Evolutionary optimization of optical antennas

The design of nano-antennas is so far mainly inspired by radio-frequency technology. However, material properties and experimental settings need to be reconsidered at optical frequencies, which entails the need for alternative optimal antenna designs. Here a checkerboard-type, initially random array of gold cubes is subjected to evolutionary optimization. To illustrate the power of the approach we demonstrate that by optimizing the near-field intensity enhancement the evolutionary algorithm finds a new antenna geometry, essentially a split-ring/two-wire antenna hybrid which surpasses by far the performance of a conventional gap antenna by shifting the n=1 split-ring resonance into the optical regime.Comment: Also see Supplementary material, as attached to the main pape

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

Biocompatibility and degradation of the open-pored magnesium scaffolds LAE442 and La2

Porous magnesium implants are of particular interest for application as resorbable bone substitutes, due to their mechanical strength and a Young's modulus similar to bone. The objective of the present study was to compare the biocompatibility, bone and tissue ingrowth, and the degradation behaviour of scaffolds made from the magnesium alloys LAE442 (n= 40) and Mg-La2 (n= 40)in vivo. For this purpose, cylindrical magnesium scaffolds (diameter 4 mm, length 5 mm) with defined, interconnecting pores were produced by investment casting and coated with MgF2. The scaffolds were inserted into the cancellous part of the greater trochanter ossis femoris of rabbits. After implantation periods of 6, 12, 24 and 36 weeks, the bone-scaffold compounds were evaluated usingex vivo µCT80 images, histological examinations and energy dispersive x-ray spectroscopy analysis. The La2 scaffolds showed inhomogeneous and rapid degradation, with inferior osseointegration as compared to LAE442. For the early observation times, no bone and tissue could be observed in the pores of La2. Furthermore, the excessive amount of foreign body cells and fibrous capsule formation indicates insufficient biocompatibility of the La2 scaffolds. In contrast, the LAE442 scaffolds showed slow degradation and better osseointegration. Good vascularization, a moderate cellular response, bone and osteoid-like bone matrix at all implantation periods were observed in the pores of LAE442. In summary, porous LAE442 showed promise as a degradable scaffold for bone defect repair, based on its degradation behaviour and biocompatibility. However, further studies are needed to show it would have the necessary mechanical properties required over time for weight-bearing bone defects

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

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

A Grassmann algebra for matroids

We introduce an idempotent analogue of the exterior algebra for which the theory of tropical linear spaces (and valuated matroids) can be seen in close analogy with the classical Grassmann algebra formalism for linear spaces. The top wedge power of a tropical linear space is its Plucker vector, which we view as a tensor, and a tropical linear space is recovered from its Plucker vector as the kernel of the corresponding wedge multiplication map. We prove that an arbitrary d-tensor satisfies the tropical Plucker relations (valuated exchange axiom) if and only if the d-th wedge power of the kernel of wedge-multiplication is free of rank one. This provides a new cryptomorphism for valuated matroids, including ordinary matroids as a special case