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Accurate orbit modeling plays a key role in contemporary and future space missions such as GRACE and its successor GRACE-FO, GNSS, and altimetry missions. To fully exploit the technological capabilities and correctly interpret measurements,…
We consider finite element approximations of ill-posed elliptic problems with conditional stability. The notion of {\emph{optimal error estimates}} is defined including both convergence with respect to mesh parameter and perturbations in…
Complete waveform models able to account for arbitrary non-planar orbits represent a holy grail in current gravitational-wave astronomy. Here, we take a step towards this direction and present a simple yet efficient prescription to obtain…
Analytic modeling of gravitational waves from inspiraling eccentric binaries poses an interesting mathematical challenge. When constructing analytic waveforms in the frequency domain, one has to contend with the fact that the phase of the…
It seems self-evident that a density functional calculation should be normalized to the number of electrons in the system. We present multiple examples where the accuracy of the approximate energy is improved (sometimes greatly) by…
This work presents a new parametrisation suitable for parameter-space studies of heliocentric Earth-impacting orbits. Originally motivated by the issue of potentially hazardous asteroids (PHAs) and the mitigation of such a risk, we show…
Implementing a single qubit unitary is often hampered by imperfect control. Systematic amplitude errors $\epsilon$, caused by incorrect duration or strength of a pulse, are an especially common problem. But a sequence of imperfect pulses…
We present a new approximate method for constructing gravitational radiation driven inspirals of test-bodies orbiting Kerr black holes. Such orbits can be fully described by a semi-latus rectum $p$, an eccentricity $e$, and an inclination…
Building initial conditions for generic binary black-hole evolutions without initial spurious eccentricity remains a challenge for numerical-relativity simulations. This problem can be overcome by applying an eccentricity-removal procedure…
The approximate Carath\'eodory theorem states that given a compact convex set $\mathcal{C}\subset\mathbb{R}^n$ and $p\in\left[2,+\infty\right[$, each point $x^*\in\mathcal{C}$ can be approximated to $\epsilon$-accuracy in the $\ell_p$-norm…
We develop a relativistically accurate formalism to model the interaction between stellar mass compact objects embedded in thin accretion disks around a non-spinning supermassive black hole, using tools from self-force theory and…
We are concerned with the homogenization of second-order linear elliptic equations with random coefficient fields. For symmetric coefficient fields with only short-range correlations, quantified through a logarithmic Sobolev inequality for…
Gravitational features are a fundamental source of information to learn more about the interior structure and composition of planets, moons, asteroids and comets. Gravitational field modeling typically approximates the target body with a…
Closed-form expressions for the ringdown complex amplitudes of nonspinning unequal-mass binaries in arbitrarily eccentric orbits are presented. They are built upon 237 numerical simulations contained within the RIT catalog, through the…
Spatially localized one-electron orbitals, orthogonal and nonorthogonal, are widely used in electronic structure theory to describe chemical bonding and speed up calculations. In order to avoid linear dependencies of localized orbitals, the…
Exploiting simple yet remarkable properties of relativistic gravitational scattering, we use first-order self-force (linear-in-mass-ratio) results to obtain arbitrary-mass-ratio results for the complete third-subleading post-Newtonian…
In hierarchical triple systems, the inner binary is slowly perturbed by a distant companion, giving rise to large-scale oscillations in eccentricity and inclination, known as von-Zeipel-Lidov-Kozai (ZLK) oscillations. Stable systems with a…
Building upon recent work, we present an improved effective-one-body (EOB) model for spin-aligned, coalescing, black hole binaries with generic orbital configurations, i.e. quasi-circular, eccentric or hyperbolic orbits. The model relies on…
This paper deals with some nonlinear problems which exponential and biexponential decays are involved in. A proof of the quasiconvexity of the error function in some of these problems of optimization is presented. This proof is restricted…
We discuss the equilibrium conditions for a body made of two homogeneous components separated by oblate spheroidal surfaces and in relative motion. While exact solutions are not permitted for rigid rotation (unless a specific ambient…