Invariant feedback control for the kinematic car on the sphere

The design of an invariant tracking control law for the kinematic car driving on a sphere is discussed. Using a Lie group framework a left-invariant description on SO(3) is derived. Basic geometric considerations allow a direct comparison of the model with the usual planar case. Exploiting the Lie group structure an invariant tracking error is defined and a feedback is designed. Finally, one possible design of an invariant asymptotic observer is sketched

Karst simulation with Lindenmayer-systems and ODSIM

International audienceKarstic systems are geological structures that strongly impact underground flows. Despite intensive explorations by speleologists, they remain partially described as many conduits are not accessible to humans. Paleokarsts are buried karstic systems with a significant reservoir potential. But they are not easily identifiable on seismic images. In those contexts, a huge uncertainty subsists on the network location and the conduit geometry. Stochastic simulations help to better assess that uncertainty. The difficulty is to reproduce the system connectivity at different scales while integrating as much geological knowledge as possible without involving poorly constrained parameters (e.g. paleo-climate, boundary conditions...). In this paper we propose to work on two aspects and scales of karstic systems. At large scale, we stochastically simulate karst network skeletons with a new method based on a formal grammar, the Lindenmayer-system. Based on an alphabet, an axiom and user-defined rules, the method puts together segments to build the network skeleton. The definition of proper rules and the introduction of karst-dedicated parameters generate curves reproducing the complex architectures encountered in those systems, mixing branchwork and anastomotic patterns. At the conduit scale, we propose to build a 3D envelope around these skeletons with an enhanced Object Distance based Simulation Method. It uses a custom distance field from the skeleton which takes into account geological features influencing karstogenesis (horizons, faults or fractures). This controls the first-order shape of the conduits. It is then combined to a custom random threshold controlling finer-scale features of the conduits. This threshold is generated with several parameter values depending on the involved geological structures. This workflow is demonstrated on a synthetic case, showing the potentialities of the approach at both scales. Results are encouraging and various improvements are in focus. Data conditioning, both to karst observations and local shape information has to be enhanced. The network simulation has the advantage to be grid-free, meaning that no background grid is needed to perform the simulation. Thus, it avoids the stair-step effect that can be observed in other techniques. On the opposite, the method used to simulate the conduit shapes relies on a grid, necessary to compute the distance fields and to perform the threshold geostatistical simulation. For detailed conduit geometry, the grid requires a high resolution, which impacts directly the computational efficiency. Finally, it would be interesting to test the approach on a real dataset and to develop a coupling with a flow simulator to evaluate the impact of the shape and of the network connections on the flow response

Risk-Averse Model Predictive Operation Control of Islanded Microgrids

In this paper we present a risk-averse model predictive control (MPC) scheme for the operation of islanded microgrids with very high share of renewable energy sources. The proposed scheme mitigates the effect of errors in the determination of the probability distribution of renewable infeed and load. This allows to use less complex and less accurate forecasting methods and to formulate low-dimensional scenario-based optimisation problems which are suitable for control applications. Additionally, the designer may trade performance for safety by interpolating between the conventional stochastic and worst-case MPC formulations. The presented risk-averse MPC problem is formulated as a mixed-integer quadratically-constrained quadratic problem and its favourable characteristics are demonstrated in a case study. This includes a sensitivity analysis that illustrates the robustness to load and renewable power prediction errors

Comparing connected structures in ensemble of random fields

International audienceVery different connectivity patterns may arise from using different simulation methods or sets of parameters, and therefore different flow properties. This paper proposes a systematic method to compare ensemble of categorical simulations from a static connectivity point of view. The differences of static connectivity cannot always be distinguished using two point statistics. In addition, multiple-point histograms only provide a statistical comparison of patterns regardless of the connectivity. Thus, we propose to characterize the static connectivity from a set of 12 indicators based on the connected components of the realizations. Some indicators describe the spatial repartition of the connected components, others their global shape or their topology through the component skeletons. We also gather all the indicators into dissimilarity values to easily compare hundreds of realizations. Heat maps and multidimensional scaling then facilitate the dissimilarity analysis. The application to a synthetic case highlights the impact of the grid size on the connectivity and the indicators. Such impact disappears when comparing samples of the realizations with the same sizes. The method is then able to rank realizations from a referring model based on their static connectivity. This application also gives rise to more practical advices. The multidimensional scaling appears as a powerful visualization tool, but it also induces dissimilarity misrepresentations: it should always be interpreted cautiously with a look at the point position confidence. The heat map displays the real dissimilarities and is more appropriate for a detailed analysis. The comparison with a multiple-point histogram method shows the benefit of the connected components: the large-scale connectivity seems better characterized by our indicators, especially the skeleton indicators

Re-measurement of the 33{}^{33}S(α\alpha,p)36{}^{36}Cl cross section for Early solar system enrichment

Short-lived radionuclides (SLRs) with half-lives less than 100 Myr are known to have existed around the time of the formation of the solar system around 4.5 billion years ago. Understanding the production sources for SLRs is important for improving our understanding of processes taking place just after solar system formation as well as their timescales. Early solar system models rely heavily on calculations from nuclear theory due to a lack of experimental data for the nuclear reactions taking place. In 2013, Bowers et al. measured ${}^{36}$Cl production cross sections via the ${}^{33}$S($\alpha$,p) reaction and reported cross sections that were systematically higher than predicted by Hauser-Feshbach codes. Soon after, a paper by Peter Mohr highlighted the challenges the new data would pose to current nuclear theory if verified. The ${}^{33}$S($\alpha$,p)${}^{36}$Cl reaction was re-measured at 5 energies between 0.78 MeV/A and 1.52 MeV/A, in the same range as measured by Bowers et al., and found systematically lower cross sections than originally reported, with the new results in good agreement with the Hauser-Feshbach code TALYS. Loss of Cl carrier in chemical extraction and errors in determination of reaction energy ranges are both possible explanations for artificially inflated cross sections measured in the previous work

Tracing Noble Gas Radionuclides in the Environment

Trace analysis of radionuclides is an essential and versatile tool in modern science and technology. Due to their ideal geophysical and geochemical properties, long-lived noble gas radionuclides, in particular, 39Ar (t1/2 = 269 yr), 81Kr (t1/2 = 2.3x10^5 yr) and 85Kr (t1/2 = 10.8 yr), have long been recognized to have a wide range of important applications in Earth sciences. In recent years, significant progress has been made in the development of practical analytical methods, and has led to applications of these isotopes in the hydrosphere (tracing the flow of groundwater and ocean water). In this article, we introduce the applications of these isotopes and review three leading analytical methods: Low-Level Counting (LLC), Accelerator Mass Spectrometry (AMS) and Atom Trap Trace Analysis (ATTA)

A Study of the Residual 39Ar Content in Argon from Underground Sources

The discovery of argon from underground sources with significantly less 39Ar than atmospheric argon was an important step in the development of direct-detection dark matter experiments using argon as the active target. We report on the design and operation of a low background detector with a single phase liquid argon target that was built to study the 39Ar content of the underground argon. Underground argon from the Kinder Morgan CO2 plant in Cortez, Colorado was determined to have less than 0.65% of the 39Ar activity in atmospheric argon.Comment: 21 pages, 10 figure