Related papers: Closed-Form Statistical Relations Between Projecte…
Recently it was shown that the ratio of kinetic and potential energy at the perihelion of a Kepler orbit relates to the ellipse eccentricity. Here, a general expression for the that ratio at any position on the orbit is presented.
Estimating the marginal likelihoods is an essential feature of model selection in the Bayesian context. It is especially crucial to have good estimates when assessing the number of planets orbiting stars when the models explain the noisy…
We describe a fast, approximate method to characterize the orbits of satellites around a central binary in numerical simulations. A goal is to distinguish the free eccentricity -- random motion of a satellite relative to a dynamically cool…
In the present work, metrics which lead to projected closed orbits are found by comparing the relativistic differential equation of orbits with the corresponding classical differential equation. Physical and geometrical properties of these…
Shapes of relative emission sources can be accessed by expanding shapes of correlations at low relative velocities in pair center of mass in Cartesian harmonics. Coefficients of expansion for correlations are related to the respective…
An analysis of the data on forward $pp, \bar pp, \pi^{\pm}p$ and $K^{\pm}p$ scattering is performed making use of the single- and double-subtraction integral and comparing with derivative dispersion relations for amplitudes. Various pomeron…
We present \texttt{ethraid}, an open source Python package designed to measure the mass ($m_c$) and separation ($a$) of a bound companion from measurements covering a fraction of the orbital period. \texttt{ethraid} constrains $m_c$ and $a$…
Propulsion of otherwise passive objects is achieved by mechanisms of active driving. We concentrate on cases in which the direction of active drive is subject to spontaneous symmetry breaking. In our case, this direction will be maintained,…
Discrete mechanics is used to present fluid mechanics, fluid-structure interactions, electromagnetism and optical physics in a coherent theoretical and numerical approach. Acceleration considered as an absolute quantity is written as a sum…
We present the statistical-mechanical theory of semiflexible polymers based on the connection between the Kratky-Porod model and the quantum rigid rotator in an external homogeneous field, and treatment of the latter using the quantum…
Following the suggestion of Black (1997) that some massive extrasolar planets may be associated with the tail of the distribution of stellar companions, we investigate a scenario in which 5 < N < 100 planetary mass objects are assumed to…
Some principles in the distribution of Centaurs and the "Scattered Disk" objects, as well as the Kuiper belt objects for its semi-major axes, eccentricities and inclinations of the orbits have been investigated. It has been established,…
A method is developed to calculate collision probability in this paper. Based on the encounter geometric features of space objects, it is reasonable to separate the radial orbital motions from that in the cross section for most encounter…
We discuss the probability distribution of relative speed $\Delta V$ of inertial particles suspended in a highly turbulent gas when the Stokes numbers, a dimensionless measure of their inertia, is large. We identify a mechanism giving rise…
In this paper we compute general-relativistic polytropic models simulating rigidly rotating, pulsating neutron stars. These relativistic compact objects, with a radius of $\sim 10 \, \mathrm{km}$ and mass between $\sim 1.4$ and $3.2$ solar…
Distance covariance and distance correlation are scalar coefficients that characterize independence of random vectors in arbitrary dimension. Properties, extensions, and applications of distance correlation have been discussed in the recent…
The research of exoplanets has entered an era in which we characterize extrasolar planets. This has become possible with measurements of radii and luminosities. Meanwhile, radial velocity surveys discover also very low-mass planets. Uniting…
We present a general method for determining the masses and orbital parameters of binary millisecond pulsars with long orbital periods (P_orb >> 1 yr), using timing data in the form of pulse frequency derivatives. We apply our method to…
This article provides an overview on the statistical modeling of complex data as increasingly encountered in modern data analysis. It is argued that such data can often be described as elements of a metric space that satisfies certain…
The computation of the two-point correlation form factor K(t) is performed for a rectangular billiard with a small size impurity inside for both periodic or Dirichlet boundary conditions. It is demonstrated that all terms of perturbation…