Related papers: Envelopes for orbits around axially symmetric sour…

We recently found that regular orbits in axially symmetric galactic disks have their envelopes $Z(R)$ accurately described by the relation $Z(R)\propto[\Sigma_I(R)]^{-1/3}$, if their amplitudes are comparable to the disk thickness, where…

A class of complete potential-density basis sets in cylindrical (R,phi,z) coordinates is presented. This class is suitable for stability studies of galactic disks in three dimensions and includes basis sets tailored for disks with vertical…

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…

This paper explores orbits in extended mass distributions and develops an analytic approximation scheme based on epicycloids (spirograph patterns). We focus on the Hernquist potential which provides a good model for many astrophysical…

A closed-form expression is obtained for the density of a simple layer, equipotential to an oblate level ellipsoid of revolution in an outer space. The potential of any level spheroid of positive mass with the inward direction of attracting…

Massive planetary cores embedded in protoplanetary discs are believed to accrete extended atmospheres, providing a pathway to forming gas giants and gas-rich super-Earths. The properties of these atmospheres strongly depend on the nature of…

Obtaining general relations between macroscopic properties of random assemblies, such as density, and the microscopic properties of their constituent particles, such as shape, is a foundational challenge in the study of amorphous materials.…

Stellar-mass compact binaries in eccentric orbits are almost guaranteed sources of gravitational waves for Laser Interferometer Space Antenna. We present a prescription to compute accurate and efficient gravitational-wave polarizations…

The asymptotic form of the energy density for a gas of particles surrounding a sphere of mass $M$ and radius $R$ is studied using Einstein's equations. It is shown that if the pressure of the gas $p$ varies linearly with the energy density…

We provide a description of a thin accretion disc for a static spherically symmetric black holes in $f(R)$ gravity. In this regard, we first study the horizons of black holes in $f(R)$ gravity. The equation of motion and effective potential…

We show that the gravitational waveform emitted by a binary on an eccentric orbit can be naturally decomposed into a series of harmonics. The frequencies of these harmonics depend upon the radial frequency, $f_{\mathrm{r}}$, determined by…

In this study, we begin by revisiting the oscillatory behavior of radiative quantities-energy, angular momentum, and linear momentum-linked with initial eccentricities in binary black hole (BBH) mergers. By varying the mean anomaly $l_0$…

Spiral density waves observed in protoplanetary discs have often been used to infer the presence of embedded planets. This inference relies both on simulations as well as the linear theory of planet-disc interaction developed for planets on…

We derive a semiclassical trace formula for a symmetry reduced part of the spectrum in axially symmetric systems. The classical orbits that contribute are closed in (\rho,z,p_\rho,p_z) and have p_\phi = m\hbar where m is the azimuthal…

We consider anisotropic fluids with directional pressures $p_i = w_i \rho$ ($\rho$ is the density, $w_i = $const, $i = 1,2,3$) as sources of gravity in stationary cylindrically symmetric space-times. We describe a general way of obtaining…

We propose a system of real-space envelope function equations without fitting parameters for modeling the electronic spectrum and wave functions of a phosphorus donor atom embedded in silicon. The approach relies on the Burt-Foreman…

Suppose A is a finite set equipped with a probability measure P and let M be a ``mass'' function on A. We give a probabilistic characterization of the most efficient way in which A^n can be almost-covered using spheres of a fixed radius. An…

A useful crude approximation for Abelian functions is developed and applied to orbits. The bound orbits in the power-law potentials A*r^{-alpha} take the simple form (l/r)^k = 1 + e cos(m*phi), where k = 2 - alpha > 0 and 'l' and 'e' are…

Let $M$ be a compact $n$-dimensional Riemanian manifold, End($M$) the set of the endomorphisms of $M$ with the usual $\mathcal{C}^0$ topology and $\phi: M\to\mathbb{R}$ continuous. We prove that there exists a dense subset of $\mathcal{A}$…

For a continuous map $f$ on a compact metric space we study the geometry and entropy of the generalized rotation set $\R(\Phi)$. Here $\Phi=(\phi_1,...,\phi_m)$ is a $m$-dimensional continuous potential and $\R(\Phi)$ is the set of all…