Lipschitz-continuity of the integrated density of states for Gaussian random potentials

The integrated density of states of a Schroedinger operator with random potential given by a homogeneous Gaussian field whose covariance function is continuous, compactly supported and has positive mean, is locally uniformly Lipschitz-continuous. This is proven using a Wegner estimate

Existence and uniqueness of the integrated density of states for Schr\"odinger operators with magnetic fields and unbounded random potentials

The object of the present study is the integrated density of states of a quantum particle in multi-dimensional Euclidean space which is characterized by a Schr\"odinger operator with a constant magnetic field and a random potential which may be unbounded from above and from below. For an ergodic random potential satisfying a simple moment condition, we give a detailed proof that the infinite-volume limits of spatial eigenvalue concentrations of finite-volume operators with different boundary conditions exist almost surely. Since all these limits are shown to coincide with the expectation of the trace of the spatially localized spectral family of the infinite-volume operator, the integrated density of states is almost surely non-random and independent of the chosen boundary condition. Our proof of the independence of the boundary condition builds on and generalizes certain results by S. Doi, A. Iwatsuka and T. Mine [Math. Z. {\bf 237} (2001) 335-371] and S. Nakamura [J. Funct. Anal. {\bf 173} (2001) 136-152].Comment: This paper is a revised version of the first part of the first version of math-ph/0010013. For a revised version of the second part, see math-ph/0105046. To appear in Reviews in Mathematical Physic

The absolute continuity of the integrated density of states for magnetic Schr\"odinger operators with certain unbounded random potentials

The object of the present study is the integrated density of states of a quantum particle in multi-dimensional Euclidean space which is characterized by a Schr{\"o}dinger operator with magnetic field and a random potential which may be unbounded from above and below. In case that the magnetic field is constant and the random potential is ergodic and admits a so-called one-parameter decomposition, we prove the absolute continuity of the integrated density of states and provide explicit upper bounds on its derivative, the density of states. This local Lipschitz continuity of the integrated density of states is derived by establishing a Wegner estimate for finite-volume Schr\"odinger operators which holds for rather general magnetic fields and different boundary conditions. Examples of random potentials to which the results apply are certain alloy-type and Gaussian random potentials. Besides we show a diamagnetic inequality for Schr\"odinger operators with Neumann boundary conditions.Comment: This paper will appear in "Communications in Mathematical Physics". It is a revised version of the second part of the first version of math-ph/0010013, which in its second version only contains the (revised) first par

Spectral induced polarisation for an enhanced pore-space characterisation and analysis of dissolution processes of carbonate rocks

Subrosion, d.h. die unterirdische Auslaugung von leicht löslichen Gesteinen wie z.B. Karbonat, ist eine weltweit auftretende Erscheinung, die letztlich zu subrosionsbedingten Erdfällen und Senken führt. Grundlagenforschung im Bereich von Lösungsprozessen an Karbonaten ist erforderlich für ein besseres Prozessverständnis dieser Ereignisse, um die Risikoeinschätzung sowie die Vorhersagemöglichkeiten zu verbessern. Diese Dissertation befasst sich mit der erweiterten Porenraumcharakterisierung und Auswertung mittels Spektraler induzierter Polarisation (SIP) von Lösungsprozessen in Karbonaten. SIP ist eine etablierte Methode für die Durchführung von Grundlagenforschung auf Porenskala im Bereich der Porenraumcharakterisierung und Bestimmung von Gesteinseigenschaften. Systematische Labormessungen an Karbonaten werden durchgeführt, um Gesteinscharakteristika und deren Einfluss auf die IP-Parameter als auch ihre Sensitivität auf Lösungsprozesse zu untersuchen. Die gesteinsspezifischen Untersuchungen umfassen ein multimethodisches Herangehen, welches petrophysikalische, mineralogische und geochemische Verfahren kombiniert, u.a. Spektren der komplexen elektrischen Leitfähigkeit und Daten von 2D und 3D Bildgebungsverfahren als auch Messgrößen wie Porosität, Permeabilität, spezifische Oberfläche und Verteilungen der Nuklear-Magnetischer Resonanz Relaxationszeiten. Zuerst werden für ein besseres Verständnis der IP-Parameter sowie Polarisationsmechanismen in Karbonaten Probensätze vier verschiedener Typlokationen mit einer großen Variation ihrer petrophysikalischen Eigenschaften untersucht. Zur Untersuchung des Polarisationsverhaltens der Karbonatproben werden verschiedene IP-Experimente durchgeführt und die Ergebnisse mit den vorhandenen Erkenntnissen über Sandsteine verglichen. Vier verschiedene Typen des Polarisationsverhalten können im Phasenspektrum ermittelt werden: (1) ein konstanter Phasenwinkel, (2) ein kontinuierlicher Phasenanstieg, (3) eine Kombinaten aus beiden sowie (4) ein Maximumtyp. Die explizite Zuordnung eines Karbonattyps zu einem charakteristischen Kurventyp ist übertragbar für den gesamten Probensatz. Der Vergleich von IP-Parametern mit petrophysikalischen Daten zeigt, dass es anspruchsvoller ist klare Korrelationen zwischen den Parametern festzustellen, vor allem im Vergleich zu Sandsteinen. Die Übertragbarkeit von empirischen Beziehungen und Modellannahmen, wie z.B. Formationsfaktorabschätzung und Permeabilitätsvorhersage, ist dennoch realisierbar. Im zweiten Schritt wurde ein Messplatz für systematische Lösungen sowie ein maßgeschneidertes experimentelles Konzept erfolgreich konzipiert und angewendet, um den Einfluss von Lösungsprozessen auf Mineral- und Porenstrukturen unter kontrollierten Laborbedingungen zu untersuchen. Zur systematischen Erfassung der Änderungen im Porenraum wurden vor und nach jeder Lösung gesteinsspezifische Untersuchen vorgenommen. Der Lösungsprozess beeinflusst verschiedene petrophysikalische Parameter mit unterschiedlicher Ausprägung. Während die Korndichte und Porosität zunehmen, erhöht sich zunächst die spezifische Oberfläche und verringert sich in späteren Stufen. Die Porenradienverteilungen aus Quecksilberporosimetrie und μ-CT Daten weisen auf eine Vergrößerung des dominanten Porenradius mit zunehmenden Lösungstufen hin. Die durch die Lösungsprozesse hervorgerufenen Änderungen in den Karbonaten lassen sich bis zu einem gewissen Grad mit SIP beobachten. Der Anstieg im Realteil der elektrischen Leitfähigkeit ergibt sich aus der zunehmenden Porosität sowie dem abnehmenden Formationsfaktor und der abnehmenden Volumentortuosität. Die Form der 00-Spektren ändert sich ebenfalls, da bei höheren Frequenzen der Imaginärteil der elektrischen Leitfähigkeit zunimmt, was auf die Entstehung kleinerer Poren hindeutet. Die gegensätzlichen Prozesse Glättung und Aufrauung der Porenoberflächen haben eine Abnahme bzw. Zunahme der Oberflächentortuosität zur Folge, was dementsprechend das Verhalten des Imaginärteils der elektrischen Leitfähigkeit beeinflusst. Insgesamt nimmt die Volumenleitfähigkeit stärker zu als die Oberflächenleitfähigkeit. Aufgrund der durch die Lösungsprozesse verursachten kleinen Änderungen der Gesteinsparameter ist die Dateninterpretation herausfordernd. Daher ist weitere Forschung im Bereich von Lösungsprozessen an Karbonaten erforderlich. Diese Dissertation verdeutlicht das Potential von SIP zur erweiterten Porenraumcharakterisierung sowie Auswertung von Lösungsprozessen von Karbonaten.Subrosion due to the subsurface leaching of soluble rocks, e.g. carbonates, is a global phenomenon that results in surface depressions and sinkholes. Fundamental research on dissolution processes of carbonates is necessary to better understand subrosion processes, to improve risk assessment and forecasting. This thesis deals with enhanced pore-space characterisation and analysis of dissolution processes in carbonates using spectral induced polarisation (SIP). SIP is a suitable method to conduct fundamental research to characterise the pore space and to obtain detailed information on rock properties. Systematic laboratory measurements on carbonates are conducted to investigate rock characteristics and their influence on IP responses and their sensitivity to dissolution processes. The core analysis program includes a multi-methodical approach that combines petrophysical, mineralogical and geochemical techniques, e.g. complex conductivity spectra, and data from 2D and 3D imaging techniques, as well as quantities such as porosity, permeability, specific surface area, and nuclear magnetic-resonance decay-time distributions. First, carbonate sample sets from four different type locations with a broad range of petrophysical parameters are investigated to better understand IP responses and mechanisms in carbonates. Different IP experiments are conducted to investigate the polarisation behaviour of the carbonate samples and the results are compared with the existing knowledge of SIP on sandstones. I show that four different types of polarisation behaviour can be observed in the spectra of the phase shift: (1) a constant phase angle, (2) a continuous increase, (3) a combination of both, and (4) a maximum type. Each carbonate type can be assigned to a characteristic curve type, which is reproducible for the whole sample set. Comparison of SIP with petrophysical parameters shows that it is more challenging to find clear correlations, especially compared to sandstones. However, it is possible to transfer empirical relationships and model assumptions from sandstones to carbonates, e.g. formation factor estimation and permeability prediction. In the second step, an experimental setup for systematic dissolution under monitoring conditions and an uniquely tailored experimental concept was successfully developed to investigate the impact of dissolution procedures on mineral and pore structure under controlled conditions. Before and after each dissolution step, the core analysis program was carried out to systematically record the changes of pore space. Dissolution processes change distinct petrophysical parameters on different scales. Grain density and porosity increase, whereas the specific surface increases at first and decreases at later stages, depending on contrary scenarios of specific surface variation on pore scale. The pore radii distributions of mercury intrusion porosimetry and μ-CT data reveal an enlargement of the dominant pore radii with increasing dissolution. Changes within the carbonate due to dissolution can be observed by SIP to a certain extent. An increased porosity, a decreased formation factor, and a decreased volume tortuosity leads to an increased real part of electrical conductivity. The shape of the 00-spectra changes as well. The imaginary part of electrical conductivity increases for higher frequencies due to dissolution processes, which indicates the formation of smaller pores. Contradictory processes of smoothing and roughing of the pore surface leads to both decreased and increased surface tortuosities, which affects the behaviour of the imaginary part of conductivity during dissolution. In summary, the volume conductivity increases more strongly than the surface conductivity. Due to small, dissolution-induced changes of the rock parameters, data interpretation is challenging. Hence, further research regarding dissolution processes of carbonates is required. This work demonstrates the potential of enhanced pore-space characterisation and analysis of dissolution processes of carbonate rocks using SIP

Turbulent viscosity and Lambda-effect from numerical turbulence models

Homogeneous anisotropic turbulence simulations are used to determine off-diagonal components of the Reynolds stress tensor and its parameterization in terms of turbulent viscosity and Lambda-effect. The turbulence is forced in an anisotropic fashion by enhancing the strength of the forcing in the vertical direction. The Coriolis force is included with a rotation axis inclined relative to the vertical direction. The system studied here is significantly simpler than that of turbulent stratified convection which has often been used to study Reynolds stresses. Certain puzzling features of the results for convection, such as sign changes or highly concentrated latitude distributions, are not present in the simpler system considered here.Comment: 3 pages, 2 figures, accepted for publication in Astronomische Nachrichte

Performance and Functionality Based Design Methods for Improved and Novel Aircraft Engine Components for Additive Manufacturing

For aircraft engine manufacturers the technology of AM appears promising. AM provides the opportunity for a highly flexible and a cost effective part production. Furthermore AM offers new potentials and possibilities for lightweight designs. The implementation and applications of AM can be divided in three different strategic application levels. The first level includes manufacturing simple existing parts; these kinds of parts are already in production. In the second level, new design tools, such as structural optimization, are used to improve an existing part by benefiting from the new design freedom but without changing its functionality. The third level includes novel parts with new functionality. This paper presents design methods for AM parts for the second and third level: performance and solution based approach, respectively. Also the safety classification of engine parts is looked into. Step-by-step design methods are presented, accompanied by case studies that demonstrate improvement to the initial design: a light weight, topology optimized turbine guide vane (level two) and an aircraft engine casing design that has an improved tip clearance behavior under transient operating cycles (level three).Mechanical Engineerin

Lifshitz Tails in Constant Magnetic Fields

We consider the 2D Landau Hamiltonian $H$ perturbed by a random alloy-type potential, and investigate the Lifshitz tails, i.e. the asymptotic behavior of the corresponding integrated density of states (IDS) near the edges in the spectrum of $H$. If a given edge coincides with a Landau level, we obtain different asymptotic formulae for power-like, exponential sub-Gaussian, and super-Gaussian decay of the one-site potential. If the edge is away from the Landau levels, we impose a rational-flux assumption on the magnetic field, consider compactly supported one-site potentials, and formulate a theorem which is analogous to a result obtained in the case of a vanishing magnetic field

Adoption and Use of Community Municipal Portals

Initial findings from a project examining community municipal portal adoption are reported. The study employs a theoretical model showing a causal effect of organizational factors and portal interface characteristics on a person’s intentions to use a community municipal portal and how individual demographics and perceptions mediate this effect. Six community municipal portals in Ontario, Canada participated. A questionnaire completed by internal portal stakeholders gives background on the portals’ purpose, history, functionality, IT support, and governance. An enduser survey administered to 1,753 respondents polls end-user demographics, perceptions, and behaviors. First phase results give insight on the organizational factors surrounding the implementation of community municipal portals (e.g., partner tensions, governance issues, low end-user involvement, marketing and financial concerns) and how they may influence low usage behaviors exhibited by a narrow demographic. Future phases of the study that further explore the impact of organizational factors and end-user characteristics on portal use are described