Paley-Littlewood decomposition for sectorial operators and interpolation spaces

We prove Paley-Littlewood decompositions for the scales of fractional powers of $0$-sectorial operators $A$ on a Banach space which correspond to Triebel-Lizorkin spaces and the scale of Besov spaces if $A$ is the classical Laplace operator on $L^p(\mathbb{R}^n).$We use the $H^\infty$-calculus, spectral multiplier theorems and generalized square functions on Banach spaces and apply our results to Laplace-type operators on manifolds and graphs, Schr\"odinger operators and Hermite expansion.We also give variants of these results for bisectorial operators and for generators of groups with a bounded $H^\infty$-calculus on strips.Comment: 2nd version to appear in Mathematische Nachrichten, Mathematical News / Mathematische Nachrichten, Wiley-VCH Verlag, 201

Spectral multiplier theorems and averaged R-boundedness

Let $A$ be a $0$-sectorial operator with a bounded $H^\infty(\Sigma\_\sigma)$-calculus for some $\sigma \in (0,\pi),$ e.g. a Laplace type operator on $L^p(\Omega),\: 1 < p < \infty,$ where $\Omega$ is a manifold or a graph. We show that $A$ has a H{\"o}rmander functional calculus if and only if certain operator families derived from the resolvent $(\lambda - A)^{-1},$ the semigroup $e^{-zA},$ the wave operators $e^{itA}$ or the imaginary powers $A^{it}$ of $A$ are $R$-bounded in an $L^2$-averaged sense. If $X$ is an $L^p(\Omega)$ space with $1 \leq p < \infty,$ $R$-boundedness reduces to well-known estimates of square sums.Comment: Error in the title correcte

Manifold tensor categories

We introduce Manifold tensor categories, which make precise the notion of a tensor category with a manifold of simple objects. A basic example is the category of vector spaces graded by a Lie group. Unlike classic tensor category theory, our setup keeps track of the smooth (and topological) structure of the manifold of simple objects. We set down the necessary definitions for Manifold tensor categories and a generalisation we term Orbifold tensor categories. We also construct a number of examples, most notably two families of examples we call Interpolated Tambara-Yamagami categories and Interpolated quantum group categories. Finally, we show conditions under which pointwise duality data in an Orbifold tensor category automatically assembles into smooth duality data. Our proof uses the classic Implicit function theorem from differential geometry.Comment: This document is an edited excerpt of the author's thesi

Simulation strategies for the massless lattice Schwinger model in the dual formulation

The dual form of the massless Schwinger model on the lattice overcomes the complex action problems from two sources: a topological term, as well as non-zero chemical potential, making these physically interesting cases accessible to Monte Carlo simulations. The partition function is represented as a sum over fermion loops, dimers and plaquette-surfaces such that all contributions are real and positive. However, these new variables constitute a highly constrained system and suitable update strategies have to be developed. In this exploratory study we present an approach based on locally growing plaquette-surfaces surrounded by fermion loop segments combined with a worm based strategy for updating chains of dimers, as well as winding fermion loops. The update strategy is checked with conventional simulations as well as reference data from exact summation on small volumes and we discuss some physical implications of the results

Single Ion Impact Detection & Scanning Probe Aligned Ion Implantation for Quantum Bit Formation

Daten- und Informationsverarbeitung via Quantencomputer ist ein viel versprechender Ansatz, um die klassische Art und Weise via Digitalrechner, welche sich fundamentalen physikalischen Grenzen annŠhern, zu ersetzen. Anstelle von klassischen Bits werden Quantenbits (Qubits) fŸr Rechenoperationen verwendet. Aufgrund quantenmechanischer PhŠnomene wie Superposition und VerschrŠnkung, wird die Informationsverarbeitung in einer ganz anderen Art und Weise umgesetzt und eine Leistungssteigerung fŸr bestimmte Aufgabenstellungen erreicht. Es gibt verschiedene VorschlŠge zur technischen Umsetzung von Quanten-Bits. Unter ihnen sind Elektronen- oder Kernspins von Defektstellen in Festkšrpern. Zwei solche Kandidaten mit Spinfreiheitsgraden sind einzelne Donatoren in Silizium und Stickstoff Fehlstellen (NV) Zentren in Diamant. Beide Qubit-Kandidaten besitzen aussergewšhnliche Eigenschaften, welche sie zu vielversprechenden Bausteinen machen. Neben gewissen Vorteilen verbindet die beiden Qubits auch die Notwendigkeit, diese prŠzise in ihren TrŠgermaterialien und Bauelementstrukturen zu platzieren. Eine hŠufig verwendete Methode, die Fremdatome in die Substratmaterialien einzubringen, ist die Ionenimplantation. HierfŸr kšnnen fokussierte Ionenstrahl-Systeme verwendet werden, oder Kollimationstechniken, wie in dieser Arbeit. Ein ausgedehnter Ionenstrahl trifft die RŸckseite einer Rastersondenmikroskopspitze mit integrierten …ffnungen. Das Rastersondenmikroskop ermšglichen die zerstšrungsfreie und hochauflšsende Abbildung von Bauteilstrukturen und die Platzierung der Rastersondenmikroskopspitze, und damit des kollimierten Ionenstrahls, um ausgewŠhlte Regionen zu implantieren. In der vorgelegten Arbeit wird diese Technik angewendet und weiterentwickelt, um notwendige PrŠzisionskriterien zu erfŸllen. Die Platzierung des Ionenstrahls auf Bauelementstrukturen, welche empfindsam auf Ionenbombardement reagieren und damit Detektoren darstellen, wurde demonstriert. Die gleiche Technik wird auch zur Anordnung von NV-Zentren in Diamantsubstraten verwendet. Des weiteren werden einzelne IoneneinschlŠge in Siliziumbauteilen erfasst, wodurch das gezielte Dotieren Ion fŸr Ion ermšglicht wird.Quantum computing and quantum information processing is a promising path to replace classical information processing via conventional computers which are approaching fundamental physical limits. Instead of classical bits, quantum bits (qubits) are utilized for computing operations. Due to quantum mechanical phenomena such as superposition and entanglement, a completely different way of information processing is achieved, enabling enhanced performance for certain problem sets. Various proposals exist on how to realize a quantum bit. Among them are electron or nuclear spins of defect centers in solid state systems. Two such candidates with spin degree of freedom are single donor atoms in silicon and nitrogen vacancy (NV) defect centers in diamond. Both qubit candidates possess extraordinary qualities which makes them promising building blocks. Besides certain advantages, the qubits share the necessity to be placed precisely in their host materials and device structures. A commonly used method is to introduce the donor atoms into the substrate materials via ion implantation. For this, focused ion beam systems can be used, or collimation techniques as in this work. A broad ion beam hits the back of a scanning probe microscope (SPM) cantilever with incorporated apertures. The high resolution imaging capabilities of the SPM allows the non destructive location of device areas and the alignment of the cantilever and thus collimated ion beam spot to the desired implant locations. In this work, this technique is explored, applied and pushed forward to meet necessary precision requirements. The alignment of the ion beam to surface features, which are sensitive to ion impacts and thus act as detectors, is demonstrated. The technique is also used to create NV center arrays in diamond substrates. Further, single ion impacts into silicon device structures are detected which enables deliberate single ion doping

Organizational Water Footprint to Support Decision Making: a Case Study for a German Technological Solutions Provider for the Plumbing Industry

With water scarcity representing an increasing threat to humans, the environment and the economy, companies are interested in exploring how their operations and supply chains affect water resources globally. To allow for systematically compiling the water footprint at the company level, the organizational water footprint method based on ISO 14046 and ISO/TS 14072 was developed. This paper presents the first complete organizational water scarcity footprint case study carried out for Neoperl GmbH, a German company that offers innovative solutions regarding drinking water for the plumbing industry. The cradle-to-gate assessment for one year includes, besides facility-based production activities, purchased materials, electricity and fuels, and supporting activities, such as company vehicles and infrastructure. Neoperl’s total freshwater consumption amounts to approximately 110,000 m3, 96% thereof being attributable to the supply chain, with freshwater consumption through purchased metals playing the predominant role. Metals (mainly stainless steel and brass) are major hotspots, also when considering the water scarcity-related local impacts resulting from freshwater consumption, which mainly affect China and Chile. These results can be used to improve the company’s supply chain water use in cooperation with internal and external stakeholders by means of, e.g., sustainable purchase strategies or eco-design options to substitute water intensive materials.BMBF, 02WGR1429, GROW - Verbundprojekt WELLE: Wasserfußabdruck für Unternehmen - Lokale Maßnahmen in Globalen WertschöpfungskettenDFG, 414044773, Open Access Publizieren 2019 - 2020 / Technische Universität Berli

An interactive stated adaptation survey of activity scheduling decisions

The paper reports on current research in a project exploring new approaches for analyzing travel demand induced by changes in generalized costs of travel and activity participation. A sample of respondents were administered a five-day travel diary, from which one day was selected for further analysis. The conditions of that day were changed using predefined heuristics based on the household characteristics, to attain significant changes in the generalized costs of the reported trips. The households were then faced with these hypothetical scenarios in face-to-face interviews. All household members are asked to state how the implied changes would have affected their activity scheduling on the specified day, that is to adapt their reported schedule to the new conditions. The data will allow the computation of discrete choice models of activity scheduling. The results are expected to reflect the effects of the changes in generalized costs on activity generation. The results will be applied in MATSim, an agent-based micro-simulation. The application will allow the validation of the model results and the evaluation of aggregated effects of measures changing generalized costs, as well as their repercussions on the transport system and the resulting feedback effects, thus allowing the assessment of total induced demand and a comparison to the results from earlier aggregate models. The paper focuses on the description of the survey approach, which to our best knowledge is novel in its application, and reports preliminary analyses of the respondents’ reactions to the changes implied in the household interviews

Amount of water needed to save 1 m3 of water: life cycle assessment of a flow regulator

Water saving devices in the sanitary equipment, such as flow regulators, are assumed to be environmentally advantageous even though their environmental benefit has never been compared to the environmental burden caused during their production und disposal. Therefore, a life cycle assessment according to ISO 14044 has been conducted to identify and quantify the environmental effects throughout the lifespan of a flow regulator. The analysis comprises the production of materials, manufacturing of components at suppliers, the assembly at NEOPERL®, all transports, savings of water and thermal energy during use as well as waste incineration including energy recovery in the end-of-life stage. Results show that the production of one flow regulator causes 0.12 MJ primary energy demand, a global warming potential of 5.9 g CO2-equivalent, and a water consumption of 30.3 ml. On the other hand, during a use of 10 years, it saves 19,231 MJ primary energy, 1223 kg CO2-equivalent, and avoids a water consumption of 790 l (166,200 l water use). Since local impacts of water consumption are more relevant than volumes, consequences of water consumption have been analyzed using recently developed impact assessment models. Accordingly, the production of a flow regulator causes 8.5 ml freshwater depletion, 1.4 × 10−13 disability adjusted life years, and 4.8 × 10−6 potentially disappeared fractions of species m2 a. Even though avoided environmental impacts resulting from water savings highly depend on the region where the flow regulator is used, the analysis has shown that environmental benefits are at least 15,000 times higher than impacts caused during the production

3D direct pore level simulations of radiant porous burners

Inside porous burners, chemical combustion reactions coincide with complex interaction between thermo-physical transport processes that occur within solid and gaseous phase and across phase boundary. Fluid flow, heat release and resulting heat flows influence each other. The numerical model used in this work considers gaseous and solid phases, includes fluid flow, enthalpy transport, conjugate heat transfer, and radiative heat transfer between solid surfaces, as well as combustion kinetics according to a skeletal chemical reaction mechanism, fully resolved on the pore scale in three-dimensional space (Direct Pore Level Simulation, DPLS). The calculations are performed based on the finite volume method using standard applications implemented in the OpenFOAM library. The present study presents simulations of three different structures, each at four settings of specific thermal power. Results indicate that specific surface area of the porous structure is a major influencing parameter for increasing radiation efficiency, whereas no correlation of the orientation of an anisotropic structure on radiation efficiency was observed