Random Block Operators

We study fundamental spectral properties of random block operators that are common in the physical modelling of mesoscopic disordered systems such as dirty superconductors. Our results include ergodic properties, the location of the spectrum, existence and regularity of the integrated density of states, as well as Lifshits tails. Special attention is paid to the peculiarities arising from the block structure such as the occurrence of a robust gap in the middle of the spectrum. Without randomness in the off-diagonal blocks the density of states typically exhibits an inverse square-root singularity at the edges of the gap. In the presence of randomness we establish a Wegner estimate that is valid at all energies. It implies that the singularities are smeared out by randomness, and the density of states is bounded. We also show Lifshits tails at these band edges. Technically, one has to cope with a non-monotone dependence on the random couplings.Comment: 22 pages, 3 figure

Lifshitz tails for spectra of Erd\H{o}s--R\'{e}nyi random graphs

We consider the discrete Laplace operator $\Delta^{(N)}$ on Erd\H{o}s--R\'{e}nyi random graphs with $N$ vertices and edge probability $p/N$. We are interested in the limiting spectral properties of $\Delta^{(N)}$ as $N\to\infty$ in the subcritical regime $0<p<1$ where no giant cluster emerges. We prove that in this limit the expectation value of the integrated density of states of $\Delta^{(N)}$ exhibits a Lifshitz-tail behavior at the lower spectral edge E=0.Comment: Published at http://dx.doi.org/10.1214/1050516000000719 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Molecular equilibria determined by van der Waals' attraction.

This thesis is primarily concerned with a nuclear magnetic resonance study on the effect of intramolecular van der Waals' attractive forces between alkyl groups. This phenomenon is investigated by devising certain two-fold conformational equilibria, such that one side of the equilibrium has two alkyl groups positioned relatively close to one another and attracting one another, the other side has the alkyl groups further apart and experiencing a greatly reduced interaction. The valence bond isomerisation between 1,4 and 1,6-dialkylcyclooctatetraenes 7(R=Me), 8(R=Et), 9(R=ipr), 10(R='Bu) is observed to favour the more compact 1,6-isomers in solution. This preference is attributed to van der Waals' attraction between the pendant alkyl groups. Molecular mechanics agree as to the preferred valence isomer and confirm it has greater attractive steric interactions. The two-fold 1-(3-alkylphenyl)-group rotational equilibrium in 1 (e)-(3-alkylphenyl)-2(e),6(e)-dimethylcyclohexan-1 -ols 23(R=Me), 24(R='Bu) and 1 (e)(3-alkylphenyl)-2(e),6(e)-dimethylcyclohexanes 25(R=Me), 26(R='Bu) is observed to favour the more compact conformer for 23, 24 but the less compact conformer for 26, while no preference is seen for 25. A combination of buttressing and attractive steric effects are postulated to explain these preferences, the results being supplemented with molecular mechanics calculations. The l-(l-methylneopentyl) rotational equlibrium in 1-(1-methylneopentyl)-3-alkylbenzenes 33(R=Me), 34(R='Bu) and 3-(1-methylneopentyl)phenanthrene 35 favours the less compact conformers for 34 and 35, while no preference is seen for 33. Buttressing is invoked to explain the observed conformational preferences, the results being supplemented with molecular mechanics calculations. The rotational conformations of a 2-methylalkyl-group in 2-methylalkyl-4,4-dimethyl-1,3-dioxanes 39(R=ipr), 40(R=1-Ad), 41(R=Ph) are investigated via analysis of the three bond methyl 1H-NMR coupling constants. For 41, two unequally populated gauche conformations are indicated while for 39,40 no population difference is observed about the indicated bond. However, spin decoupling at the 2-H ring hydrogen in 39 suggests a preferred conformation about the ipr-CH2 bond in this compound. These results are interpreted in terms of buttressing and attractive steric effects. An assignment of NMR signals to rotamers for 23, 24, 25, 26 is performed via an NOE difference experiment on 1 (a)-(3-tBuphenyl)-2(e),6(e)-dimethylcyclohexane, 30. Signal assignment for meta-alkylbenzenes 33, 34, 35 is via an NOE difference experiment on 35

Protected steel and composite connections in fire, Simulation of the mechanical behaviour of steel and composite connections protected by intumescent coating in fire

Actual developments in numerical simulations of the structural behaviour in fire situation are focussed on taking into consideration the interaction of all structural members in a global approach. Therefore it is necessary to simulate the load bearing behaviour of connections.With this motivation, the authors conducted experiments and thermal FE-simulations on two different connection types. In this paper, the accompanying mechanical FE-simulations of both investigated connection types will be described. The joints are defined as an end plate connection in a steel structure and a fin plate connection in a composite structure. Besides the validation of the numerical models, the results of the described investigations show that it is possible to activate a significant moment resistance within fin plate connections of composite structures. The main requirement for this activation is sufficient reinforcement strength

Characterization of Water Dissociation on α\alpha-Al2_{2}O3_{3}(11ˉ02)(1\bar{1}02): Theory and Experiment

The interaction of water with $\alpha$-alumina (i.e. $\alpha$-Al$_{2}$O$_{3}$ surfaces is important in a variety of applications and a useful model for the interaction of water with environmentally abundant aluminosilicate phases. Despite its significance, studies of water interaction with $\alpha$-Al$_{2}$O$_{3}$ surfaces other than the $(0001)$ are extremely limited. Here we characterize the interaction of water (D$_{2}$O) with a well defined $\alpha$-Al$_{2}$O$_{3}$$(1\bar{1}02)$ surface in UHV both experimentally, using temperature programmed desorption and surface-specific vibrational spectroscopy, and theoretically, using periodic-slab density functional theory calculations. This combined approach makes it possible to demonstrate that water adsorption occurs only at a single well defined surface site (the so-called 1-4 configuration) and that at this site the barrier between the molecularly and dissociatively adsorbed forms is very low: 0.06 eV. A subset of OD stretch vibrations are parallel to this dissociation coordinate, and thus would be expected to be shifted to low frequencies relative to an uncoupled harmonic oscillator. To quantify this effect we solve the vibrational Schr\"odinger equation along the dissociation coordinate and find fundamental frequencies red-shifted by more than 1,500 cm$^{\text{-1}}$. Within the context of this model, at moderate temperatures, we further find that some fraction of surface deuterons are likely delocalized: dissociatively and molecularly absorbed states are no longer distinguishable.Comment: Paper: 22 pages, 9 figures , ESI: 6 pages, 1 figur

The Role of the Federal Energy Regulatory Commission in Protecting Non-Consumptive Water Uses

55 pages

Random block operators

We study fundamental spectral properties of random block operators that are common in the physical modelling of mesoscopic disordered systems such as dirty superconductors. Our results include ergodic properties, the location of the spectrum, existence and regularity of the integrated density of states, as well as Lifshits tails. Special attention is paid to the peculiarities arising from the block structure such as the occurrence of a robust gap in the middle of the spectrum. Without randomness in the off-diagonal blocks the density of states typically exhibits an inverse square-root singularity at the edges of the gap. In the presence of randomness we establish a Wegner estimate that is valid at all energies. It implies that the singularities are smeared out by randomness, and the density of states is bounded. We also show Lifshits tails at these band edges. Technically, one has to cope with a non-monotone dependence on the random coupling

Eigenfunctions and Quantum Transport with Applications to Trimmed Schrodinger Operators

We provide a simple proof of dynamical delocalization, that is, time-increasing lower bounds on quantum transport for discrete, one-particle Schrodinger operators on $\ell^2 (\mathbb{Z}^d)$, provided solutions to the Schrodinger equation satisfy certain growth conditions. The proof is based on basic resolvent identities and the Combes-Thomas estimate on the exponential decay of the Green's function. As a consequence, we prove that generalized eigenfunctions for energies outside the spectrum of $H$ must grow exponentially in some directions. We also prove that if $H$ has any absolutely continuous spectrum, then the Schrodinger operator exhibits dynamical delocalization. We apply the general result to $\Gamma$-trimmed Schrodinger operators, with periodic $\Gamma$, and prove dynamical delocalization for these operators. These results also apply to the $\Gamma$-trimmed Anderson model, providing a random, ergodic model exhibiting both dynamical localization in an energy interval and dynamical delocalization

Einflussfaktoren der öffentlichen Förderung in Ostdeutschland : eine Auswertung des IAB-Betriebspanels

In diesem Beitrag wird zunächst ein Überblick über die Ausgestaltung des Förderinstrumentariums für ostdeutsche Betriebe im Bereich der betrieblichen Wirtschafts- und betriebsnahen Arbeitsmarktpolitik gegeben. Darauf aufbauend wird die Inanspruchnahme der diskutierten Maßnahmen zwischen 1997 und 2002 untersucht. Ein besonderes Augenmerk wird dabei auf die Rolle des Betriebsrats gelegt. Anschließend wird über die Anwendung multivariater Verfahren analysiert, welche Einflussgrößen dafür verantwortlich sind, dass Betriebe Fördermaßnahmen nutzen. --