Tropical surface singularities

In this paper, we study tropicalisations of singular surfaces in toric threefolds. We completely classify singular tropical surfaces of maximal-dimensional type, show that they can generically have only finitely many singular points, and describe all possible locations of singular points. More precisely, we show that singular points must be either vertices, or generalized midpoints and baricenters of certain faces of singular tropical surfaces, and, in some cases, there may be additional metric restrictions to faces of singular tropical surfaces.Comment: A gap in the classification was closed. 37 pages, 29 figure

Permutonestohedra

There are several real spherical models associated with a root arrangement, depending on the choice of a building set. The connected components of these models are manifolds with corners which can be glued together to obtain the corresponding real De Concini–Procesi models. In this paper, starting from any root system with finite Coxeter group W and any W -invariant building set, we describe an explicit realization of the real spherical model as a union of polytopes (nestohedra) that lie inside the chambers of the arrangement. The main point of this realization is that the convex hull of these nestohedra is a larger polytope, a permutonestohedron, equipped with an action of W or also, depending on the building set, of Aut ( ). The permutonestohedra are natural generalizations of Kapranov’s permutoassociahedra

Around the tangent cone theorem

A cornerstone of the theory of cohomology jump loci is the Tangent Cone theorem, which relates the behavior around the origin of the characteristic and resonance varieties of a space. We revisit this theorem, in both the algebraic setting provided by cdga models, and in the topological setting provided by fundamental groups and cohomology rings. The general theory is illustrated with several classes of examples from geometry and topology: smooth quasi-projective varieties, complex hyperplane arrangements and their Milnor fibers, configuration spaces, and elliptic arrangements.Comment: 39 pages; to appear in the proceedings of the Configurations Spaces Conference (Cortona 2014), Springer INdAM serie

Resonant behavior of a single plasmonic helix

Chiral plasmonic nanostructures will be of increasing importance for future applications in the field of nano optics and metamaterials. Their sensitivity to incident circularly polarized light in combination with the ability of extreme electromagnetic field localization renders them ideal candidates for chiral sensing and for all-optical information processing. Here, the resonant modes of single plasmonic helices are investigated. We find that a single plasmonic helix can be efficiently excited with circularly polarized light of both equal and opposite handedness relative to that of the helix. An analytic model provides resonance conditions matching the results of full-field modeling. The underlying geometric considerations explain the mechanism of excitation and deliver quantitative design rules for plasmonic helices being resonant in a desired wavelength range. Based on the developed analytical design tool, single silver helices were fabricated and optically characterized. They show the expected strong chiroptical response to both handednesses in the targeted visible range. With a value of 0.45 the experimentally realized dissymmetry factor is the largest obtained for single plasmonic helices in the visible range up to now.Comment: main: typo in the author's name corrected, SI: update

New insights into colloidal gold flakes: structural investigation, micro-ellipsometry and thinning procedure towards ultrathin monocrystalline layers

High-quality fabrication of plasmonic devices often relies on wet-chemically grown ultraflat, presumably single-crystalline gold flakes due to their superior materials properties. However, important details about their intrinsic structure and their optical properties are not well understood yet. In this study, we present a synthesis routine for large flakes with diameters of up to 70 μm and an in-depth investigation of their structural and optical properties. The flakes are precisely analyzed by transmission electron microscopy, electron backscatter diffraction and micro-ellipsometry. We found new evidence for the existence of twins extending parallel to the Au flake {111} surfaces which have been found to not interfere with the presented nanopatterning. Micro-Ellipsometry was carried out to determine the complex dielectric function and to compare it to previous measurements of bulk single crystalline gold. Finally, we used focused ion beam milling to prepare smooth crystalline layers and high-quality nanostructures with desired thickness down to 10 nm to demonstrate the outstanding properties of the flakes. Our findings support the plasmonics and nano optics community with a better understanding of this material which is ideally suited for superior plasmonic nanostructures

A Review on the Modelling of Wave-Structure Interactions Based on OpenFOAM

The modelling of wave-structure interaction (WSI) has significant applications in understanding natural processes as well as securing the safety and efficiency of marine engineering. Based on the technique of Computational Fluid Dynamics (CFD) and the open-source simulation framework - OpenFOAM, this paper provides a state-of-the-art review of WSI modelling methods. The review categorises WSI scenarios and suggests their suitable computational approaches, concerning a rigid, deformable or porous structure in regular, irregular, non-breaking or breaking waves. Extensions of WSI modelling for wave-structure-seabed interactions and various wave energy converters are also introduced. As a result, the present review aims to help understand the CFD modelling of WSI and guide the use of OpenFOAM for target WSI problems

Small-Group Learning in an Upper-Level University Biology Class Enhances Academic Performance and Student Attitudes Toward Group Work

To improve science learning, science educators' teaching tools need to address two major criteria: teaching practice should mirror our current understanding of the learning process; and science teaching should reflect scientific practice. We designed a small-group learning (SGL) model for a fourth year university neurobiology course using these criteria and studied student achievement and attitude in five course sections encompassing the transition from individual work-based to SGL course design. All students completed daily quizzes/assignments involving analysis of scientific data and the development of scientific models. Students in individual work-based (Individualistic) sections usually worked independently on these assignments, whereas SGL students completed assignments in permanent groups of six. SGL students had significantly higher final exam grades than Individualistic students. The transition to the SGL model was marked by a notable increase in 10th percentile exam grade (Individualistic: 47.5%; Initial SGL: 60%; Refined SGL: 65%), suggesting SGL enhanced achievement among the least prepared students. We also studied student achievement on paired quizzes: quizzes were first completed individually and submitted, and then completed as a group and submitted. The group quiz grade was higher than the individual quiz grade of the highest achiever in each group over the term. All students – even term high achievers –could benefit from the SGL environment. Additionally, entrance and exit surveys demonstrated student attitudes toward SGL were more positive at the end of the Refined SGL course. We assert that SGL is uniquely-positioned to promote effective learning in the science classroom

Systematic development and adjustment of the German version of the Supportive and Palliative Care Indicators Tool (SPICT-DE)

Abstract Background The Supportive and Palliative Care Indicators tool (SPICT) supports the identification of patients with potential palliative care (PC) needs. An Austrian-German expert group translated SPICT into German (SPICT-DE) in 2014. The aim of this study was the systematic development, refinement, and testing of SPICT-DE for its application in primary care (general practice). Methods SPICT-DE was developed by a multiprofessional research team according to the TRAPD model: translation, review, adjudication, pretesting and documentation. In a pretest, five general practitioners (GPs) rated four case vignettes of patients with different PC needs. GPs were asked to assess whether each patient might benefit from PC or not (I) based on their subjective appraisal (“usual practice”) and (II) by using SPICT-DE. After further refinement, two focus groups with 28 GPs (68% with a further qualification in PC) were conducted to test SPICT-DE. Again, participants rated two selected case vignettes (I) based on their subjective appraisal and (II) by using SPICT-DE. Afterwards, participants reflected the suitability of SPICT-DE for use in their daily practice routine within the German primary care system. Quantitative data were analysed with descriptive statistics and non-parametric tests for small samples. Qualitative data were analysed by conventional content analysis. Focus group discussion was analysed combining formal and conventional content analysis. Results Compared to the spontaneous rating of the case vignettes based on subjective appraisal, participants in both the pretest and the focus groups considered PC more often as being beneficial for the patients described in the case vignettes when using SPICT-DE. Participants in the focus groups agreed that SPICT-DE includes all relevant indicators necessary for an adequate clinical identification of patients who might benefit from PC. Conclusions SPICT-DE supports the identification of patients who might benefit from PC and seems suitable for routine application in general practice in Germany. The systematic development, refinement, and testing of SPICT-DE in this study was successfully completed by using a multiprofessional and participatory approach

Legitimacy in the Multilevel European Polity

In order to be simultaneously effective and liberal, governments must normally be able to count on voluntary compliance – which, in turn, depends on the support of socially shared legitimacy beliefs. In Western constitutional democracies, such beliefs are derived from the distinct but coexistent traditions of “republican” and “liberal” political philosophy. When judged by these criteria, the European Union – if considered by itself – appears as a thoroughly liberal polity which, however, lacks all republican credentials. But this view (which seems to structure the debates about the “European democratic deficit”) ignores the multilevel nature of the European polity, where the compliance of citizens is requested, and needs to be legitimated by member states – whereas the Union appears as a “government of governments” which is entirely dependent on the voluntary compliance of its member states. What matters primarily, therefore, is the compliance-legitimacy relationship between the Union and its member states – which, however, is normatively constrained by the basic compliance-legitimacy relationship between member governments and their constituents. Given the high consensus requirements of European legislation, member governments could and should be able to assume political responsibility for European policies in which they had a voice, and to justify them in “communicative discourses” in the national public space. This is not necessarily true of “non-political” policy choices imposed by the European Court of Justice. By enforcing its “liberal” program of liberalization and deregulation, the ECJ may presently be undermining the “republican” bases of member-state legitimacy. Where this is the case, open non-compliance is a present danger, and political controls of judicial legislation may be called for.Um gleichzeitig effektiv und liberal sein zu können, ist staatliche Herrschaft auf freiwillige Folgebereitschaft angewiesen – die ihrerseits der Unterstützung durch sozial geteilte Legitimitätsüberzeugungen bedarf. In den demokratischen Verfassungsstaaten des Westens werden solche Überzeugungen aus den unterschiedlichen, aber komplementär zusammenwirkenden Traditionen der „republikanischen“ und der „liberalen“ politischen Philosophie hergeleitet. An diesen Kriterien gemessen erscheint die Europäische Union – wenn man sie für sich betrachtet – als eine „liberale“ politische Ordnung, der jedoch alle „republikanischen“ Legitimitätsmerkmale fehlen. Aber eine solche Sichtweise, die auch die derzeitige Diskussion über ein „europäisches Demokratiedefizit“ bestimmt, verkennt den Mehrebenencharakter des europäischen Gemeinwesens. In ihm sind es die Mitgliedstaaten, die Entscheidungen der Union gegenüber den eigenen Bürgern durchsetzen und auch legitimieren müssen, während es für die Union ihrerseits auf die freiwillige Folgebereitschaft ihrer Mitgliedstaaten ankommt. Dabei werden diese jedoch durch die normativen Grundlagen ihrer eigenen Legitimität begrenzt. Politische Entscheidungen auf europäischer Ebene setzen breiten Konsens voraus, und die Regierungen sollten sie deshalb auch gegenüber den eigenen Bürgern in „kommunikativen Diskursen“ vertreten und dafür die politische Verantwortung übernehmen können. Dies gilt jedoch nicht notwendigerweise auch für Entscheidungen der europäischen Politik, die im nichtpolitischen Modus ohne Beteiligung des Rates und des Parlaments vom Europäischen Gerichtshof bestimmt werden. Mit der gegenwärtigen Radikalisierung seines „liberalen“ Programms der Liberalisierung und Deregulierung des nationalen Rechts könnte der Gerichtshof in der Tat die „republikanischen“ Grundlagen der mitgliedstaatlichen Legitimität unterminieren. In diesem Falle könnte die Union sich nicht länger auf die Folgebereitschaft ihrer Mitgliedstaaten verlassen. Um diese Gefahr für die europäische Integration zu vermeiden, sollte eine stärkere politische Kontrolle der richterlichen Rechtsetzung erwogen werden.1 Legitimacy Republican and liberal legitimating discourses Constitutional democracies – and the EU? 2 Legitimacy in multilevel polities 3 Legitimating member state compliance Political modes of policy making Non-political policy making 4 The need for justification 5 The Court is pushing against the limits of justifiability 6 The liberal undermining of republican legitimacy 7 Needed: A political balance of community and autonomy Reference