Body Perturbation Research Articles

Low-thrust trajectory design in low-energy regimes using variational equations

This paper proposes a novel description of the equations of motion for low-thrust trajectory design in the presence of a third-body perturbation. The framework is formulated using Gauss’ Variational Equations (GVE) with two distinct accelerations: the one produced by the electric engine and the disturbing term of the third-body effect, which is computed using the disturbing potential of the previously studied Keplerian Map. The presented GVE third-body (GVE-3B) framework allows for a simple and intuitive description of the low-thrust optimisation problem. It is accurate until very close to the sphere of influence of the perturbing body, and thus can be used to target trajectories in low-energy regimes. Together with the framework, this paper develops a methodology to generate low-energy first-guess solutions for low-thrust trajectories. Both the methodology and the framework are showcased in the design of two distinct missions: a rendezvous with asteroid 2017 SV19 during its next Earth encounter, after departing from the unstable invariant manifold of the L2 point in the Sun-Earth system, and the capture of asteroid 2018 AV2 to a stable invariant manifold of the same point.

Detweiler’s redshift invariant for extended bodies orbiting a Schwarzschild black hole

We compute the first-order self-force contribution to Detweiler's redshift invariant for extended bodies endowed with both dipolar and quadrupolar structure (with spin-induced quadrupole moment) moving along circular orbits on a Schwarzschild background. Our analysis includes effects which are second order in spin, generalizing previous results for purely spinning particles. The perturbing body is assumed to move on the equatorial plane, the associated spin vector being orthogonal to it. The metric perturbations are obtained by using a standard gravitational self-force approach in a radiation gauge. Our results are accurate through the 6.5 post-Newtonian order, and are shown to reproduce the corresponding post-Newtonian expression for the same quantity computed by using the available Hamiltonian from an effective field theory approach for the dynamics of spinning binaries.

On the Evolution of Orbits in the Outer Version of the Restricted Elliptic Doubly Averaged Three-Body Problem

The outer version of the restricted elliptic three-body problem, where a perturbed body of negligible mass is far from two bodies of finite masses (the main and perturbing ones) close to one another and its orbit is located entirely outside the orbit of the perturbing body, is considered. The terms up to the fourth order inclusive in the ratio of the orbital semimajor axes of the perturbing and perturbed bodies are retained in the expansion of the perturbing function for the problem. Explicit analytical expressions for the doubly averaged perturbing function and its derivatives with respect to the orbital elements on the right-hand sides of the evolution equations are presented. The integrable cases of the doubly averaged elliptic problem are investigated: planar and orthogonal apsidal orbits. Qualitative differences compared to the inner (satellite) version are pointed out. The evolution system is numerically integrated in the general (nonintegrable) case for a number of special initial conditions that hypothetically correspond to the orbital evolution of low-mass bodies (planetesimals, low-mass planets) in the exoplanetary system GJ 3512.

On the local and global properties of gravitational spheres of influence

ABSTRACT We revisit the concept of spheres of gravitational activity, to which we give both a geometrical and a physical meaning. This study aims to refine this concept in a much broader context that could, for instance, be applied to exo-planetary problems (in a Galactic stellar disc–star–planets system) in order to define a first-order ‘boundary’ of a planetary system. The methods used in this paper rely on classical Celestial Mechanics and develop the equations of motion in the framework of the three-body problem (e.g. Star-Planet-Satellite System). We start with the basic definition of a planet’s sphere of activity as the region of space in which it is feasible to assume the planet as the central body and the Sun as the perturbing body when computing perturbations of the satellite’s motion. We then investigate the geometrical properties and physical meaning of the ratios of solar accelerations (central and perturbing) and planetary accelerations (central and perturbing), and the boundaries they define. Throughout the paper, we clearly distinguish amongst the sphere of activity, the Chebotarev sphere (a particular case of the sphere of activity), the Laplace sphere, and the Hill sphere. The last two are often wrongfully thought to be one and the same. Furthermore, by taking a closer look at and comparing the ratio of the star’s accelerations (central/perturbing) with that of the planetary accelerations (central/perturbing) as a function of the planeto-centric distance, we have identified different dynamical regimes, which are presented in the semi-analytical analysis.

Studies on covalent functionalization of single layer black phosphorus from GW calculations based on the many body perturbation theory

The major challenge of black phosphorus (BP) is its fast-oxidative degradation in air. Organic covalent chemical modification of BP flakes could suppress the chemical degradation. Here we focus on the effects of covalent chemical modification on the electronic structures of single layer BP. We employed the state-of-the-art first principles GW method, which is based on the many body green functions, to study the covalent modification of single layer BP by forming P–C bonds. Our results show that the functional group chemisorbed at perfect lattice site results in deep in-gap state, which may deteriorate its performance, while the P–C bonds forming at single vacancies are electrically inactive. In addition, our results show that functional groups at low concentration would be preferably chemisorbed at single vacancies. At high concentration, functional groups would lead to the breaking of P–P bonds, and hence, oxygen impurity will easily insert in the interstitial position. Finally, we propose that functional groups at low concentration would protect BP from deterioration, and at high concentrations, functional groups would accelerate the deterioration of BP performance.

A study of the moderate altitude frozen orbits around the Moon

Lunar frozen orbits, characterized by fixed eccentricity and argument of perigee on average, have been previously studied using different dynamical models. In this work, frozen orbits about the Moon are investigated on the basis of an averaged Hamiltonian. The gravitational field of the Moon is considered up to the seven zonal harmonic plus the third body perturbation (Earth). The third body is assumed to move in an elliptic inclined orbit. The averaging procedure is performed through Lie transformation method. We used the eccentricity-inclination diagrams to obtain a deep insight about the evolution of frozen orbits. For the reduced system, we found two frozen solutions which correspond to argument of perigee ω=π2,3π2. Moreover, we studied the evolution of the eccentricity and inclination as a function of time. The results showed that, for moderate altitude orbits, the eccentricity oscillates with small amplitudes around its initial value, while the inclination almost remains constant. In higher altitudes case, we observed that variations in eccentricity and inclination are larger than the moderate ones. The present dynamical model gives acceptable results for low initial eccentricity and inclination.

Linearity and repeatability of postural responses in relation to peak force and impulse of manually delivered perturbations: a preliminary study.

Postural reactions (PR) of standing subjects have been mostly investigated in response to platform displacements or body perturbations of fixed magnitude. The objective of this study was to investigate the relationship between PR and the peak force and impulse of the perturbation. In ten healthy young men, standing balance was challenged by anteriorly directed perturbations (peak force: 20-60N) delivered to the back, at the lumbar (L) or inter-scapular (IS) level, by means of a manual perturbator equipped with a force sensor. Postural reactions as expressed by the displacement of the center of pressure (CoP) were recorded using a force platform. Two sets of 20 randomly ordered perturbations (10 to each site) were delivered in two separate testing sessions. The magnitude of CoP response (∆CoP) was better correlated with the impulse (I) than with the peak force of the perturbation. The normalized response, ∆CoPn = ∆CoP/I, exhibited good reliability (ICCs of 0.93 for IS and 0.82 for L), was higher with IS than with L perturbations (p < 0.01), and was significantly correlated with the latency of CoP response: r = 0.69 and 0.71 for IS and L, respectively. These preliminary findings support the concept that manually delivered perturbations can be used to reliably assess individual PR and that ∆CoPn may effectively express a relevant aspect of postural control.

Visual field motion during a body pull affects compensatory standing and stepping responses.

It is unclear whether the visual input that accompanies a perturbation of a standing person can affect whether a recovery step is taken. Visual motion speeds were manipulated during unexpected forward and backward shoulder pulls. Visual motion that appeared slower than actual body motion reduced the initial in-place resistance to the perturbation. As a result of the modulation of the in-place response, less pull force was needed to trigger a step when visual velocity appeared slower than normal. The visuomotor postural response occurred earlier and was larger when the full-field visual input was paired with a mechanical perturbation. The present study aimed to determine how visual motion evoked by an upper body perturbation during standing affects compensatory postural responses. This was investigated by rotating the visual field forwards or backwards about the ankle, time-locked to a forwards or backwards shoulder pull. Kinematic, kinetic and electromyographic responses were recorded to a range of pull forces over 160 trials in 12healthy adults (mean±SD=31±5.8years). Stepping threshold forces and in-place postural responses were compared between conditions. When the visual field moved in the same direction as the pull, so that the apparent velocity of the body was reduced (SLOW condition), the pull-force required to induce a step was less than when the visual field either rotated in the opposite direction (FAST) or was unaltered (NATURAL). For in-place responses, the body was displaced further in the direction of the pull in the SLOW condition. This was the result of a reduction in the resistive force from lower leg muscles 130ms after the visual motion onset. In trials with no pull, the visual motion induced postural responses that were later (290ms) and had smaller amplitudes compared to when visual motion is paired with an unexpected perturbation of the body. The results suggest that the apparent speed of the visual environment during a perturbation does influence whether a compensatory step is taken, not via a direct effect on the decision to step but by modulating the initial in-place response.

Frozen Orbits Construction for a Lunar Solar Sail

Frozen orbit is an attractive option for orbital design owing to its characteristics (its argument of pericenter and eccentricity are kept constant on an average). Solar sails are attractive solutions for massive and expensive missions. However, the solar radiation pressure effect represents an additional force on the solar sail that may greatly affect its orbital behavior in the long run. Thus, this force must be included as a perturbation force in the dynamical model for more accuracy. This study shows the calculations of initial conditions for a lunar solar sail frozen orbit. The disturbing function of the problem was developed to include the lunar gravitational field that is characterized by uneven mass distribution, third body perturbation, and the effect of solar radiation. An averaging technique was used to reduce the dynamical problem to a long period system. Lagrange planetary equations were utilized to formulate the rate of change of the argument of pericenter and eccentricity. Using the reduced system, frozen orbits for the Moon sail orbiter were constructed. The resulting frozen orbits are shown by two 3Dsurface (semimajor, eccentricity, inclination) figures. To simplify the analysis, we showed inclination–eccentricity contours for different values of semi-major axis, argument of pericenter, and values of sail lightness number.

(INVITED) Resonances in the Earth’s space environment

We study the presence of resonances in the region of space around the Earth. We consider a massless body (e.g, a dust particle or a small space debris) subject to different forces: the gravitational attraction of the geopotential, the effects of Sun and Moon. We distinguish different types of resonances: tesseral resonances are due to a commensurability involving the revolution of the particle and the rotation of the Earth, semi-secular resonances include the rates of variation of the mean anomalies of Moon and Sun, while secular resonances just depend on the rates of variation of the arguments of perigee and the longitudes of the ascending nodes of the massless object and perturbing bodies. We characterize such resonances, giving precise statements on the regions where the resonances can be found and provide examples of some specific commensurability relations.

Thermal evolution of silicon carbide electronic bands

Direct observation of temperature dependence of individual bands of semiconductors for a wide temperature region is not straightforward, in particular. However, this fundamental property is a prerequisite in understanding the electron-phonon coupling of semiconductors. Here we apply \emph{ab initio} many body perturbation theory to the electron-phonon coupling on hexagonal silicon carbide (SiC) crystals and determine the temperature dependence of the bands. We find a significant electron-phonon renormalization of the band gap at 0~K. Both the conduction and valence bands shift at elevated temperatures exhibiting a different behavior. We compare our theoretical results with the observed thermal evolution of SiC band edges, and discuss our findings in the light of high temperature SiC electronics and defect qubits operation.

Some Peculiarities of the Evolution of Orbits in the Satellite Restricted Elliptic Doubly Averaged Three-Body Problem

The inner (or satellite) version of the restricted elliptic three-body problem is considered. The terms up to the fourth order inclusive in small parameter are retained in the expansion of the perturbing function for the problem. The ratio of the orbital semimajor axes of perturbed and perturbing bodies is such a parameter, while their mean longitudes are the fastest variables. The Gauss scheme of independent double averaging over fast variables is used to analyze the orbital evolution of a body of negligible mass. Explicit analytical expressions for the doubly averaged perturbing function and its derivatives with respect to the elements on the right-hand sides of the evolution equations are presented. The integrable cases of the doubly averaged problem are studied in detail: planar and orthogonal apsidal orbits. The evolution system is numerically integrated in the general (nonintegrable) case for some special values of the problem parameters and initial conditions, in particular, for a set of orbital elements in which the so-called “flips”, i.e., transitions of the orbit from prograde to retrograde and vice versa, manifest themselves. In the Sun–Jupiter–asteroid model using some special asteroid orbits as an example, we show the influence of the retained fourth-order terms and the ellipticity of Jupiter’s orbit on their evolution.

Combined MCDHF-CI and MBPT calculations for n=4 to n=3 x-ray transitions in Ni-like tungsten

SynopsisThe 4d → 3p, 4p → 3s, and 4f → 3p x-ray transitions in Ni-like tungsten ions have been studied theoretically. The Multiconfiguration Dirac–Hartree–Fock method and the large-scale relativistic Configuration Interaction and Many Body Perturbation Theory methods have been employed in order to take into account electron correlation effects on the lines wavelengths.

Surface chemistry effects on work function, ionization potential and electronic affinity of Si(100), Ge(100) surfaces and SiGe heterostructures.

We combine density functional theory and many body perturbation theory to investigate the electronic properties of Si(100) and Ge(100) surfaces terminated with halogen atoms (-I, -Br, -Cl, -F) and other chemical functionalizations (-H, -OH, -CH3) addressing the absolute values of their work function, electronic affinity and ionization potential. Our results point out that electronic properties of functionalized surfaces strongly depend on the chemisorbed species and much less on the surface crystal orientation. The presence of halogens at the surface always leads to an increment of the work function, ionization potential and electronic affinity with respect to fully hydrogenated surfaces. On the contrary, the presence of polar -OH and -CH3 groups at the surface leads to a reduction of the aforementioned quantities with respect to the H-terminated system. Starting from the work functions calculated for the Si and Ge passivated surfaces, we apply a simple model to estimate the properties of functionalized SiGe surfaces. The possibility of modulating the work function by changing the chemisorbed species and composition is predicted. The effects induced by different terminations on the band energy line-up profile of SiGe surfaces are then analyzed. Interestingly, our calculations predict a type-II band offset for the H-terminated systems and a type-I band offset for the other cases.

Coupled electron-impurity and electron-phonon systems as trivial non-Fermi liquids

We consider an electron gas, both in two (2D) and three (3D) dimensions, interacting with quenched impurities and phonons within leading order finite-temperature many body perturbation theories, calculating the electron self-energies, spectral functions, and momentum distribution functions at finite temperatures. The resultant spectral function is in general highly non-Lorentzian, indicating that the system is not a Fermi liquid in the usual sense. The calculated momentum distribution function cannot be approximated by a Fermi function at any temperature, providing a rather simple example of a non-Fermi liquid with well-understood properties.

MBPT Calculations of Energy Levels for 1s2 and 1snl (N=2-5) Configuration of Helium Like Lithium Ion

In this paper, we carried out accurate energy levels calculations among the lowest 49 levels arising from the 1s2 and 1snl (n=2-5) configuration of the He-like-Li ion using the standard relativistic configuration interaction (RCI) approach and the second-order many body perturbation theory (MBPT). Both methods were implemented in the relativistic atomic code FAC. The self-consistent field approximation and the Hamiltonian effects of the Breit interaction as well as the QED effects were included to the different calculation methods. To assess the accuracy of our calculations, we performed comparison to available experimental (NIST database) and previous theoretical results. Comparisons are made with the available data in the literature and good agreement has been found which confirms the reliability of our results. Comparatively to the NIST database, it was found that our calculated energy levels using three methods, mainly standard FAC, RCI and MBPT are assessed to be mainly accurate to better than 1.33%, 0.47% and 0.06%. Our data are with great interest in plasma diagnostics.

Questaal: A package of electronic structure methods based on the linear muffin-tin orbital technique

This paper summarises the theory and functionality behind Questaal, an open-source suite of codes for calculating the electronic structure and related properties of materials from first principles. The formalism of the linearised muffin-tin orbital (LMTO) method is revisited in detail and developed further by the introduction of short-ranged tight-binding basis functions for full-potential calculations. The LMTO method is presented in both Green’s function and wave function formulations for bulk and layered systems. The suite’s full-potential LMTO code uses a sophisticated basis and augmentation method that allows an efficient and precise solution to the band problem at different levels of theory, most importantly density functional theory, LDA+U, quasi-particle self-consistent GW and combinations of these with dynamical mean field theory. This paper details the technical and theoretical bases of these methods, their implementation in Questaal, and provides an overview of the code’s design and capabilities. Program summaryProgram Title: QuestaalProgram Files doi:http://dx.doi.org/10.17632/35jxxtzpdn.1Code Ocean Capsule:https://doi.org/10.24433/CO.3778701.v1Licensing provisions: GNU General Public License, version 3Programming language: Fortran, C, Python, ShellNature of problem: Highly accurate ab initio calculation of the electronic structure of periodic solids and of the resulting physical, spectroscopic and magnetic properties for diverse material classes with different strengths and kinds of electronic correlation.Solution method: The many electron problem is considered at different levels of theory: density functional theory, many body perturbation theory in the GW approximation with different degrees of self consistency (notably quasiparticle self-consistent GW) and dynamical mean field theory. The solution to the single-particle band problem is achieved in the framework of an extension to the linear muffin-tin orbital (LMTO) technique including a highly precise and efficient full-potential implementation. An advanced fully-relativistic, non-collinear implementation based on the atomic sphere approximation is used for calculating transport and magnetic properties.

The effects of electromyography-triggered neuromuscular electrical stimulation plus tilt sensor functional electrical stimulation training on gait performance in patients with subacute stroke: a randomized controlled pilot trial.

The effects of electromyography-triggered neuromuscular electrical stimulation and tilt sensor functional electrical stimulation on ankle dorsiflexion during walking are unclear. This study investigated whether combined electrical stimulation training affects gait performance in patients with stroke. Thirty-six patients were randomly assigned to a control (n = 13), electromyography-triggered neuromuscular electrical stimulation training (single electrical stimulation group, n = 12), or a combined electromyography-triggered neuromuscular electrical stimulation and tilt sensor functional electrical stimulation training (combined electrical stimulation group, n = 11) group. Both experimental groups undertook 60-minute interventions for two weeks. All patients' gait performances were evaluated according to walking speed and trunk acceleration during 10-meter walking tests undertaken pre-intervention and at two weeks post-intervention. A wireless triaxial accelerometer measured trunk acceleration, and the root mean square values of the vertical, mediolateral, and anterioposterior planes were calculated from randomly selected 10-step sequences. Compared with baseline, the 10-meter walking tests improved significantly after two weeks in the single and combined electrical stimulation groups. In the combined electrical stimulation group, the 10-meter walking tests scores and root mean square of the mediolateral plane improved significantly compared with those in the control group. Electromyography-triggered neuromuscular electrical stimulation and tilt sensor functional electrical stimulation training may improve body perturbation stability and walking quality.

A Search for Multiplanet Systems with TESS Using a Bayesian N-body Retrieval and Machine Learning

Abstract Transiting exoplanets in multiplanet systems exhibit non-Keplerian orbits as a result of the gravitational influence from companions, which can cause the times and durations of transits to vary. The amplitude and periodicity of the transit time variations are characteristic of the perturbing planet’s mass and orbit. The objects of interest from the Transiting Exoplanet Survey Satellite (TESS) are analyzed in a uniform way to search for transit timing variations (TTVs) with sectors 1–3 of data. Due to the volume of targets in the TESS candidate list, artificial intelligence is used to expedite the search for planets by vetting nontransit signals prior to characterizing the light-curve time series. The residuals of fitting a linear orbit ephemeris are used to search for TTVs. The significance of a perturbing planet is assessed by comparing the Bayesian evidence between a linear and nonlinear ephemeris, which is based on an N-body simulation. Nested sampling is used to derive posterior distributions for the N-body ephemeris and in order to expedite convergence, custom priors are designed using machine learning. A dual-input, multi-output convolutional neural network is designed to predict the parameters of a perturbing body given the known parameters and measured perturbation (O − C). There is evidence for three new multiplanet candidates (WASP-18, WASP-126, TOI 193) with nontransiting companions using the two-minute cadence observations from TESS. This approach can be used to identify stars in need of longer radial velocity and photometric follow-up than those already performed.

Perception of whole-body motion during balance perturbations is impaired in Parkinson's disease and is associated with balance impairment

BackgroundIn addition to motor deficits, Parkinson's disease (PD) may cause perceptual impairments. The role of perceptual impairments in sensorimotor function is unclear, and has typically been studied in single-joint motions. Research questionWe hypothesized that perception of whole-body motion is impaired in PD and contributes to balance impairments. We tested (1) whether directional acuity to whole body perturbations during standing was worse in people with PD compared to neurotypical older adults (NOA), and (2) whether balance ability, as assessed by the MiniBESTest, was associated with poor directional acuity in either group. MethodsParticipants were exposed to pairs of support-surface translation perturbations in a two-alternative forced choice testing paradigm developed previously in a young healthy population. The first perturbation of each pair that was to be judged by participants was directly backward, and the second perturbation deviated from the left or right from the backward direction by 1°–44°. Participants reported whether the perturbations in each pair were in the “same” or “different” direction. Judgements from 24 to 67 perturbation pairs were used to calculate directional acuity thresholds corresponding to “just-noticeable differences” in perturbation direction. Linear mixed models determined associations between directional thresholds and clinical variables including MDS-UPDRS-III score, age, and MiniBESTest score. Results20 PD (64 ± 7 y, 12 male, ≥12 h since last intake of antiparkinsonian medications) and 12 NOA (64 ± 8, 6 male) were assessed. Directional thresholds were higher (worse) among PD participants (17.6 ± 5.9° vs. 12.8 ± 3.3°, P < 0.01). Linear mixed models further showed that higher thresholds were associated with MDS-UPDRS-III score (P < 0.01), and were associated with poorer balance ability among PD participants (P < 0.01), but not among NOA participants (P = 0.40). SignificancePerception of whole-body motion is impaired in PD and may contribute to impaired balance and falls.