841 research outputs found
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 fĂĽr die DurchfĂĽhrung von Grundlagenforschung auf Porenskala im Bereich der Porenraumcharakterisierung
und Bestimmung von Gesteinseigenschaften. Systematische Labormessungen an Karbonaten
werden durchgefĂĽhrt, 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 durchgefĂĽhrt und die Ergebnisse mit den vorhandenen Erkenntnissen ĂĽber
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 ĂĽbertragbar fĂĽr 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 Ăśbertragbarkeit
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 ÎĽ-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
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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 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 . 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
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