Related papers: Orbital Divergence and Relaxation in the Gravitati…
We study the relaxation towards thermodynamical equilibrium of a 1-D gravitational system. This OSC model shows a series of critical energies $E_{cn}$ where new equilibria appear and we focus on the homogeneous ($n=0$), one-peak ($n=\pm 1$)…
Using the Ricci and scalar curvatures of the configuration manifold of gravitational N-body systems, we study the exponential instability in their trajectories. It is found that the exponentiation time-scale for isotropic Plummer spheres…
The evolution of closed gravitational systems is studied by means of $N$-body simulations. This, as well as being interesting in its own right, provides insight into the dynamical and statistical mechanical properties of gravitational…
Collisional relaxation describes the stochastic process with which a self-gravitating system near equilibrium evolves in phase space due to the fluctuating gravitational field of the system. The characteristic timescale of this process is…
We report results of collisional N-body simulations aimed to study the N-dependance of the dynamical evolution of star clusters. Our clusters consist of equal-mass stars and are in virial equilibrium. Clusters moving in external tidal…
Using direct $N$-body simulations of self-gravitating systems we study the dependence of dynamical chaos on the system size $N$. We find that the $N$-body chaos quantified in terms of the largest Lyapunov exponent $\Lambda_{\rm max}$…
The stability of the dynamical trajectories of softened spherical gravitational systems is examined, both in the case of the full $N$-body problem and that of trajectories moving in the gravitational field of non-interacting background…
The gravitational three-body problem is a fundamental problem in physics and has significant applications to astronomy. Three-body configurations are often considered stable as long the system is hierarchical; that is, the two orbital…
The gravitational interaction among bodies orbiting in a spherical potential leads to the rapid relaxation of the orbital planes' distribution, a process called vector resonant relaxation. We examine the statistical equilibrium of this…
We consider the use of N-body simulations for studying the evolution of rich star clusters (i.e. globular clusters). The dynamical processes included in this study are restricted to gravitational (point-mass) interactions, the steady tidal…
I consider a self-gravitating, N-body system assuming that the N constituents follow regular orbits about the center of mass of the cluster, where a central massive object may be present. I calculate the average over a characteristic…
This paper summarises a numerical investigation of the statistical properties of orbits evolved in `frozen,' time-independent N-body realisations of smooth, time-independent density distributions, allowing for 10^(2.5)<N<10^(5.5). Two…
I present empirical measurements of the rate of relaxation in N-body simulations of stable spherical systems and distinguish two separate types of relaxation: energy diffusion that is largely independent of particle mass, and energy…
We address the dynamical evolution of an isolated self--gravitating system with two stellar mass groups. We vary the individual ratio of the heavy to light bodies, $\mu$ from 1.25 to 50 and alter also the fraction of the total heavy mass…
We present N-body simulations of dissolving star clusters close to galactic centres. For this purpose, we developed a new N-body program called nbody6gc based on Aarseth's series of N-body codes. We describe the algorithm in detail. We…
Some points related to the exponential instability of N-body gravitating systems and which are misinterpreted in various papers are clarified. Exponential instability is a phenomenon essentially responsible for the relaxation, evolutionary,…
We revisit the r\^{o}le of discreteness and chaos in the dynamics of self-gravitating systems by means of $N$-body simulations with active and frozen potentials, starting from spherically symmetric stationary states and considering the…
We study the phase-space behaviour of nearby trajectories in integrable potentials. We show that the separation of nearby orbits initially diverges very fast, mimicking a nearly exponential behaviour, while at late times it grows linearly.…
Simulations of purely self-gravitating N-body systems are often used in astrophysics and cosmology to study the collisionless limit of such systems. Their results for macroscopic quantities should then converge well for sufficiently large…
Evaporative evolution of stellar clusters is shown to be relaxation limited when the number of stars satisfies $N>>N_c$, where $N_c\simeq 1600$. For a Maxwell velocity distribution that extends beyond the escape velocity, this process is…