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We introduce new machine-learning techniques for analyzing chaotic dynamical systems. The primary objectives of the study include the development of a new and simple method for calculating the Lyapunov exponent using only two trajectory…
For a fast particle moving within a two-dimensional array of soft scatterers - centers of weak and short-range potential - the dependence of the Lyapunov exponent on the system parameters is studied. The use of the linearized equations for…
The threshold, or saturation phenomenon of spatially coupled systems is revisited in the light of Lyapunov's theory of dynamical systems. It is shown that an application of Lyapunov's direct method can be used to quantitatively describe the…
Preliminary low-thrust spacecraft mission design is a global search problem characterized by a complex solution landscape, multiple objectives, and numerous local minima. During this phase, mission parameters are often not yet fully…
The rapid growth of cislunar activities, including lunar landings, the Lunar Gateway, and in-space refueling stations, requires advances in cost-efficient trajectory design and reliable integration of navigation and remote sensing.…
Electric propulsion is used to maximize payload capacity in communication satellites. These orbit raising maneuvers span several months and hundreds of revolutions, making trajectory design a complex challenge. The literature typically…
Several studies have shown that stellar activity features, such as occulted and non-occulted starspots, can affect the measurement of transit parameters biasing studies of transit timing variations and transmission spectra. We present…
During recent decades, there has been a substantial development in optimal mass transport theory and methods. In this work, we consider multi-marginal problems wherein only partial information of each marginal is available, which is a setup…
Radiative transfer calculations are essential for modeling planetary atmospheres. However, standard methods are computationally demanding and impose accuracy-speed trade-offs. High computational costs force numerical simplifications in…
The Lyapunov exponent, serving as an indicator of the localized state, is commonly utilized to identify localization transitions in disordered systems. In non-Hermitian quasicrystals, the non-Hermitian effect induced by non-reciprocal…
Recently Kipping (2021) identified the so-called "exomoon corridor", a potentially powerful new tool for identifying possible exomoon hosts, enabled by the observation that fully half of all planets hosting an exomoon will exhibit transit…
We present a purely algebraic formulation (i.e. polynomial equations only) of the minimum-cost multi-impulse orbit transfer problem without time constraints, while keeping all the variables with a precise physical meaning. We apply general…
The increasing number of transiting exoplanets sparked a significant interest in discovering their moons. Most of the methods in the literature utilize timing analysis of the raw light curves. Here we propose a new approach for the direct…
In this paper, we present a new method for the solution of those linear transport processes that may be described by a Master Equation, such as electron, neutron and photon transport, and more exotic variants thereof. We base our algorithm…
Modern theoretical estimates show that with the help of real equipment we are able to detect large satellites of exoplanets (about the size of the Ganymede), although, numerical attempts of direct exomoon detection were unsuccessful. Lots…
This paper presents the use of multi-sensor measurement system to guide autonomous mobile robot in the house. The system allows the 3D image acquisition to global mapping, and algorithms to reduce the dimensionality of images to 2D global…
Transmission spectroscopy is a key technique in the characterization of exoplanet atmospheres and has been widely applied to planets undergoing hydrodynamic escape. While a robust analytic theory exists for transmission spectra of…
We propose an extension of the computational fluid mechanics approach to the Monge-Kantorovich mass transfer problem, which was developed by Benamou-Brenier. Our extension allows optimal transfer of unnormalized and unequal masses. We…
We present an efficient and validated method for approximating the stationary measures of random dynamical systems with smooth additive noise. The approach leverages the strong regularizing properties of the associated transfer operator…
Transition path theory (TPT) offers a powerful formalism for extracting the rate and mechanism of rare dynamical transitions between metastable states. Most applications of TPT either focus on systems with modestly sized state spaces or use…