Circular Dichroism in Biological Photonic Crystals and Cubic Chiral Nets

Nature provides impressive examples of chiral photonic crystals, with the notable example of the cubic so-called srs network (the label for the chiral degree-three network modeled on SrSi2) or gyroid structure realized in wing scales of several butterfl

Development and refinement of proxy-climate indicators from peats

Peat, especially from acidic mires (bogs), is a natural archive of past environmental change. Reconstructions of past climate from bogs commenced in the 19th Century through examination of visible peat stratigraphy, and later formed the basis for a postglacial climatic scheme widely used in Northwest Europe. Nevertheless, misconceptions as to how bogs grow led to a 50-year lacuna in peat-climate study, before the concept of "cyclic regeneration" in bogs was refuted. In recent decades, research using proxyclimate indicators from bogs has burgeoned. A range of proxies for past hydrological change has been developed, as well as use of pollen, bog oaks and pines and other data to reconstruct past temperatures. Most of this proxy-climate research has been carried out in Northern Europe, but peat-based research in parts of Asia and North America has increased, particularly during the last decade, while research has also been conducted in Australia, New Zealand and South America. This paper reviews developments in proxy-climate reconstructions from peatlands; chronicles use of a range of palaeo-proxies such as visible peat stratigraphy, plant macrofossils, peat humification, testate amoebae and non-pollen palynomorphs; and explains the use of wiggle-match radiocarbon dating and relationship to climate shifts. It details other techniques being used increasingly, such as biomarkers, stable-isotopes, inorganic geochemistry and estimation of dust flux; and points to new proxies under development. Although explicit protocols have been developed recently for research on ombrotrophic mires, it must be recognised that not all proxies and techniques have universal applicability, owing to differences in species assemblages, mire formation, topographic controls, and geochemical characteristics

Photonic band gaps in materials with triply periodic surfaces and related tubular structures

We calculate the photonic band gap of triply periodic bicontinuous cubic structures and of tubular structures constructed from the skeletal graphs of triply periodic minimal surfaces. The effect of the symmetry and topology of the periodic dielectric structures on the existence and the characteristics of the gaps is discussed. We find that the C(I2-Y**) structure with Ia3d symmetry, a symmetry which is often seen in experimentally realized bicontinuous structures, has a photonic band gap with interesting characteristics. For a dielectric contrast of 11.9 the largest gap is approximately 20% for a volume fraction of the high dielectric material of 25%. The midgap frequency is a factor of 1.5 higher than the one for the (tubular) D and G structures

An Algorithm for Discrete Constant Mean Curvature Surfaces

. We present a new algorithm for computing discrete constant mean curvature surfaces in R 3 . It is based on the definition of a discrete version of the conjugate surface construction for cmc surfaces. Here we solve a Plateau problem for a discrete minimal surface in S 3 by computing a sequence of discrete harmonic maps F i : S 3 ! S 3 . The definition of a discrete conjugation allows to transform this sequence to a sequence of conjugate discrete maps which converges to a discrete cmc surface in R 3 . The algorithm is applicable to free boundary value problems for cmc surfaces and led to the recent discovery of new compact cmc surfaces. 1. Introduction Surfaces with constant mean curvature (cmc surfaces) are the mathematical abstraction of physical soap films and soap bubbles. Such surfaces behave like rubber bands which try to contract under their surface tension and thereby to minimize their total surface area under the restriction of enclosing a given amount of volume. T..

Numerical examples of compact constant mean curvature surfaces

We construct new examples of compact constant mean curvature surfaces numerically. A conjugate surface method allows to explicitly construct examples. We employ the numerical algorithm of Oberknapp and Polthier based on discrete techniques to find area minimizers in the sphere S 3 and to conjugate them to surfaces of constant mean curvature in IR 3 . We compute examples of genus 5 and 30 and discuss a further example of genus 3. Contents 1 Introduction 2 2 The conjugate surface construction 3 2.1 A C 1 -description of conjugation : : : : : : : : : : : : : : : : : : : : : : : 7 2.2 The period problem : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 9 3 Numerical algorithm for discrete MC1 surfaces 9 4 Candidates and necessary conditions 12 4.1 The balancing formula : : : : : : : : : : : : : : : : : : : : : : : : : : : : 14 4.2 Stability : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 14 5 The examples and their numerics 16 1 1 Introduction ..