which these planets accrete are difficult to…
We present a catalog of precise eclipse times and analysis of third body signals among 1279 close binaries in the latest Kepler Eclipsing Binary Catalog. For these short period binaries, Kepler's 30 minute exposure time causes significant…
To improve our understanding of orbital instabilities in compact planetary systems, we compare suites of $N$-body simulations against numerical integrations of simplified dynamical models. We show that, surprisingly, dynamical models that…