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Reliable studies of the long-term dynamics of planetary systems require numerical integrators that are accurate and fast. The challenge is often formidable because the chaotic nature of many systems requires relative numerical error bounds…
A considerable number of astrometric binaries whose positions on the sky do not obey the standard model of mean position, parallax and linear proper motion, were observed by the Hipparcos satellite. Some of them remain non-discovered, and…
We analyze archival data from Bailey and co-workers from the $Magellan$ adaptive optics system and present the first 0.9 $\mu$m detection ($z' = 20.3\pm0.4$ mag; $\Delta z'=13.0\pm0.4$ mag) of the 11 $M_\mathrm{Jup}$ circumbinary planet HD…
This paper introduces a novel Homogeneous Second-order Descent Ascent (HSDA) algorithm for nonconvex-strongly concave minimax optimization problems. At each iteration, HSDA uniquely computes a search direction by solving a homogenized…
We report the discovery of a multi-planet system orbiting HD 106315, a rapidly rotating mid F-type star, using data from the K2 mission. HD 106315 hosts a $2.51\pm0.12\,R_\oplus$ sub-Neptune in a 9.5 day orbit, and a…
We study the dynamics of systems consisting of two spatially segregated ODE compartments coupled through a one-dimensional bulk diffusion field. For this coupled PDE-ODE system, we first employ a multi-scale asymptotic expansion to derive…
We present IAS15, a 15th-order integrator to simulate gravitational dynamics. The integrator is based on a Gau\ss-Radau quadrature and can handle conservative as well as non-conservative forces. We develop a step-size control that can…
Many physical systems are governed by ordinary or partial differential equations (see, for example, Chapter ''Differential equations'', ''System of Differential Equations''). Typically the solution of such systems are functions of time or…
In this paper, a novel mutation operator of differential evolution algorithm is proposed. A new algorithm called divergence differential evolution algorithm (DDEA) is developed by combining the new mutation operator with divergence operator…
Accurate and efficient aeroelastic models are critically important for enabling the optimization and control of highly flexible aerospace structures, which are expected to become pervasive in future transportation and energy systems.…
The current orbital geometries of exoplanet systems offer a fossilized record of the systems' dynamical histories. A particularly rich set of dynamical mechanisms is available to exoplanets residing in multi-star systems, which may have…
The orbits in the HD 160691 planetary system at first appeared highly unstable, but using the MEGNO and FLI techniques of global dynamics analysis in the orbital parameter space we have found a stabilizing mechanism that could be the key to…
Many of exoplanetary systems consist of more than one planet and the study of planetary orbits with respect to their long-term stability is very interesting. Furthermore, many exoplanets seem to be locked in a mean-motion resonance (MMR),…
The new 2-planetary system around HD169830 has been announced during the XIX-th IAP Colloquium "Extrasolar Planets: Today & Tomorrow" (Paris, June 30 - July 4, 2003) by the Geneva Extrasolar Planet Search team. We study the orbital dynamics…
The intention of this article is to illustrate the use of methods from symplectic geometry for practical purposes. Our intended audience is scientists interested in orbits of Hamiltonian systems (e.g. the three-body problem). The main…
Modern Earth Observation (EO) missions generate massive volumes of imagery that challenge existing downlink and ground-processing capabilities, particularly for time-critical applications. This work investigates how a low Earth orbit (LEO)…
The method of weighted least squares is widely used in parameter estimation problems such as asteroid orbit determination. A key difficulty is the treatment of observational uncertainties, especially when combining heterogeneous datasets…
The HR 2562 system is a rare case where a brown dwarf companion resides in a cleared inner hole of a debris disk, offering invaluable opportunities to study the dynamical interaction between a substellar companion and a dusty disk. We…
HR 8799 is currently the only multiple-planet system that has been detected with direct imaging, with four giant planets orbiting at large separations from this young late A star. Orbital motion provides insight into the stability, and…
Context. The presence of a stellar companion can strongly influence the architecture and long-term stability of planetary systems. Motivated by the discovery of exoplanets exhibiting extremely high eccentricities (e >= 0.8) in systems with…