Hermitian Interpolation Subject to Uncertainties

The book was dedicated to Professor P. Neittaanmaki on His 60th BirthdayInternational audienceThis contribution is a sequel of the report [1]. In PDE-constrained global optimization (e.g., [3]), iterative algorithms are commonly efficiently accelerated by techniques relying on approximate evaluations of the functional to be minimized by an economical but lower-fidelity model ("meta-model"), in a so-called "Design of Experiment" (DoE) [6]. Various types of meta-models exist (interpolation polynomials, neural networks, Kriging models, etc.). Such meta-models are constructed by pre-calculation of a database of functional values by the costly high-fidelity model. In adjoint-based numerical methods, derivatives of the functional are also available at the same cost, although usually with poorer accuracy. Thus, a question arises: should the derivative information, available but known to be less accurate, be used to construct the meta-model or be ignored? As the first step to investigate this issue, we consider the case of the Hermitian interpolation of a function of a single variable, when the function values are known exactly, and the derivatives only approximately, assuming a uniform upper bound ε on this approximation is known. The classical notion of best approximation is revisited in this context, and a criterion is introduced to define the best set of interpolation points. This set is identified by either analytical or numerical means. If n+1 is the number of interpolation points, it is advantageous to account for the derivative information when ε -> ε_0, where ε_0 decreases with n, and this is in favor of piecewise, low-degree Hermitian interpolants. In all our numerical tests, we have found that the distribution of Chebyshev points is always close to optimal, and provides bounded approximants with close-to-least sensitivity to the uncertainties

Honeybee Colony Vibrational Measurements to Highlight the Brood Cycle

Insect pollination is of great importance to crop production worldwide and honey bees are amongst its chief facilitators. Because of the decline of managed colonies, the use of sensor technology is growing in popularity and it is of interest to develop new methods which can more accurately and less invasively assess honey bee colony status. Our approach is to use accelerometers to measure vibrations in order to provide information on colony activity and development. The accelerometers provide amplitude and frequency information which is recorded every three minutes and analysed for night time only. Vibrational data were validated by comparison to visual inspection data, particularly the brood development. We show a strong correlation between vibrational amplitude data and the brood cycle in the vicinity of the sensor. We have further explored the minimum data that is required, when frequency information is also included, to accurately predict the current point in the brood cycle. Such a technique should enable beekeepers to reduce the frequency with which visual inspections are required, reducing the stress this places on the colony and saving the beekeeper time

Emotional intelligence buffers the effect of physiological arousal on dishonesty

We studied the emotional processes that allow people to balance two competing desires: benefitting from dishonesty and keeping a positive self-image. We recorded physiological arousal (skin conductance and heart rate) during a computer card game in which participants could cheat and fail to report a certain card when presented on the screen to avoid losing their money. We found that higher skin conductance corresponded to lower cheating rates. Importantly, emotional intelligence regulated this effect; participants with high emotional intelligence were less affected by their physiological reactions than those with low emotional intelligence. As a result, they were more likely to profit from dishonesty. However, no interaction emerged between heart rate and emotional intelligence. We suggest that the ability to manage and control emotions can allow people to overcome the tension between doing right or wrong and license them to bend the rules

The benefits of very low earth orbit for earth observation missions

Very low Earth orbits (VLEO), typically classified as orbits below approximately 450 km in altitude, have the potential to provide significant benefits to spacecraft over those that operate in higher altitude orbits. This paper provides a comprehensive review and analysis of these benefits to spacecraft operations in VLEO, with parametric investigation of those which apply specifically to Earth observation missions. The most significant benefit for optical imaging systems is that a reduction in orbital altitude improves spatial resolution for a similar payload specification. Alternatively mass and volume savings can be made whilst maintaining a given performance. Similarly, for radar and lidar systems, the signal-to-noise ratio can be improved. Additional benefits include improved geospatial position accuracy, improvements in communications link-budgets, and greater launch vehicle insertion capability. The collision risk with orbital debris and radiation environment can be shown to be improved in lower altitude orbits, whilst compliance with IADC guidelines for spacecraft post-mission lifetime and deorbit is also assisted. Finally, VLEO offers opportunities to exploit novel atmosphere-breathing electric propulsion systems and aerodynamic attitude and orbit control methods. However, key challenges associated with our understanding of the lower thermosphere, aerodynamic drag, the requirement to provide a meaningful orbital lifetime whilst minimising spacecraft mass and complexity, and atomic oxygen erosion still require further research. Given the scope for significant commercial, societal, and environmental impact which can be realised with higher performing Earth observation platforms, renewed research efforts to address the challenges associated with VLEO operations are required

On the exploitation of differential aerodynamic lift and drag as a means to control satellite formation flight

For a satellite formation to maintain its intended design despite present perturbations (formation keeping), to change the formation design (reconfiguration) or to perform a rendezvous maneuver, control forces need to be generated. To do so, chemical and/or electric thrusters are currently the methods of choice. However, their utilization has detrimental effects on small satellites’ limited mass, volume and power budgets. Since the mid-80s, the potential of using differential drag as a means of propellant-less source of control for satellite formation flight is actively researched. This method consists of varying the aerodynamic drag experienced by different spacecraft, thus generating differential accelerations between them. Its main disadvantage, that its controllability is mainly limited to the in-plain relative motion, can be overcome using differential lift as a means to control the out-of-plane motion. Due to its promising benefits, a variety of studies from researchers around the world have enhanced the state-of-the-art over the past decades which results in a multitude of available literature. In this paper, an extensive literature review of the efforts which led to the current state-of-the-art of different lift and drag-based satellite formation control is presented. Based on the insights gained during the review process, key knowledge gaps that need to be addressed in the field of differential lift to enhance the current state-of-the-art are revealed and discussed. In closer detail, the interdependence between the feasibility domain/the maneuver time and increased differential lift forces achieved using advanced satellite surface materials promoting quasi-specular or specular reflection, as currently being developed in the course of the DISCOVERER project, is discussed

A review of gas-surface interaction models for orbital aerodynamics applications

Renewed interest in Very Low Earth Orbits (VLEO) - i.e. altitudes below 450 km - has led to an increased demand for accurate environment characterisation and aerodynamic force prediction. While the former requires knowledge of the mechanisms that drive density variations in the thermosphere, the latter also depends on the interactions between the gas-particles in the residual atmosphere and the surfaces exposed to the flow. The determination of the aerodynamic coefficients is hindered by the numerous uncertainties that characterise the physical processes occurring at the exposed surfaces. Several models have been produced over the last 60 years with the intent of combining accuracy with relatively simple implementations. In this paper the most popular models have been selected and reviewed using as discriminating factors relevance with regards to orbital aerodynamics applications and theoretical agreement with gas-beam experimental data. More sophisticated models were neglected, since their increased accuracy is generally accompanied by a substantial increase in computation times which is likely to be unsuitable for most space engineering applications. For the sake of clarity, a distinction was introduced between physical and scattering kernel theory based gas-surface interaction models. The physical model category comprises the Hard Cube model, the Soft Cube model and the Washboard model, while the scattering kernel family consists of the Maxwell model, the Nocilla-Hurlbut-Sherman model and the Cercignani-Lampis-Lord model. Limits and assets of each model have been discussed with regards to the context of this paper. Wherever possible, comments have been provided to help the reader to identify possible future challenges for gas-surface interaction science with regards to orbital aerodynamic applications

Attitude control for satellites flying in VLEO using aerodynamic surfaces

This paper analyses the use of aerodynamic control surfaces, whether passive or active, in order to carry out very low Earth orbit (VLEO) attitude maneuver operations. Flying a satellite in a very low Earth orbit with an altitude of less than 450 km, namely VLEO, is a technological challenge. It leads to several advantages, such as increasing the resolution of optical payloads or increase signal to noise ratio, among others. The atmospheric density in VLEO is much higher than in typical low earth orbit altitudes, but still free molecular flow. This has serious consequences for the maneuverability of a satellite because significant aerodynamic torques and forces are produced. In order to guarantee the controllability of the spacecraft they have to be analyzed in depth. Moreover, at VLEO the density of atomic oxygen increases, which enables the use of air-breathing electric propulsion (ABEP). Scientists are researching in this field to use ABEP as a drag compensation system, and consequently an attitude control based on aerodynamic control could make sense. This combination of technologies may represent an opportunity to open new markets. In this work, several satellite geometric configurations were considered to analyze aerodynamic control: 3-axis control with feather configuration and 2-axis control with shuttlecock configuration. The analysis was performed by simulating the attitude of the satellite as well as the disturbances affecting the spacecraft. The models implemented to simulate the disturbances were the following: Gravitational gradient torque disturbance, magnetic dipole torque disturbance (magnetic field model IGRF12), and aerodynamic torque disturbances (aerodynamic model DTM2013 and wind model HWM14).The maneuvers analyzed were the following: detumbling or attitude stabilization, pointing and demisability. Different VLEO parameters were analyzed for every geometric configuration and spacecraft maneuver. The results determined which of the analyzed geometric configurations suits better for every maneuver

Temperature Modulates Coccolithophorid Sensitivity of Growth, Photosynthesis and Calcification to Increasing Seawater pCO2

Increasing atmospheric CO2 concentrations are expected to impact pelagic ecosystem functioning in the near future by driving ocean warming and acidification. While numerous studies have investigated impacts of rising temperature and seawater acidification on planktonic organisms separately, little is presently known on their combined effects. To test for possible synergistic effects we exposed two coccolithophore species, Emiliania huxleyi and Gephyrocapsa oceanica, to a CO2 gradient ranging from ,0.5–250 mmol kg21 (i.e. ,20–6000 matm pCO2) at three different temperatures (i.e. 10, 15, 20uC for E. huxleyi and 15, 20, 25uC for G. oceanica). Both species showed CO2-dependent optimum-curve responses for growth, photosynthesis and calcification rates at all temperatures. Increased temperature generally enhanced growth and production rates and modified sensitivities of metabolic processes to increasing CO2. CO2 optimum concentrations for growth, calcification, and organic carbon fixation rates were only marginally influenced from low to intermediate temperatures. However, there was a clear optimum shift towards higher CO2 concentrations from intermediate to high temperatures in both species. Our results demonstrate that the CO2 concentration where optimum growth, calcification and carbon fixation rates occur is modulated by temperature. Thus, the response of a coccolithophore strain to ocean acidification at a given temperature can be negative, neutral or positive depending on that strain’s temperature optimum. This emphasizes that the cellular responses of coccolithophores to ocean acidification can only be judged accurately when interpreted in the proper eco-physiological context of a given strain or species. Addressing the synergistic effects of changing carbonate chemistry and temperature is an essential step when assessing the success of coccolithophores in the future ocean

Concepts and Applications of Aerodynamic Attitude and Orbital Control for Spacecraft in Very Low Earth Orbit

Spacecraft operations below 450km, namely Very Low Earth Orbit (VLEO), can offer significant advantages over traditional low Earth orbits, for example enhanced ground resolution for Earth observation, improved communications latency and link budget, or improved signal-to-noise ratio. Recently, these lower orbits have begun to be exploited as a result of technology development, particularly component miniaturisation and cost-reduction, and concerns over the increasing debris population in commercially exploited orbits. However, the high cost of orbital launch and challenges associated with atmospheric drag, causing orbital decay and eventually re-entry are still a key barrier to their wider use for large commercial and civil spacecraft. Efforts to address the impact of aerodynamic drag are being sought through the development of novel drag-compensation propulsion systems and identification of materials which can reduce aerodynamic drag by specularly reflecting the incident gas. However, the presence of aerodynamic forces can also be utilised to augment or improve spacecraft operations at these very low altitudes by providing the capability to perform coarse pointing control and trim or internal momentum management for example. This paper presents concepts for the advantageous use of spacecraft aerodynamics developed as part of DISCOVERER, a Horizon 2020 funded project with the aim to revolutionise Earth observation satellite operations in VLEO. The combination of novel spacecraft geometries and use of aerodynamic control methods are explored, demonstrating the potential for a new generation of Earth observation satellites operating at lower altitudes

Discoverer - Making commercial satellite operations in very low earth orbit a reality

DISCOVERER is a €5.7M European Commission funded Horizon 2020 project developing technologies to enable commercially-viable sustained-operation of satellites in very low Earth orbits. Why operate closer to the Earth? For communications applications latency is significantly reduced and link budgets improved, and for remote sensing improved link budgets allow higher resolution or smaller instruments, all providing cost benefits. In addition, all applications benefit from increased launch mass to lower altitudes, whilst end-of-life removal is ensured due to the increased atmospheric drag. However, this drag must also be minimised and compensated for. One of the key technologies being developed by DISCOVERER are materials that encourage specular reflection of the residual atmosphere at these altitudes. Combined with appropriate geometric designs these can significantly reduce drag, provide usable lift for aerodynamic attitude and orbit control, and improve the collection efficiency of aerodynamic intakes for atmosphere breathing electric propulsion systems, all of which are being developed as part of DISCOVERER. The paper provides highlights from the developments to date, and the potential for a new class of aerodynamic commercial satellites operating at altitudes below the International Space Station