Two Non-Vanishing results concerning the Anti-Canonical Bundle

Let $(X, \Delta)$ be a klt pair with nef anti-log canonical bundle $-(K_X+\Delta)$. We prove that $\kappa(X, -(K_X+\Delta))\geq 0$ assuming that either $X$ is of low dimension or that the generalised (numerical) non-vanishing conjecture holds. To do so, we prove a more general equivariant non-vanishing result for anti-log canonical bundles.Comment: Comments are very welcome

Canonical extensions of manifolds with nef tangent bundle

To any compact K\"ahler manifold $(X, \omega)$ one may associate a bundle of affine spaces $Z_X\rightarrow X$ called a $\textit{canonical extension}$ of $X$. In this paper we prove that (assuming a well-known conjecture of Campana-Peternell to hold true) if the tangent bundle of $X$ is nef, then the total space $Z_X$ is a Stein manifold. This partially answers a question raised by Greb-Wong of whether these two properties are actually equivalent. We also complement some known results for surfaces in the converse direction.Comment: 23 page

Multimodal microscopy in mid-infrared via flexible pulse shaping

In this thesis, mid-infrared (MIR) pulses with arbitrary temporal and spectral shape are generated via a difference-frequency process for application in a non-linear Raman microscope. Solely by shaping the sub 10 fs driving pulses, the broadband spectra of the MIR pulses are switched to narrowband and tuneable ones. In MIR transmission spectroscopy, these narrowband MIR spectra allow for investigating molecular vibrations from 1250 to 3250 cm-1 with spectral resolutions below 20 cm-1. Furthermore, MIR transmission microspectroscopy is combined with coherent-anti-Stokes Raman scattering (CARS) to provide a direct comparison of spectra and images obtained in one spot of the sample. Sum-frequency (SF) microspectroscopy is an additional technique, which complements the toolbox of this non-linear Raman microscope with the potential to investigate non-centrosymmetric systems. The flexibility of the pulse shaper allows for implementing two different SF-methods. Whereas the heterodyne multiplex method acquires the whole SF spectrum by imprinting only three different phase functions, the homodyne MIR-scanning method generates a high SF intensity directly linked to one vibrational mode. In all applications, the phase of MIR pulses must be well-known. This phase is determined in the focal plane of the microscope over more than 1000 cm-1 via two methods based on the dispersion-scan

Dressing the chopped-random-basis optimization: a bandwidth-limited access to the trap-free landscape

In quantum optimal control theory the success of an optimization algorithm is highly influenced by how the figure of merit to be optimized behaves as a function of the control field, i.e. by the control landscape. Constraints on the control field introduce local minima in the landscape --false traps-- which might prevent an efficient solution of the optimal control problem. Rabitz et al. [Science 303, 1998 (2004)] showed that local minima occur only rarely for unconstrained optimization. Here, we extend this result to the case of bandwidth-limited control pulses showing that in this case one can eliminate the false traps arising from the constraint. Based on this theoretical understanding, we modify the Chopped Random Basis (CRAB) optimal control algorithm and show that this development exploits the advantages of both (unconstrained) gradient algorithms and of truncated basis methods, allowing to always follow the gradient of the unconstrained landscape by bandwidth-limited control functions. We study the effects of additional constraints and show that for reasonable constraints the convergence properties are still maintained. Finally, we numerically show that this approach saturates the theoretical bound on the minimal bandwidth of the control needed to optimally drive the system.Comment: 8 pages, 6 figure

Dividend Smoothing in Sweden - An Empirical Investigation of Determinants of Dividend Smoothing

Purpose: The main purpose is to see if dividend smoothing is a pertinent phenomenon among Swedish public firms. The study also aims to identify what firm characteristics that drive dividend smoothing. Theoretical Framework: The theoretical framework covers different explanations of dividend smoothing behavior, such as information asymmetries, agency issues and investor clientele motivations. Also, share repurchases are given as an explanation of dividend smoothing behavior. Empirical Foundation: The study covers firms listed on Nasdaq OMX Stockholm, that have been paying dividends every single year during the period of 2001-2012, or for as long as the company has been listed, for a minimum of 7 years. 85 companies are making the cut. Methodology: Quantitative approach using Lintner’s partial adjustment model as well as multiple regression analyses. Conclusion: Dividend smoothing seems to be an occurring phenomena among Swedish public firms. The results of this study mainly support agency theory as being a determining factor of dividend smoothing, while there is no support for information asymmetry and investor clientele motivations. Further, firms that repurchase shares seem to be more likely to smooth their dividends than other firms

Quantitative measurement of combustion gases in harsh environments using NDIR spectroscopy

The global climate change calls for a more environmental friendly use of energy and has led to stricter limits and regulations for the emissions of various greenhouse gases. Consequently, there is nowadays an increasing need for the detection of exhaust and natural gases. This need leads to an ever-growing market for gas sensors, which, at the moment, is dominated by chemical sensors. Yet, the increasing demands to also measure under harsh environmental conditions pave the way for non-invasive measurements and thus to optical detection techniques. Here, we present the development of a non-dispersive infrared absorption spectroscopy (NDIR) method for application to optical detection systems operating under harsh environments.Comment: 10 pages, 8 figure

Strong magnetic fields and non equilibrium dynamics in QCD

The concept of symmetry is without doubt the most significant centerpiece of modern science. Our current understanding of the visible universe is phrased into a basic set of equations describing what we call 'gauge theories'. The laws governing the dynamics of nature have been derived studying the symmetry properties of these equations, that is their invariance or non-invariance under certain symmetry 'transformations'. Because of their grand success and while seeming omnipotent, it came as a sensational surprise, that nature mysteriously does not obey some of the above symmetry principles by mechanisms that are elusive: Quantum Anomalies. The intriguing feature of the anomalous violation of symmetries is that it cannot be understood by the defining set of equations that were postulated to comprise the physical content of nature, but rather from the structures of quantum theories itself. Quantum anomalies emerge from the transition from the classical to the quantum level of nature, and researchers have realized that the properties of the physical vacuum (that is the quantum equivalent of 'nothing') are very non-trivial. Symmetries are the cornerstones of gauge theories and the fundamental forces they describe. The vast majority of visible matter is governed by the strong interactions, formulated through the theory of Quantum Chromodynamics (QCD). In this context, symmetry principles also dictate the existence of another mysterious concept: topology. Topology is the principle used to describe the fundamental structure of an object, invariant under a certain transformation. In physics it describes the invariance of the aforementioned basic set of equations under continuous and hence structure-preserving manipulations. It is very suggestive that quantum anomalies and the concept of topology should be intimately related and in fact this assertion is most famously confirmed by the so-called axial anomaly. The physics of quantum anomalies and topology is intriguing and often mysterious, yet central to many of the fundamental mechanisms of nature. As the anomalous violation of classical symmetries in the earliest stages of the universe is conjectured to be responsible for the dominance of matter over anti-matter, researchers attempt to recreate the dynamics of matter under extreme conditions at heavy ion collider experiments and thus understand these challenging mechanisms. In the early universe as well as in present day experiments the emergence of quantum anomalies is tied to \textit{out-of-equilibrium} systems. In this thesis we focus on a comprehensive attempt at establishing the theoretical foundations of the non-equilibrium description of anomalous and topological dynamics. To this end we present a selection of different techniques and approximation schemes, which are motivated by the properties of the space-time evolution of QCD matter in ultra-relativistic heavy ion collisions. Most importantly we aim to illustrate that the techniques, which are presented here, are applicable to a number of systems in nature, starting from strong-field laser physics to cosmology. The nature of topological effects is much richer in out-of-equilibrium systems and in accord with present progress in the experimental study of anomalous effects, we hope to contribute to the establishment of a novel view on anomalies and topology beyond the previous equilibrium paradigm

Role of Dynamical Asymmetry on the Orientation of Block Copolymers in Shear Flow: Computer Simulation and Experiment

The ability of diblock copolymers to self-assemble into periodic microstructures with length scales in the nanometer range offers many opportunities for fundamental research and applications. For practical applications, it is often desirable that the microstructures have a high degree of order on macroscopic length scales and are oriented in a desired direction. This can be achieved in a large volume by shearing the copolymer melt. In experiments, different orientations are observed depending on the copolymer characteristics and the applied shear conditions. However, details of the orientation mechanism under shear are not completely understood. Studying structurally and thermodynamically symmetric, lamellae-forming diblock copolymers by molecular simulation using a highly coarse-grained model, we analyze the effect of dynamical asymmetry on the stable orientation in steady-shear flow. We control the dynamical asymmetry via (i) the segmental friction in our dissipative particle dynamics DPD simulation or via (ii) slip springs, which mimic physical entanglements of the polymers. We study the kinetics of structure formation after a quench from the disordered state in the presence of shear and the ordering of a system, initially comprised of two orthogonally oriented lamellar grains, under shear. In both simulation settings and for both mechanisms of dynamical asymmetry, the perpendicular orientation, where the lamellae normals are perpendicular to the shear gradient, is preferred for approximately equal dynamics of the two blocks, whereas the parallel orientation becomes stable when the ratio of the relaxation times of the blocks exceeds an order of magnitude. We rationalize this finding by the minimum of the Rayleighian, i.e., the energy dissipation rate of the nonequilibrium steady state. We compare these simulation results to experimental diblock copolymer model systems, polystyrene-b-poly-2-vinylpyridine, with slightly different glass transition temperatures of the two polymer blocks. Adjustment of the polymer block mobility by different temperatures for alignment experiments confirms the trend toward a parallel orientation with increasing dynamical asymmetry of the polymer blocks, when the rigid lamellae slide past the opposing brushes of the more mobile polymer block