Formulation and convergence of the finite volume method for conservation laws on spacetimes with boundary

We study nonlinear hyperbolic conservation laws posed on a differential (n+1)-manifold with boundary referred to as a spacetime, and defined from a prescribed flux field of n-forms depending on a parameter (the unknown variable), a class of equations proposed by LeFloch and Okutmustur in 2008. Our main result is a proof of the convergence of the finite volume method for weak solutions satisfying suitable entropy inequalities. A main difference with previous work is that we allow for slices with a boundary and, in addition, introduce a new formulation of the finite volume method involving the notion of total flux functions. Under a natural global hyperbolicity condition on the flux field and the spacetime and by assuming that the spacetime admits a foliation by compact slices with boundary, we establish an existence and uniqueness theory for the initial and boundary value problem, and we prove a contraction property in a geometrically natural L1-type distance.Comment: 32 page

Measuring well-being: W3 indicators to complement GDP

"Numerous people in Germany, including politicians and researchers, believe that the gross domestic product (GDP) is an outdated indicator of a society’s prosperity. Therefore, at the end of 2010, the German Bundestag, the federal parliament, established a study commission (Enquete-Kommission) tasked with developing an alternative to the GDP for measuring growth, prosperity, and quality of life. This commission has now submitted a proposal: to supplement the GDP with nine additional indicators, including a wide range of factors such as the distribution of income, biodiversity, and life expectancy. The ten indicators cover three dimensions of well-being-economy, ecology, and social wealth-and hence are called W3 Indicators. Replacing the gross domestic product by a single alternative index was rejected by the commission, however, since it is not possible to reduce citizens' very different wishes and expectations to "a common denominator". A representative survey of registered voters conducted by DIW Berlin and TNS Infratest shows that citizens consider the indicators proposed by the commission to be important. Respondents ranked preserving "democracy and freedom" as the most relevant indicator and "further increasing life expectancy" as the least relevant. The average per capita income -as an indicator of the gross domestic product- is the second least relevant factor as far as registered voters in Germany are concerned. However, the study also shows that opinions on the importance of different indicators vary widely. Moreover, there are systematic differences in the relevance of various policy areas for different social groups." (author's abstract

Using Neural Networks to Estimate Wind Turbine Power Generation

This paper uses data collected at Central and South West Services Fort Davis wind farm to develop a neural network based prediction of power produced by each turbine. The power generated by electric wind turbines changes rapidly because of the continuous fluctuation of wind speed and direction. It is important for the power industry to have the capability to perform this prediction for diagnostic purposes—lower-than-expected wind power may be an early indicator of a need for maintenance. In this paper, characteristics of wind power generation are first evaluated in order to establish the relative importance for the neural network. A four input neural network is developed and its performance is shown to be superior to the single parameter traditional model approach

A posteriori error analysis and adaptive non-intrusive numerical schemes for systems of random conservation laws

In this article we consider one-dimensional random systems of hyperbolic conservation laws. We first establish existence and uniqueness of random entropy admissible solutions for initial value problems of conservation laws which involve random initial data and random flux functions. Based on these results we present an a posteriori error analysis for a numerical approximation of the random entropy admissible solution. For the stochastic discretization, we consider a non-intrusive approach, the Stochastic Collocation method. The spatio-temporal discretization relies on the Runge--Kutta Discontinuous Galerkin method. We derive the a posteriori estimator using continuous reconstructions of the discrete solution. Combined with the relative entropy stability framework this yields computable error bounds for the entire space-stochastic discretization error. The estimator admits a splitting into a stochastic and a deterministic (space-time) part, allowing for a novel residual-based space-stochastic adaptive mesh refinement algorithm. We conclude with various numerical examples investigating the scaling properties of the residuals and illustrating the efficiency of the proposed adaptive algorithm

Antiferroelectric liquid crystal mixture without smectic layer shrinkage at the direct sma* - smca* transition

We report results of x-ray, optic, electro-optic, and dielectric investigations on an antiferroelectric liquid- crystal mixture exhibiting a direct second-order phase transition between the Sm-A* and Sm-Ca* phases with virtually no shrinkage in the smectic layer spacing. The birefringence measurements and texture observations suggest that the phase transition follows the diffuse cone model of Adrian de Vries, which explains the constant layer spacing. The antiferroelectric nature of the tilted phase is verified by the presence of twin polarization reversal peaks in the current response and by the absence of strong absorptions in the dielectric spectrum. The threshold for switching this phase to the synclinic, ferroelectric state is sharp and occurs at a very low voltage

Politikziele im Spiegel der Bevölkerung: Erhalt der freiheitlich-demokratischen Ordnung weiterhin am wichtigsten

Nicht wenige PolitikerInnen und WissenschaftlerInnen sehen in einer primären Ausrichtung der Politik an ökonomischen Wohlstandsindikatoren eine Schieflage. Angesichts wissenschaftlicher und öffentlicher Diskurse zum Thema Wohlstand analysiert dieser Bericht, wie die Wahlberechtigten in Deutschland die Bedeutung verschiedener Politikziele 2013 und zu Beginn des Jahres 2017 einschätzten. Grundlage sind zwei mit Kantar Public (vormals TNS Infratest) durchgeführte repräsentative Befragungen, in denen die Relevanz verschiedener Politikziele direkt ermittelt wurde. Die Auswahl der Ziele orientierte sich dabei an den von der Enquete- Kommission „Wachstum, Wohlstand, Lebensqualität“ ausgewählten zehn Wohlstandsindikatoren, die die Ergebnisse von Politik quantifizieren, sowie an 20 der 46 von der Bundesregierung ausgewählten Indikatoren, welche die Lebensqualität („Gut leben in Deutschland“) beschreiben sollen. Dieser Bericht zeigt, dass diese Indikatoren tatsächlich von den Bürgerinnen und Bürgern überwiegend als wichtige Politikziele angesehen werden. An der Spitze der Relevanz lag 2013 wie 2017 der Erhalt der Demokratie. Auf Platz zwei landet 2017 die Verbesserung der Pflege alter Menschen und den dritten Rang nimmt eine wirksamere Bekämpfung der Kriminalität ein, der ein etwas höheres Gewicht als Vollbeschäftigung zugemessen wird. Gleichzeitig zeigt sich, dass die Menschen verschiedene Politikbereiche erkennbar unterschiedlich gewichten. Zusätzlich wird deutlich, dass es auch systematische Unterschiede in der Relevanz von Politikbereichen bei verschiedenen sozialen Gruppen gibt. Nach dem Themenbereich „Geflüchtete“ wurde nicht gefragt, da die Zahl der Geflüchteten in beiden Indikatorensystemen nicht als Politikbereich enthalten ist

Orientational order parameters of a de Vries–type ferroelectric liquid crystal obtained by polarized Raman spectroscopy and x-ray diffraction

The orientational order parameters 〈P2〉 and 〈P4〉 of the ferroelectric, de Vries–type liquid crystal 9HL have been determined in the SmA* and SmC* phases by means of polarized Raman spectroscopy, and in the SmA* phase using x-ray diffraction. Quantum density functional theory predicts Raman spectra for 9HL that are in good agreement with the observations and indicates that the strong Raman band probed in the experiment corresponds to the uniaxial, coupled vibration of the three phenyl rings along the molecular long axis. The magnitudes of the orientational order parameters obtained in the Raman and x-ray experiments differ dramatically from each other, a discrepancy that is resolved by considering that the two techniques probe the orientational distributions of different molecular axes. We have developed a systematic procedure in which we calculate the angle between these axes and rescale the orientational order parameters obtained from x-ray scattering with results that are then in good agreement with the Raman data. At least in the case of 9HL, the results obtained by both techniques support a “sugar loaf” orientational distribution in the SmA* phase with no qualitative difference to conventional smectics A. The role of individual molecular fragments in promoting de Vries–type behavior is considered

Field-Dependent Tilt and Birefringence of Electroclinic Liquid Crystals: Theory and Experiment

An unresolved issue in the theory of liquid crystals is the molecular basis of the electroclinic effect in the smectic-A phase. Recent x-ray scattering experiments suggest that, in a class of siloxane-containing liquid crystals, an electric field changes a state of disordered molecular tilt in random directions into a state of ordered tilt in one direction. To investigate this issue, we measure the optical tilt and birefringence of these liquid crystals as functions of field and temperature, and we develop a theory for the distribution of molecular orientations under a field. Comparison of theory and experiment confirms that these materials have a disordered distribution of molecular tilt directions that is aligned by an electric field, giving a large electroclinic effect. It also shows that the net dipole moment of a correlated volume of molecules, a key parameter in the theory, scales as a power law near the smectic-A--smectic-C transition.Comment: 18 pages, including 9 postscript figures, uses REVTeX 3.0 and epsf.st

Structured light enables biomimetic swimming and versatile locomotion of photoresponsive soft microrobots.

Microorganisms move in challenging environments by periodic changes in body shape. In contrast, current artificial microrobots cannot actively deform, exhibiting at best passive bending under external fields. Here, by taking advantage of the wireless, scalable and spatiotemporally selective capabilities that light allows, we show that soft microrobots consisting of photoactive liquid-crystal elastomers can be driven by structured monochromatic light to perform sophisticated biomimetic motions. We realize continuum yet selectively addressable artificial microswimmers that generate travelling-wave motions to self-propel without external forces or torques, as well as microrobots capable of versatile locomotion behaviours on demand. Both theoretical predictions and experimental results confirm that multiple gaits, mimicking either symplectic or antiplectic metachrony of ciliate protozoa, can be achieved with single microswimmers. The principle of using structured light can be extended to other applications that require microscale actuation with sophisticated spatiotemporal coordination for advanced microrobotic technologies.This work was in part supported by the European Research Council under the ERC Grant agreements 278213 and 291349, and the DFG as part of the project SPP 1726 (microswimmers, FI 1966/1-1). SP acknowledges support by the Max Planck ETH Center for Learning Systems.This is the author accepted manuscript. The final version is available from Nature Publishing Group via http://dx.doi.org/10.1038/nmat456