SAMBA: Sparse Approximation of Moment-Based Arbitrary Polynomial Chaos

A new arbitrary Polynomial Chaos (aPC) method is presented for moderately high-dimensional problems characterised by limited input data availability. The proposed methodology improves the algorithm of aPC and extends the method, that was previously only introduced as tensor product expansion, to moderately high-dimensional stochastic problems. The fundamental idea of aPC is to use the statistical moments of the input random variables to develop the polynomial chaos expansion. This approach provides the possibility to propagate continuous or discrete probability density functions and also histograms (data sets) as long as their moments exist, are finite and the determinant of the moment matrix is strictly positive. For cases with limited data availability, this approach avoids bias and fitting errors caused by wrong assumptions. In this work, an alternative way to calculate the aPC is suggested, which provides the optimal polynomials, Gaussian quadrature collocation points and weights from the moments using only a handful of matrix operations on the Hankel matrix of moments. It can therefore be implemented without requiring prior knowledge about statistical data analysis or a detailed understanding of the mathematics of polynomial chaos expansions. The extension to more input variables suggested in this work, is an anisotropic and adaptive version of Smolyak's algorithm that is solely based on the moments of the input probability distributions. It is referred to as SAMBA (PC), which is short for Sparse Approximation of Moment-Based Arbitrary Polynomial Chaos. It is illustrated that for moderately high-dimensional problems (up to 20 different input variables or histograms) SAMBA can significantly simplify the calculation of sparse Gaussian quadrature rules. SAMBA's efficiency for multivariate functions with regard to data availability is further demonstrated by analysing higher order convergence and accuracy for a set of nonlinear test functions with 2, 5 and 10 different input distributions or histograms

PNEUMATOSE KYSTIQUE INTESTINALE ASSOCIEE A UNE STENOSE BULBAIRE SUR ULCERE

Cystic Pneumatosis or pneumatises cystoides of small intestine is a rare affection. Its defined by the existence of gas is found in the digestive tract wall. This affection can be primitive or more often associated to systematic intestinal inflammatory diseases. The signs of this affection are not specific and most of cases are discovered incidentally during surgery or endoscopies. The diagnosis is based on radiological findings. The treatment, however, remains conservative because of the benignity of this disease. The prognosis is conditioned by the underlying disease. We report two cases of cystic Pneumatosis of the small intestine associated to ulcer pyloric stenosis, and we discuss through these cases all diagnosis and therapeutic features of this disease.La Pneumatose kystique intestinale (PKG) est une affection rare, définie par la présence de gaz dans la paroi du tube digestif. Elle peut être primitive ou le plus souvent associée à des maladies inflammatoires systémiques du tube digestif. Symptomatologie non spécifique, parfois de découverte fortuite. Le diagnostic est porté sur la radiologie.  Le traitement est essentiellement  conservateur vu la bénignité de l’affection. Le pronostic étant conditionné par la maladie sous-jacente. Nous rapportons deux cas de pneumatose kystiques intestinale associé à une sténose bulbaire sur ulcère.  A partir de ces deux cas nous avons discuté les éléments du diagnostiques Et l’attitude thérapeutique généralement conservatrice

LYMPHOME NON HODGKINIEN PRIMITIF DU FOIE : A PROPOS D’UN CAS ET REVUE DE LA LITTERATURE

The invasion secondary liver is common during the evolution of systemic lymphoma, primary lymphoma of the liver are very rare estimated at 1% of all extranodal lymphomas. We report a patient of 37 years, without previous medical history especially, who consulted for isolated pain in the right hypochondrium lasting for five months in a conservation context of general condition, abdominal ultrasound revealed a mass of malignant appearance of the left liver, confirmed by an abdominal CT scan. A liver biopsy was performed, showing the histology associated with immunohistochemistry; non-Hodgkin lymphoma, diffuse large B cells expressing CD20, the rest of the staging did not reveal any other location, including not of lymph node involvement. The patient received chemotherapy: RCHOP: rituximab, cyclophosphamide, doxorubicin, vincristine and prednisone, eight treatments, with good clinical and radiological response and good tolerance, with a decline in 4 months.L’envahissement secondaire du foie est fréquent au cours de l’évolution des lymphomes systémiques. Les lymphomes primitifs du foie sont très rares estimés à 1% de tous les lymphomes extraganglionnaire [1,2]. Nous rapportons l’observation d’une patiente de 37 ans, sans antécédents pathologiques particuliers, qui a consulté pour des douleurs isolées de l’hypochondre droit, évoluant depuis 5 mois dans un contexte de conservation de l’état général, l’échographie abdominale et la tomodensitométrie abdominale ont révélé ; une masse du foie gauche d’allure maligne. Une biopsie du foie a été réalisée, montrant à l’étude histologique associée à l’immunohistochimie ; un lymphome non hodgkinien type B diffus à grandes cellules exprimant CD20, le reste du bilan d’extension n’a révélé aucune autre localisation, notamment pas d’atteinte ganglionnaire. La patiente a reçu une chimiothérapie de type RCHOP : rituximab, cyclophosphamide, doxorubicine, vincristine et prednisone, huit cures, avec une bonne réponse clinique et radiologique et une bonne tolérance, avec un recule de 4 mois

In-orbit aerodynamic coefficient measurements using SOAR (Satellite for Orbital Aerodynamics Research)

The Satellite for Orbital Aerodynamics Research (SOAR) is a CubeSat mission, due to be launched in 2021, to investigate the interaction between different materials and the atmospheric flow regime in very low Earth orbits (VLEO). Improving knowledge of the gas–surface interactions at these altitudes and identification of novel materials that can minimise drag or improve aerodynamic control are important for the design of future spacecraft that can operate in lower altitude orbits. Such satellites may be smaller and cheaper to develop or can provide improved Earth observation data or communications link-budgets and latency. In order to achieve these objectives, SOAR features two payloads: (i) a set of steerable fins which provide the ability to expose different materials or surface finishes to the oncoming flow with varying angle of incidence whilst also providing variable geometry to investigate aerostability and aerodynamic control; and (ii) an ion and neutral mass spectrometer with time-of-flight capability which enables accurate measurement of the in-situ flow composition, density, velocity. Using precise orbit and attitude determination information and the measured atmospheric flow characteristics the forces and torques experienced by the satellite in orbit can be studied and estimates of the aerodynamic coefficients calculated. This paper presents the scientific concept and design of the SOAR mission. The methodology for recovery of the aerodynamic coefficients from the measured orbit, attitude, and in-situ atmospheric data using a least-squares orbit determination and free-parameter fitting process is described and the experimental uncertainty of the resolved aerodynamic coefficients is estimated. The presented results indicate that the combination of the satellite design and experimental methodology are capable of clearly illustrating the variation of drag and lift coefficient for differing surface incidence angle. The lowest uncertainties for the drag coefficient measurement are found at approximately 300 km, whilst the measurement of lift coefficient improves for reducing orbital altitude to 200 km

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

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

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

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

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

Inductive Plasma Thruster (IPT) design for an Atmosphere-Breathing Electric Propulsion System (ABEP)

Challenging space missions include those at very low altitudes, where the atmosphere is source of aerodynamic drag on the spacecraft, therefore an efficient propulsion system is required to extend the mission lifetime. One solution is Atmosphere-Breathing Electric Propulsion (ABEP). It collects atmospheric particles to use as propellant for an electric thruster. This would minimize the requirement of limited propellant availability. The system could be applied to any planet with atmosphere, enabling new mission at these altitude ranges for continuous orbiting. Challenging is also the presence of reactive chemical species, such as atomic oxygen in Earth orbit. Such components are erosion source of (not only) propulsion system components, i.e. acceleration grids, electrodes, and discharge channels of conventional EP systems (RIT and HET). IRS is developing within the DISCOVERER project an intake and a thruster for an ABEP system. This paper deals with the design and first operation of the inductive plasma thruster (IPT) developed at IRS. The paper describes its design aided by numerical tools such as HELIC and ADAMANT. Such a device is based on RF electrodeless discharge aided by externally applied static magnetic field. The IPT is composed by a movable injector, to variate the discharge channel length, and a movable electromagnet to variate position and intensity of the magnetic field. By changing these parameters along with a novel antenna design for electric propulsion, the aim is to achieve the highest efficiency for the ionization stage by enabling the formation of helicon-based discharge. Finally, the designed IPT is presented and the feature of the birdcage antenna highlighted