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Assemblies of anisotropic particles commonly appear in studies of active many-body systems. However, in two dimensions, the geometric ramifications of the finite density of such objects are not entirely understood. To fully characterize…
A method is presented for finding anisotropic distribution functions for stellar systems with known, spherically symmetric, densities, which depends only on the two classical integrals of the energy and the magnitude of the angular…
Planets and satellites orbiting a binary system exist in the solar system and extrasolar planetary systems. Their orbits can be significantly different from Keplerian orbits, if they are close to the binary and the secondary-to-primary mass…
We develop an analytic approach to evaluating the density $\rho ({\cal E},\Gamma)$ of complex resonance poles with real energies $\mathcal{E}$ and widths $\Gamma$ in the pure reflection problem from a one-dimensional disordered sample with…
Approximate analytical closed energy formulas for semirelativistic Hamiltonians of the form $\sigma\sqrt{\bm p^{2}+m^2}+V(r)$ are obtained within the framework of the auxiliary field method. This method, which is equivalent to the envelope…
We study eccentric equatorial orbits of a test-body around a Kerr black hole under the influence of gravitational radiation reaction. We have adopted a well established two-step approach: assuming that the particle is moving along a…
Given a point $A$ in the convex hull of a given adjoint orbit $\mathcal{O}(F)$ of a compact Lie group $G$, we give a polynomial time algorithm to compute the probability density supported on $\mathcal{O}(F)$ whose expectation is $A$ and…
We study surfaces in Euclidean space ${\mathbb R}^3$ that are minimal for a log-linear density $\phi(x,y,z)=\alpha x+\beta y+\gamma y$, where $\alpha,\beta,\gamma$ are real numbers not all zero. We prove that if a surface is $\phi$-minimal…
Compact binaries can have non-negligible orbital eccentricities in the frequency band of ground-based gravitational-wave detectors, depending on their astrophysical formation channels. To accurately determine the parameters of such systems,…
As a generalisation of the periodic orbit structure often seen in reflection or mirror symmetric MHD equilibria, we consider equilibria with other orientation-reversing symmetries. An example of such a symmetry, which is a not a reflection,…
Recently, gas giant planets in nearly circular orbits with large semimajor axes ($a \sim$ 30--1000AU) have been detected by direct imaging. We have investigated orbital evolution in a formation scenario for such planets, based on core…
Motivated by recent experimental progress, we study scalar wave propagation over an imperfect draining vortex, which can serve as an analogue for rotating and non-rotating extreme compact objects (ECOs). We encapsulate the absorbing…
We use archived IRAC images from the Spitzer Space Telescope to show that many Class 0 protostars exhibit complex, irregular, and non-axisymmetric structure within their dusty envelopes. Our 8 $\mu$m extinction maps probe some of the…
We investigate the set of parameters $\kappa\in\C$ for which the singular orbit $(0,e^{\kappa},...)$ of $E_{\kappa}(z):=\exp(z+\kappa)$ converges to $\infty$. These parameters are organized in smooth curves in parameter space called…
In this paper we prove the following theorem. Let $f:\mathbb{A}^2\rightarrow \mathbb{A}^2$ be a dominate polynomial endomorphisms defined over an algebraically closed field $k$ of characteristic $0$. If there are no nonconstant rational…
In this work we present an alternative method to obtain a distribution of particles over an hyper surface, such that they obey a rest-mass density distribution $\rho(x^i)$. We use density profiles that can be written as…
Accurate inclusion of both spin precession and orbital eccentricity effects in gravitational waveform models represents a key hurdle in our ability to fully characterize the properties of compact binaries. Virtually all efforts to model…
We investigate the dynamics in a galactic potential with two reflection symmetries. The phase-space structure of the real system is approximated with a resonant detuned normal form constructed with the method based on the Lie transform.…
We show that the aspherical manifolds produced via the relative strict hyperbolization of polyhedra enjoy many group-theoretic and topological properties of open finite volume negatively pinched manifolds, including relative hyperbolicity,…
Although shape correspondence is a central problem in geometry processing, most methods for this task apply only to two-dimensional surfaces. The neglected task of volumetric correspondence--a natural extension relevant to shapes extracted…