Evaluating Lebesgue constants by Chebyshev polynomial meshes on cube, simplex and ball

We show that product Chebyshev polynomial meshes can be used, in a fully discrete way, to evaluate with rigorous error bounds the Lebesgue constant, i.e. the maximum of the Lebesgue function, for a class of polynomial projectors on cube, simplex and ball, including interpolation, hyperinterpolation and weighted least-squares. Several examples are presented and possible generalizations outlined. A numerical software package implementing the method is freely available online

Design and properties of silicon charged-particle detectors developed at the Institute of Electron Technology (ITE).

The paper discusses the design of charged-particle detectors commissioned and developed at the Institute of Electron Technology (ITE) in collaboration with foreign partners, used in international research on transactinide elements and to build personal radiation protection devices in Germany. Properties of these detectors and the results obtained using the devices are also presented. The design of the following epiplanar detector structures is discussed: ◆ 64-element chromatographic arrays for the COMPACT (Cryo On-line Multidetector for Physics And Chemistry of Transactinides) detection system used at the GSI Helmholtzzentrum für Schwerionenforschung in Darmstadt (GSI) for research on Hassium, Copernicium and Flerovium, as well as elements 119 and 120, ◆ 2-element flow detectors for the COLD (Cryo On-Line Detector) system used for research on Copernicium and Flerovium at the Joint Institute for Nuclear Research, Dubna, ◆ detectors for a radon exposimeter and sensors for a neutron dosimeter developed at the Institut für Strahlenschutz, Helmholtz Zentrum München. The design of planar detectors - single-sided and double-sided strip detectors for the Focal Plane Detector Box used at GSI for research on Flerovium and elements 119 and 120 is also discussed

A minimal information set to enable verifiable theoretical battery research

Batteries are an enabling technology for addressing sustainability through the electrification of various forms of transportation (1) and grid storage. (2) Batteries are truly multi-scale, multi-physics devices, and accordingly various theoretical descriptions exist to understand their behavior (3−5) ranging from atomistic details to techno-economic trends. As we explore advanced battery chemistries (6,7) or previously inaccessible aspects of existing ones, (8−10) new theories are required to drive decisions. (11−13) The decisions are influenced by the limitations of the underlying theory. Advanced theories used to understand battery phenomena are complicated and require substantial effort to reproduce. However, such constraints should not limit the insights from these theories. We can strive to make the theoretical research verifiable such that any battery stakeholder can assess the veracity of new theories, sophisticated simulations or elaborate analyses. We distinguish verifiability, which amounts to “Can I trust the results, conclusions and insights and identify the context where they are relevant?”, from reproducibility, which ensures “Would I get the same results if I followed the same steps?” With this motivation, we propose a checklist to guide future reports of theoretical battery research in Table 1. We hereafter discuss our thoughts leading to this and how it helps to consistently document necessary details while allowing complete freedom for creativity of individual researchers. Given the differences between experimental and theoretical studies, the proposed checklist differs from its experimental counterparts. (14,15) This checklist covers all flavors of theoretical battery research, ranging from atomic/molecular calculations (16−19) to mesoscale (20,21) and continuum-scale interactions, (9,22) and techno-economic analysis. (23,24) Also, as more and more experimental studies analyze raw data, (25) we feel this checklist would be broadly relevant