Macro-element interpolation on tensor product meshes

A general theory for obtaining anisotropic interpolation error estimates for macro-element interpolation is developed revealing general construction principles. We apply this theory to interpolation operators on a macro type of biquadratic $C^1$ finite elements on rectangle grids which can be viewed as a rectangular version of the $C^1$ Powell-Sabin element. This theory also shows how interpolation on the Bogner-Fox-Schmidt finite element space (or higher order generalizations) can be analyzed in a unified framework. Moreover we discuss a modification of Scott-Zhang type giving optimal error estimates under the regularity required without imposing quasi uniformity on the family of macro-element meshes used. We introduce and analyze an anisotropic macro-element interpolation operator, which is the tensor product of one-dimensional $C^1-P_2$ macro interpolation and $P_2$ Lagrange interpolation. These results are used to approximate the solution of a singularly perturbed reaction-diffusion problem on a Shishkin mesh that features highly anisotropic elements. Hereby we obtain an approximation whose normal derivative is continuous along certain edges of the mesh, enabling a more sophisticated analysis of a continuous interior penalty method in another paper

The greenhouse diet : gypsy moth performance in a CO2-enriched world

Rising atmospheric CO2 is regarded as the main driver of global warming (Crowley, 2000). While temperature changes directly affect plants and animals (Root et al., 2003; Parmesan, 2006), the effects of CO2 on herbivores are mediated through changes in nutrient quality. Elevated concentrations of atmospheric CO2 are likely to increase photosynthetic activity and thus provide more C-based compounds which may alter plant chemical profiles and plant–herbivore–natural enemy interactions. There are several scenarios how insects will react when confronted with a different food quality. A nutrient poor diet, induced by nitrogen dilution, may result in compensatory feeding with either no adverse effects on insect performance or with negative effects on insect growth due to low digestibility of plant structural compounds (e.g. lignin) or toxic effects of secondary metabolites (e.g. tannins). Here we present data from on-tree feeding trials with larvae of the generalist herbivore Lymantria dispar and one of its natural enemies, the hymenopteran endoparasitoid Glyptapanteles liparidis, studied in 2005. The experiments were conducted at the Swiss free-air CO2 enrichment (FACE) site near Basel, in an approximately 80-100-yr-old, mixed-species forest. The data link changes in foliar chemistry of three tree species (Quercus petraea, Fagus sylvatica, Carpinus betulus) exposed to 540 ppm CO2 with herbivore and parasitoid performance.Steigende Konzentrationen an atmosphärischem CO2 beeinflussen den Chemismus von Pflanzen, vornehmlich durch eine Ankurbelung der Fotosynthese, wodurch sich auch die Nahrungsqualität für herbivore Insekten ändert. Die vorliegende Studie dokumentiert erste Ergebnisse aus einem Freilandversuch mit Raupen des Schwammspinners Lymantria dispar (Lep., Lymnatriidae) und seinem natürlichen Gegenspieler, der parasitischen Schlupfwespe Glyptapanteles liparidis (Hym., Braconidae), die sich auf einer web-FACE (free air CO2 enrichment) Versuchsfläche in einer 540 ppm CO2-Atmosphäre entwickelten. Die Ergebnisse verknüpfen Daten der Blattchemie von Eiche, Buche und Hainbuche mit jenen des Wachstums und der Entwicklung von Raupen und Parasitoiden. Unter erhöhten CO2 Konzentrationen produzierten die Blätter generell mehr Kohlenhydrate. Blieb in den Bäumen die Stickstoff (N)-Aufnahme hinter dem CO2-bedingten Anstieg an Kohlenstoff zurück (z.B. Eiche), konsumierten die Raupen über 50% mehr Blattmasse. Dennoch waren die Wachstumsraten dieser Tiere um ca. 15% niedriger und sie entwickelten sich langsamer als Raupen in normaler CO2 Atmosphäre (ca. 378 ppm). Bei einem gleichzeitigen Anstieg der N-Gehalte in den Blättern (z.B. Hainbuche) erreichten die Raupen trotz kürzerer Entwicklungsdauer eine deutlich höhere Biomasse. Die Puppen der Tiere, die sich in erhöhter CO2 Atmosphäre entwickelt hatten, waren bei allen 3 Baumarten schwerer als die der Kontrolltiere. Überraschenderweise zeigten sich die in der Leibeshöhle der Schwammspinnerraupen heranwachsenden Parasitoidenlarven von der veränderten Nahrungsqualität ihrer Wirte nicht beeinträchtigt. Ein etwaiges geringeres Nährstoffangebot glichen sie durch Verlängerung der endoparasitischen Entwicklungsphase aus. Die adulten Wespen von beiden CO2 Varianten unterschieden sich nicht voneinander

Early Archean (approximately 3.4 Ga) prokaryotic filaments from cherts of the apex basalt, Western Australia: The oldest cellularly preserved microfossils now known

In comparison with that known from later geologic time, the Archean fossil record is miniscule: although literally hundreds of Proterozoic formations, containing more that 2800 occurrences of bona fide microfossils are now known, fewer than 30 units containing some 43 categories of putative microfossils (the vast majority of which are of questionable authenticity) have been reported from the Archean. Among the oldest known fossils are Early Archean filaments reported from cherts of the Towers Formation and the Apex Basalt of the 3.3-3.6 Ga-old Warrawoona Group of Western Australia. The paleobiologic significance of the Towers Formation microstructures is open to question: thin aggregated filaments are properly regarded as dubiomicrofossils (perhaps biogenic, but perhaps not); therefore, they cannot be regarded as firm evidence of Archean life. Although authentic, filamentous microfossiles were reported from a second Towers Formation locality, because the precise layer containing the fossiliferous cherts was not relocated, this discovery can neither be reconfirmed by the original collector nor confirmed independently by other investigators. Discovery of microfossils in bedded cherts of the Apex Basalt, the stratigraphic unit immediately overlying the Towers Formation, obviates the difficulties stored above. The cellularly preserved filaments of the Apex Basalt meet all of the criteria required of a bona fide Archean microfossils. Recent studies indicate that the Apex assemblage includes at least six morphotypes of uniseriate filaments, composed of barrel-shaped, discoidal, or quadrate cells and exhibiting rounded or conical terminal cells and medial bifurcated and paired half-cells that reflect the occurrence of prokaryotic binary cell division. Interestingly, the majority of these morphotypes are morphologically more similar to extant cyanobacteria than to modern filamentous bacteria. Prokaryotes seem clearly to have been hypobradytelic, and the evidence suggests (but does not prove) that physiologically advanced oxygen-producing photosynthesizers may have been represented in the Early Archean biota

Micropaleontological studies of lunar samples. A search for biogenic structures in the Apollo 12 lunar samples

Biogeochemical and microstructural analyses on lunar rock and dust samples for biological compound

Five or six step scenario for evolution?

The prediction that (due to the limited amount of hydrogen available as fuel in the Sun) the future duration of our favourable terrestrial environment will be short (compared with the present age of the Earth) has been interpreted as evidence for a hard step scenario. This means that some of the essential steps (such as the development of eukaryotes) in the evolution process leading to the ultimate emergence of intelligent life would have been hard, in the sense of being against the odds in the available time, so that they are unlikely to have been achieved in most of the earth-like planets that may one day be discovered in nearby extra-solar systems. It was originally estimated that only one or two of the essential evolutionary steps had to have been hard in this sense, but it has become apparent that this figure may need upward revision, because recent studies of climatic instability suggest that the possible future duration of our biologically favourable environment may be shorter than had been supposed, only about one Giga year rather than five. On the basis of the statistical requirement of roughly equal spacing between hard steps, it is argued that the best fit with the fossil record is now obtainable by postulating the number of hard steps to be five, if our evolution was exclusively terrestrial, or six if, as now seems very plausible, the first step occurred on Mars.Comment: 11 pages Late

Una lectura finisecular de Neruda

Esta aproximación a la obra de Pablo Neruda se centra en la primera fase de su producción poética, básicamente, desde 1923 a 1936. Se estudia primero el vanguardismo de Veinte poemas de amor y una canción desesperada, para enfocar en seguida un libro central de la producción del poeta: Residencia en la tierra. Se presta atención al lenguaje residenciario y, especialmente, al sujeto poético que aquí se constituye, analizando en particular Galope muerto y El fantasma del buque de carga. El sujeto hablante es definido como discontinuo y su mundo, como disgregado. El estudio concluye abordando el tema del tiempo y el tema de la deshumanización del arte

Error analysis of the Galerkin FEM in L 2 -based norms for problems with layers: On the importance, conception and realization of balancing

In the present thesis it is shown that the most natural choice for a norm for the analysis of the Galerkin FEM, namely the energy norm, fails to capture the boundary layer functions arising in certain reaction-diffusion problems. In view of a formal Definition such reaction-diffusion problems are not singularly perturbed with respect to the energy norm. This observation raises two questions: 1. Does the Galerkin finite element method on standard meshes yield satisfactory approximations for the reaction-diffusion problem with respect to the energy norm? 2. Is it possible to strengthen the energy norm in such a way that the boundary layers are captured and that it can be reconciled with a robust finite element method, i.e.~robust with respect to this strong norm? In Chapter 2 we answer the first question. We show that the Galerkin finite element approximation converges uniformly in the energy norm to the solution of the reaction-diffusion problem on standard shape regular meshes. These results are completely new in two dimensions and are confirmed by numerical experiments. We also study certain convection-diffusion problems with characterisitc layers in which some layers are not well represented in the energy norm. These theoretical findings, validated by numerical experiments, have interesting implications for adaptive methods. Moreover, they lead to a re-evaluation of other results and methods in the literature. In 2011 Lin and Stynes were the first to devise a method for a reaction-diffusion problem posed in the unit square allowing for uniform a priori error estimates in an adequate so-called balanced norm. Thus, the aforementioned second question is answered in the affirmative. Obtaining a non-standard weak formulation by testing also with derivatives of the test function is the key idea which is related to the H^1-Galerkin methods developed in the early 70s. Unfortunately, this direct approach requires excessive smoothness of the finite element space considered. Lin and Stynes circumvent this problem by rewriting their problem into a first order system and applying a mixed method. Now the norm captures the layers. Therefore, they need to be resolved by some layer-adapted mesh. Lin and Stynes obtain optimal error estimates with respect to the balanced norm on Shishkin meshes. However, their method is unable to preserve the symmetry of the problem and they rely on the Raviart-Thomas element for H^div-conformity. In Chapter 4 of the thesis a new continuous interior penalty (CIP) method is present, embracing the approach of Lin and Stynes in the context of a broken Sobolev space. The resulting method induces a balanced norm in which uniform error estimates are proven. In contrast to the mixed method the CIP method uses standard Q_2-elements on the Shishkin meshes. Both methods feature improved stability properties in comparison with the Galerkin FEM. Nevertheless, the latter also yields approximations which can be shown to converge to the true solution in a balanced norm uniformly with respect to diffusion parameter. Again, numerical experiments are conducted that agree with the theoretical findings. In every finite element analysis the approximation error comes into play, eventually. If one seeks to prove any of the results mentioned on an anisotropic family of Shishkin meshes, one will need to take advantage of the different element sizes close to the boundary. While these are ideally suited to reflect the solution behavior, the error analysis is more involved and depends on anisotropic interpolation error estimates. In Chapter 3 the beautiful theory of Apel and Dobrowolski is extended in order to obtain anisotropic interpolation error estimates for macro-element interpolation. This also sheds light on fundamental construction principles for such operators. The thesis introduces a non-standard finite element space that consists of biquadratic C^1-finite elements on macro-elements over tensor product grids, which can be viewed as a rectangular version of the C^1-Powell-Sabin element. As an application of the general theory developed, several interpolation operators mapping into this FE space are analyzed. The insight gained can also be used to prove anisotropic error estimates for the interpolation operator induced by the well-known C^1-Bogner-Fox-Schmidt element. A special modification of Scott-Zhang type and a certain anisotropic interpolation operator are also discussed in detail. The results of this chapter are used to approximate the solution to a recation-diffusion-problem on a Shishkin mesh that features highly anisotropic elements. The obtained approximation features continuous normal derivatives across certain edges of the mesh, enabling the analysis of the aforementioned CIP method.:Notation 1 Introduction 2 Galerkin FEM error estimation in weak norms 2.1 Reaction-diffusion problems 2.2 A convection-diffusion problem with weak characteristic layers and a Neumann outflow condition 2.3 A mesh that resolves only part of the exponential layer and neglects the weaker characteristic layers 2.3.1 Weakly imposed characteristic boundary conditions 2.4 Numerical experiments 2.4.1 A reaction-diffusion problem with boundary layers 2.4.2 A reaction-diffusion problem with an interior layer 2.4.3 A convection-diffusion problem with characteristic layers and a Neumann outflow condition 2.4.4 A mesh that resolves only part of the exponential layer and neglects the weaker characteristic layers 3 Macro-interpolation on tensor product meshes 3.1 Introduction 3.2 Univariate C1-P2 macro-element interpolation 3.3 C1-Q2 macro-element interpolation on tensor product meshes 3.4 A theory on anisotropic macro-element interpolation 3.5 C1 macro-interpolation on anisotropic tensor product meshes 3.5.1 A reduced macro-element interpolation operator 3.5.2 The full C1-Q2 interpolation operator 3.5.3 A C1-Q2 macro-element quasi-interpolation operator of Scott-Zhang type on tensor product meshes 3.5.4 Summary: anisotropic C1 (quasi-)interpolation error estimates 3.6 An anisotropic macro-element of tensor product type 3.7 Application of macro-element interpolation on a tensor product Shishkin mesh 4 Balanced norm results for reaction-diffusion 4.1 The balanced finite element method of Lin and Stynes 4.2 A C0 interior penalty method 4.3 Galerkin finite element method 4.3.1 L2-norm error bounds and supercloseness 4.3.2 Maximum-norm error bounds 4.4 Numerical verification 4.5 Further developments and summary Reference

Mikrosporidien des Eichenprozessionsspinners, Thaumetopoea processionea (L.) (Lep., Thaumetopoeidae) in den Eichenwäldern Ostösterreichs

Since the late 1990s, the oak processionary moth, Thaumetopoea processionea (L.), has been occurring at high population densities in eastern Austria. Particularly, infestations in areas of human settlement have created increasing interest in this insect due to health problems caused by the urticating hairs of the larvae. New methods for biological control are desirable. Like essentially all forest Lepidoptera, T. processionea is host for entomopathogenic microsporidia. These obligatory parasitic protists have been evaluated as biocontrol agents against an other oak pest, Lymantria dispar (Weiser & Novotny, 1987; Jeffords & al., 1988). Life history traits of T. processionea make this insect an even more promising target for the use of microsporidia. The larvae are highly gregarious and stay together in nests made of larval silk for resting periods and molting. Microsporidia utilize several pathways for horizontal transmission that would be aided by these features: spores can be released after host death from cadavers as well as from living larvae via silk or feces. Additionally, many microsporidia are vertically transmitted (summarized in Maddox & al., 1998). In this project, T. processionea larvae from various regions in eastern Austria were screened for the natural occurrence of microsporidia. One isolate, Endoreticulatus sp., was further studied and mass produced in a laboratory host, L. dispar, that is easy to rear and does not pose a health hazard for people working with the insects. An inoculative release was attempted on isolated trees infested with T. processionea.In einem zweijährigen Screening untersuchten wir das Auftreten von Mikrosporidien bei Thaumetopoea processionea an verschiedenen Standorten in Ostösterreich. In neun von 18 Populationen wurden Mikrosporidiosen nachgewiesen, die Prävalenzen lagen zwischen 1,9 % und 15,4 %. Basierend auf lichtmikroskopischen Befunden waren die gefundenen Pathogene den Gattungen Endoreticulatus, Nosema, Cystosporogenes und Vairimorpha zuzuordnen. Endoreticulatus sp. vermochte im Labor Raupen von Lymantria dispar zu infizieren. Das erlaubte die einfache Produktion von Inokulum sowie Untersuchungen mit einem ungefährlichen Wirtsinsekt. Laborversuche mit L. dispar zeigten einen langsamen Krankheitsverlauf, der aber in signifikant erhöhter Mortalität resultierte (nur 26 % der oral inokulierten Tiere entwickelten sich zu Imagines), sowie eine effiziente horizontale Übertragung. Eine inokulative Freilassung wurde versucht: dazu wurden Endoreticulatus-Sporen in wässriger Suspension auf Blätter isoliert stehender, von T. processionea befallenen Eichen ausgebracht. Die Inokulation war erfolgreich, allerdings auf niedrigem Niveau – die maximale Infektionsrate lag bei 9,5 %