Related papers: Using Correlation Integrals to Characterize 3D Ste…
For almost a century, since Bernal\'s attempts at a molecular theory of liquid structure(Bernal [1]), correlation functions have been the bridge to compare theoretical calculations with experimental measurements in the study of disordered…
Recently 3D hydrodynamical simulations of stellar surface convection have become feasible thanks to advances in computer technology and efficient numerical algorithms. Available observational diagnostics indicate that these models are…
We review the available methods for estimating actions, angles and frequencies of orbits in both axisymmetric and triaxial potentials. The methods are separated into two classes. Unless an orbit has been trapped by a resonance, convergent,…
Scaling regions -- intervals on a graph where the dependent variable depends linearly on the independent variable -- abound in dynamical systems, notably in calculations of invariants like the correlation dimension or a Lyapunov exponent.…
We have developed an orbit-based method for constructing triaxial models of elliptical galaxies, which fit their observed surface brightness and kinematics. We have tested the method against analytical models with general distribution…
Using the orbit method we attempt to reveal geometric and algebraic meaning of separation of variables for the integrable systems on coadjoint orbits in an $\mathfrak{sl}(3)$ loop algebra. We consider two types of generic orbits embedded…
We present a fast method for estimating the cosmic microwave background polarization power spectra using unbiased estimates of heuristically-weighted correlation functions. This extends the O(N_pix^(3/2)) method of Szapudi et al. (2001) to…
Nine of the most important estimators known for the two-point correlation function are compared using a predetermined, rigorous criterion. The indicators were extracted from over 500 subsamples of the Virgo Hubble Volume simulation cluster…
Separation of variables by means of the orbit method is implemented to integrable systems on coadjoint orbits in an $\mathfrak{sl}(4)$ loop algebra. This is a development and a kind of explanation for Sklyanin's procedure of separation of…
The herein presented analytical framework fully describes the motion of coplanar systems consisting of a stellar binary and a planet orbiting both stars on orbital as well as secular timescales. Perturbations of the Runge-Lenz vector are…
Doppler tomography is a method to compute the emissivity distribution within the co-rotating frames of binary stars from observations of their emission line profiles at multiple orbital phases. A key assumption of the method as it is…
Properly estimating correlations between objects at different spatial scales necessitates $\mathcal{O}(n^2)$ distance calculations. For this reason, most widely adopted packages for estimating correlations use clustering algorithms to…
We present an approach for utilizing astrometric orbit information to improve the yield of planetary images and spectra from a follow-on direct detection mission. This approach is based on the notion-strictly hypothetical-that if a…
In this paper, two models of interest for Celestial Mechanics are presented and analysed, using both analytic and numerical techniques, from the point of view of the possible presence of regular and/or chaotic motion, as well as the…
Action-angle coordinates are an essential tool for understanding the properties of the six dimensional phase space involved in orbits of stars in galactic potentials. A new method, which does not require specific knowledge of a generating…
Previous work on three-point statistics of cosmic shear has mainly concentrated on the convergence, or on aperture measures of the shear. However, as has become clear recently for the two-point statistics of cosmic shear, the basic quantity…
The angular correlation is a method for measuring the distribution of structure in the Universe, through the statistical properties of the angular distribution of galaxies on the sky. We measure the angular correlation of galaxies from the…
Context: Two-point correlation functions are used throughout cosmology as a measure for the statistics of random fields. When used in Bayesian parameter estimation, their likelihood function is usually replaced by a Gaussian approximation.…
This work describes the fully analytical method for calculation of the molecular integrals over Slater-type orbitals with non-integer principal quantum numbers. These integrals are expressed through relativistic molecular auxiliary…
We review in brief the development and implementation of the Star integral, a tool yielding measurements of correlations much superior to conventional methods. A version for use in pion interferometry is explained. We also show how effects…