Related papers: Hybrid Perturbation methods based on Statistical T…
Fast and precise propagation of satellite orbits is required for mission design, orbit determination in support of operations and payload data analysis. This demand must also comply with the different accuracy requirements set by a growing…
Inspiralling and coalescing binary black holes are promising sources of gravitational radiation. The orbital motion and gravitational-wave emission of such system can be modelled using a variety of approximation schemes and numerical…
A method is suggested for treating those complicated physical problems for which exact solutions are not known but a few approximation terms of a calculational algorithm can be derived. The method permits one to answer the following rather…
This chapter provides an introduction to Hybrid High-Order (HHO) methods. These are new generation numerical methods for PDEs with several advantageous features: the support of arbitrary approximation orders on general polyhedral meshes,…
We present a new method for computing orbits in the perturbed two-body problem: the position and velocity vectors of the propagated object in Cartesian coordinates are replaced by eight orbital elements, i.e., constants of the unperturbed…
This work presents an analytical perturbation method to define and study the dynamics of frozen orbits under the perturbation effects produced by the oblatness of the main celestial body. This is done using a perturbation method purely…
This article aims to provide an accessible, tutorial-style introduction to hybrid extremum-seeking systems, which are model-free, feedback-optimization controllers that incorporate hybrid dynamics, meaning both continuous-time and…
A model-based approach to forecasting chaotic dynamical systems utilizes knowledge of the physical processes governing the dynamics to build an approximate mathematical model of the system. In contrast, machine learning techniques have…
An analytical solution to the Hill problem Hamiltonian expanded about the libration points has been obtained by means of perturbation techniques. In order to compute the higher orders of the perturbation solution that are needed to capture…
The non-integrability of the Hill problem makes that its global dynamics must be necessarily approached numerically. However, the analytical approach is feasible in the computation of relevant solutions. In particular, the nonlinear…
Explaining predictions based on multivariate time series data carries the additional difficulty of handling not only multiple features, but also time dependencies. It matters not only what happened, but also when, and the same feature could…
Fast and precise propagation of satellite orbits is required for mission design, orbit determination and payload data analysis. We present a method to improve the computational performance of numerical propagators and simultaneously…
Electromagnetic waves interacting with three--dimensional periodic structures occur in many applications of great scientific and engineering interest. These three dimensional interactions are extremely complicated and subtle, so it is…
The increasing penetration of inertialess new renewable energy sources reduces the overall mechanical inertia available in power grids and accordingly raises a number of issues of grid stability over short to medium time scales. It has been…
Perturbative gadgets are general techniques for reducing many-body spin interactions to two-body ones using perturbation theory. This allows for potential realization of effective many-body interactions using more physically viable two-body…
High levels of air pollution may seriously affect people's living environment and even endanger their lives. In order to reduce air pollution concentrations, and warn the public before the occurrence of hazardous air pollutants, it is…
We consider a class of autonomous Hamiltonian systems subject to small, time-periodic perturbations. When the perturbation parameter is set to zero, the energy of the system is preserved. This is no longer the case when the perturbation…
An efficient hybrid numerical method for multiple scattering calculations is proposed. We use the well established doubling--adding method to find the reflection function of the lowermost homogeneous slab comprising the atmosphere of our…
We present a diffusion mechanism for time-dependent perturbations of autonomous Hamiltonian systems introduced in [25]. This mechanism is based on shadowing of pseudo-orbits generated by two dynamics: an `outer dynamics', given by…
A perturbation theory modification of the Flory-Huggins polymer solution theory is presented. The proposed perturbation equation utilizes the results by Tukur et al [J. Chem. Phys. 110 (7), 3463, 1999] for hard-sphere binary mixture at…