相关论文: Orbital Acceleration Using Product of Exponentials

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…

In this work, an explicit formula is deduced for identifying the orbital angular moment (OAM) of vectorial vortex with space-variant state of polarization (SOP). Different to scalar vortex, the OAM of vectorial vortex can be attributed to…

In Paper I, the effective one-electron potentials (OEP) method was introduced and demonstrated as an efficient approach to reduce the computational cost of evaluation of the charge-transfer interaction energy within the effective fragment…

We consider functional differential equations(FDEs) which are perturbations of smooth ordinary differential equations(ODEs). The FDE can involve multiple state-dependent delays or distributed delays (forward or backward). We show that,…

An alternative derivation of the first-order relativistic contribution to perihelic precession is presented. Orbital motion in the Schwarzschild geometry is considered in the Keplerian limit, and the orbit equation is derived for…

The observation data for artificial celestial body 43096, which had been obtained during 2006-2012 within the framework of international project "The Scientific Network of Optical Instruments for Astrometric and Photometric Observations" -…

When a test particle moves about an oblate spheroid, it is acted upon, among other things, by two standard perturbing accelerations. One, of Newtonian origin, is due to the quadrupole mass moment $J_2$ of the orbited body. The other one, of…

Inspirals of stellar mass compact objects into massive black holes are an important source for future gravitational wave detectors such as Advanced LIGO and LISA. Detection of these sources and extracting information from the signal relies…

We present a novel population-based Bayesian inference approach to model the average and population variance of spatial distribution of a set of observables from ensemble analysis of low signal-to-noise ratio measurements. The method…

Eccentricity of binary systems is not a gauge invariant quantity, but has an important impact on the observed gravitational wave signal of such systems, generating power in all possible harmonics of the orbital period. We here clarify the…

We provide a recursive method for constructing product formula approximations to exponentials of commutators, giving the first approximations that are accurate to arbitrarily high order. Using these formulas, we show how to approximate…

Ordinary differential equations (ODEs) are used to model dynamic systems appearing in engineering, physics, biomedical sciences and many other fields. These equations contain unknown parameters, say $\bm\theta$ of physical significance…

Product of experts (PoE) are layered networks in which the value at each node is an AND (or product) of the values (possibly negated) at its inputs. These were introduced as a neural network architecture that can efficiently learn to…

The orbital sampling effect (OSE) appears in phase-folded transit light curves of extrasolar planets with moons. Analytical OSE models have hitherto neglected stellar limb darkening and non-zero transit impact parameters and assumed that…

Time series forecasting is an active research topic in academia as well as industry. Although we see an increasing amount of adoptions of machine learning methods in solving some of those forecasting challenges, statistical methods remain…

Parameter estimation for ordinary differential equations (ODEs) plays a fundamental role in the analysis of dynamical systems. Generally lacking closed-form solutions, ODEs are traditionally approximated using deterministic solvers.…

In the past decade, photoemission orbital tomography (POT) has evolved into a powerful tool to investigate the electronic structure of organic molecules adsorbed on (metallic) surfaces. By measuring the angular distribution of…

We study theoretically the phoretic motion of a spheroidal particle, which generates solute gradients in the surrounding unbounded solvent via chemical reactions active on its surface in a cap-like region centered at one of the poles of the…

In this paper we discuss the development of a fast and accurate waveform model for the quasi-circular orbital evolution of extreme-mass-ratio-inspirals (EMRIs). This model simply employs the data of a few numerical Teukoulsky-based energy…

The parameterised post-Newtonian (PPN) formalism is a weak-field slow-motion approximation for both GR and some of its generalisations. It permits various parameterisations of the motion, among which are the Lagrange-type and Gauss-type…