Related papers: Closed-Form Statistical Relations Between Projecte…
We present several closed-form expressions of useful mass distributions. These include the potentials and accelerations of circular rings and arcs, the potentials of uniform density rings and arcs at arbitrary eccentricities, and the…
Starting with just the assumption of uniformly distributed orbital orientations, we derive expressions for the distributions of the Keplerian orbital elements as functions of arbitrary distributions of eccentricity and semi-major axis. We…
Radial velocity searches for extrasolar planets have discovered stars undergoing slow accelerations. The accelerations are likely due to one or more gas giant planets or brown dwarfs orbiting with period longer than the total time span of…
Satellite conjunctions involving "near misses" of space objects are becoming increasingly likely. One approach to risk analysis for them involves the computation of the collision probability, but this has been regarded as having some…
Turbulent relative dispersion is studied theoretically with a focus on the evolution of probability distribution of the relative separation of two passive particles. A finite separation speed and a finite correlation of relative velocity,…
We perform direct numerical simulations of a bi-disperse suspension of heavy spherical particles in forced, homogeneous, and isotropic three-dimensional turbulence. We compute the joint distribution of relative particle distances and…
This work sheds some light on the relationship between a distribution's standard deviation and its range, a topic that has been discussed extensively in the literature. While many previous studies have proposed inequalities or relationships…
We describe statistical methods for measuring the exoplanet multiplicity function - the fraction of host stars containing a given number of planets - from transit and radial-velocity surveys. The analysis is based on the approximation of…
Mean-motion resonances between a Keplerian disc and an orbiting companion are analysed within a Hamiltonian formulation using complex canonical Poincare variables, which are ideally suited to the description of eccentricity and inclination…
The Fisher-Rao distance is the geodesic distance between probability distributions in a statistical manifold equipped with the Fisher metric, which is a natural choice of Riemannian metric on such manifolds. It has recently been applied to…
Two-body interactions play a major role in shaping the structural and dynamical properties of globular clusters (GCs) over their long-term evolution. In particular, GCs evolve toward a state of partial energy equipartition that induces a…
In order to study the internal dynamics of actual galaxy pairs, we need to derive the probability distribution function (PDF) of true 3D (orbital) intervelocities and interdistances between pair members from their observed (projected)…
There are two popular ways to speed up simulations of planet formation via increasing the collision probability: ({\it i}) confine motion to 2D, ({\it ii}) artificially enhance the physical radii of the bodies by an expansion factor. In…
The final "giant-impact" phase of terrestrial planet formation is believed to begin with a large number of planetary "embryos" on nearly circular, coplanar orbits. Mutual gravitational interactions gradually excite their eccentricities…
The statistical distribution of the radial pairwise peculiar velocity of galaxies is known to have an exponential form as implied by observations and explicitly shown in N-body simulations. Here we calculate its statistical distribution…
We derive a simple closed-form expression, relating $\vs(r)$ -- the mean relative velocity of pairs of galaxies at fixed separation $r$ -- to the two-point correlation function of mass density fluctuations, $\xi(r)$. We compare our analytic…
We use numerical $N$-body experiments to explore the statistics of multiple systems formed in small-$N$ subclusters, i.e. the distributions of orbital semi-major axis, $a$, orbital eccentricity, $e$, mass ratio, $q$, mutual orbital…
In the framework of the semiclassical approach the universal spectral correlations in the Hamiltonian systems with classical chaotic dynamics can be attributed to the systematic correlations between actions of periodic orbits which (up to…
Binary stars and higher-order multiple systems are an ubiquitous outcome of star formation, especially as the system mass increases. The companion mass-ratio distribution is a unique probe into the conditions of the collapsing cloud core…
After a brief discussion of the concepts of fractional exchange and fractional exclusion statistics, we report partly analytical and partly numerical results on thermodynamic properties of assemblies of particles obeying fractional…