Compensated Horner algorithm in K times the working precision

We introduce an algorithm to evaluate a polynomial with floating point coefficients as accurately as the Horner scheme performed in K times the working precision, for K an arbitrary integer. The principle is to iterate the error-free transformation of the compensated Horner algorithm and to accurately sum the final decomposition. We prove this accuracy property with an apriori error analysis. We illustrate its practical efficiency with numerical experiments on significant environments and IEEE-754 arithmetic. Comparing to existing alternatives we conclude that this K-times compensated algorithm is competitive for K up to 4, i.e. up to 212 mantissa bits

Compensated Horner Scheme

Using error-free transformations, we improve the classic Horner Scheme (HS) to evaluate (univariate) polynomials in floating point arithmetic. We prove that this Compensated Horner Scheme (CHS) is as accurate as HS performed with twice the working precision. Theoretical analysis and experiments exhibit a reasonable running time overhead being also more interesting than double-double implementations. We introduce a dynamic and validated error bound of the CHS computed value. The talk presents these results together with a survey about error-free transformations and related hypothesis

Algorithms for Accurate, Validated and Fast Polynomial Evaluation

International audienceWe survey a class of algorithms to evaluate polynomials with floating point coefficients and for computation performed with IEEE-754 floating point arithmetic. The principle is to apply, once or recursively, an error-free transformation of the polynomial evaluation with the Horner algorithm and to accurately sum the final decomposition. These compensated algorithms are as accurate as the Horner algorithm performed in K times the working precision, for K an arbitrary integer. We prove this accuracy property with an \apriori error analysis. We also provide validated dynamic bounds and apply these results to compute a faithfully rounded evaluation. These compensated algorithms are fast. We illustrate their practical efficiency with numerical experiments on significant environments. Comparing to existing alternatives these K-times compensated algorithms are competitive for K up to 4, i.e., up to 212 mantissa bits

Entrainment coefficient and effective mass for conduction neutrons in neutron star crust: II Macroscopic treatment

Phenomena such as pulsar frequency glitches are believed to be attributable to differential rotation of a current of ``free'' superfluid neutrons at densities above the ``drip'' threshold in the ionic crust of a neutron star. Such relative flow is shown to be locally describable by adaption of a canonical two fluid treatment that emphasizes the role of the momentum covectors constructed by differentiation of action with respect to the currents, with allowance for stratification whereby the ionic number current may be conserved even when the ionic charge number Z is altered by beta processes. It is demonstrated that the gauge freedom to make different choices of the chemical basis determining which neutrons are counted as ``free'' does not affect their ``superfluid'' momentum covector, which must locally have the form of a gradient (though it does affect the ``normal'' momentum covector characterising the protons and those neutrons that are considered to be ``confined'' in the nuclei). It is shown how the effect of ``entrainment'' (whereby the momentum directions deviate from those of the currents) is controlled by the (gauge independent) mobility coefficient K, estimated in recent microscopical quantum mechanical investigations, which suggest that the corresponding (gauge dependent) ``effective mass'' m* of the free neutrons can become very large in some layers. The relation between this treatment of the crust layers and related work (using different definitions of ``effective mass'') intended for the deeper core layers is discussed.Comment: 21 pages Latex. Part II of article whose Part I (Simple microscopic models) is given by nucl-th/0402057. New version extended to include figure

Cortical sulci model and matching from 3D brain magnetic resonance images

International audiencePositron emission tomography (PET) is one of the most popular techniques for the study of brain functional activity. Several studies show that PET is an in-vivo examination technique able to produce real images of cerebral activity, and is also neither destructive nor invasive. Unfortunately, PET images offer low resolution and signal-to-noise ratio. Moreover, they do not reflect the anatomy of patients. Accurate and reproducible analysis of PET images requires other informations, coming from aliases or other images such as magnetic resonance images (MRI) of the same patient. Hence it is of great interest to superimpose functional PET data and anatomical MRI data. Here, the authors deal with representation and identification of sulci. A first step is to choose and to automatically extract anatomical knowledge from a database, in order to adapt it to any image where the recognition has to be performed. Then, the authors introduce a stochastic method using these features to recognise human cerebral sulci

Fast pyrolysis of Miscanthus x Giganteus in an IR heated reactor

International audienceIntensive research on Miscanthus x Giganteus (MG), a large perennial grass, has been achieved in the last ten years because of its known advantages for farmers (high yield, low input, perennial crop, easy harvesting…) [refs 1,2,3,4]. MG is often considered as a good candidate to produce renewable energy. As lignocellulosic feedstock, MG could also serve to produce chemicals. This approach is far less present in the literature. Because logistics costs could affect the attractiveness of MG, pyrolysis is an interesting technology for energy densification [ref 4]. Therefore the present work describes the pyrolysis of Miscanthus x Giganteus. It is well know that pyrolysis products are solids, liquids and gas. Low residence time, enhanced by high heating rates and high flow rates, favors the production of liquids. A temperature range between 450 and 550°C is also recommended to limit gas formation. A new pyrolysis apparatus designed to achieve fast pyrolysis via infrared heating and low residence time is described. Process conditions are varied for temperature, particle size, N 2 flow rate and preheating effect. Pyrolysis temperature should be the most influential parameter upon the yield and properties of bio-oil. Tests are performed at different levels of power and duration. Temperature is measured in the border and in the center of the reactor because of the presence of radial gradients. The highest bio-oil yield and corresponding temperature profiles are presented. The effect of process conditions on bio-oil yield is assessed. The bio-oil composition is analyzed by GCMS. The results are compared with a direct analysis of MG by Py-GCMS. The bio char is characterized in terms of calorific value with respect to the raw MG High Heating Value (HHV). Furthermore, on the one hand the outlet gas composition is analyzed by online infrared spectroscopy which gives an indication of potential use as secondary source of energy. On the other hand the porosity of the bio-solid products is estimated by BET low-temperature adsorption method for further valorization purpose of pyrolysis products. Highlights: 1) New experimental results on Miscanthus x Giganteus pyrolysis are presented. 2) Characterization of every product thus resource potential is evaluated. 3) Comparison of Py-GCMS with lab scale pyrolysis of MG is performed. References: 1) Anissa Khelfa, Victor Sharypov, Gisèle Finqueneisel, Jean Victor Weber J. Anal. Appl. Pyrolysis 84 (2009) 84–88, Catalytic pyrolysis and gasification of Miscanthus Giganteus: Haematite (Fe2O3) a versatile catalyst

Trajectory planning and tracking via MPC for transient control of liquid-propellant rocket engines

International audienceThe new scenarios associated with launchers reusability force the enhancement of control algorithms for their liquid-propellant rocket engines. The transient phases of these engines are generally executed in open loop. The goal of this paper is to improve the control performance and robustness throughout the fully continuous phase of the start-up transient of a generic gas-generator cycle. The controller has to guarantee an accurate tracking in terms of combustion-chamber pressure and chambers mixture ratios, as well as to satisfy a set of hard operational constraints. The selected strategy comprises a nonlinear preprocessor and a linearised MPC (Model-Predictive Control) controller, making use of nonlinear state-space models of the engine. The former plans the reference trajectory of states and control, which is tracked by the latter. Control goals are attained with sufficient accuracy while verifying constraints within the desired throttling range. Robustness to internal parameters variations is considered in the MPC controller by means of an epigraph formulation of the minimax robust optimisation problem, where a finite set of parameter-variation scenarios is treated

Robust Transient Control of Reusable Liquid-Propellant Rocket Engines

International audienceThe current trend towards a more affordable access to space is generally materialising in reusable launchers and engines. From the control perspective, these reusable liquid-propellant rocket engines (LPRE) imply more demanding robustness requirements than expendable ones, mainly because of their multi-restart and thrust-modulation capabilities. Classically, the control system handles LPRE operation at a finite set of predefined points. That approach reduces their throttability domain to a restricted interval in which they are designed to be safe in nominal conditions. Moreover, the operation of their transient phases, which have a great impact on the duration of engine life, is not robust to the possible engine evolution. Hence, the goal of this work is to develop a control loop which is adapted to the whole set of operating phases, transient and steady-state, and which is robust to internal parametric variations. Several blocks have been assembled to constitute the control loop: engine simulation, reference generation and several controllers. First, simulators representative of the gas-generator-cycle (GG) Vulcain 1 and PROMETHEUS engines were built. The purely thermodynamic modelling of the cycle was subsequently adapted to the control framework, obtaining a nonlinear state-space model. The available actuators are continuously controllable valves, binary igniters and binary starters. These actuators are related to discrete events in transient phases. Regarding the start-up operation, the igniter, starter and valves are activated during the first seconds. Up from the end of those activations, the whole system behaves in a fully continuous way. Hence, a different control strategy is proposed for each sub-phase. For the first and discrete sub-phase, a discrete optimisation of events timing is proposed, in which the time differences between events are adapted according to operation criteria and constraints. This trajectory planning, still under implementation, is to be performed off-line. The subsequent continuous sub-phase is feedback controlled to track pre-computed reference trajectories. Apart from the start-up, throttling scenarios also present a dedicated end-state-tracking algorithm. A model-based control method, Model Predictive Control, has been applied in a linearised manner with robustness guarantees to all these scenarios, in which a set of hard state and control constraints must be respected. Tracking of pressure (thrust) and mixture-ratio operating points within the design envelope is achieved in simulation along the continuous sub-phase while respecting constraints. Robustness to variations of the parameters, which are checked to be predominant according to analyses, is also demonstrated

Continuous–Discrete Time-Observer Design for State and Disturbance Estimation of Electro-Hydraulic Actuator Systems

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