Quantum Einstein gravity - advancements of heat kernel-based renormalization group studies

The asymptotic safety scenario allows to define a consistent theory of quantized gravity within the framework of quantum field theory. The central conjecture of this scenario is the existence of a non-Gaussian fixed point of the theory's renormalization group flow, that allows to formulate renormalization conditions that render the theory fully predictive. Investigations of this possibility use an exact functional renormalization group equation as a primary non-perturbative tool. This equation implements Wilsonian renormalization group transformations, and is demonstrated to represent a reformulation of the functional integral approach to quantum field theory.rnAs its main result, this thesis develops an algebraic algorithm which allows to systematically construct the renormalization group flow of gauge theories as well as gravity in arbitrary expansion schemes. In particular, it uses off-diagonal heat kernel techniques to efficiently handle the non-minimal differential operators which appear due to gauge symmetries. The central virtue of the algorithm is that no additional simplifications need to be employed, opening the possibility for more systematic investigations of the emergence of non-perturbative phenomena. As a by-product several novel results on the heat kernel expansion of the Laplace operator acting on general gauge bundles are obtained.rnThe constructed algorithm is used to re-derive the renormalization group flow of gravity in the Einstein-Hilbert truncation, showing the manifest background independence of the results. The well-studied Einstein-Hilbert case is further advanced by taking the effect of a running ghost field renormalization on the gravitational coupling constants into account. A detailed numerical analysis reveals a further stabilization of the found non-Gaussian fixed point.rnFinally, the proposed algorithm is applied to the case of higher derivative gravity including all curvature squared interactions. This establishes an improvement of existing computations, taking the independent running of the Euler topological term into account. Known perturbative results are reproduced in this case from the renormalization group equation, identifying however a unique non-Gaussian fixed point.rn

Numerical simulation of some viscoelastic fluids

Numerical simulation of the Oldroyd-B type viscoelastic fluids is a very challenging problem. rnThe well-known High Weissenberg Number Problem" has haunted the mathematicians, computer scientists, and rnengineers for more than 40 years. rnWhen the Weissenberg number, which represents the ratio of elasticity to viscosity, rnexceeds some limits, simulations done by standard methods break down exponentially fast in time. rnHowever, some approaches, such as the logarithm transformation technique can significantly improve rnthe limits of the Weissenberg number until which the simulations stay stable. rnrnWe should point out that the global existence of weak solutions for the Oldroyd-B model is still open. rnLet us note that in the evolution equation of the elastic stress tensor the terms describing diffusive rneffects are typically neglected in the modelling due to their smallness. However, when keeping rnthese diffusive terms in the constitutive law the global existence of weak solutions in two-space dimension rncan been shown. rnrnThis main part of the thesis is devoted to the stability study of the Oldroyd-B viscoelastic model. rnFirstly, we show that the free energy of the diffusive Oldroyd-B model as well as its rnlogarithm transformation are dissipative in time. rnFurther, we have developed free energy dissipative schemes based on the characteristic finite element and finite difference framework. rnIn addition, the global linear stability analysis of the diffusive Oldroyd-B model has also be discussed. rnThe next part of the thesis deals with the error estimates of the combined finite element rnand finite volume discretization of a special Oldroyd-B model which covers the limiting rncase of Weissenberg number going to infinity. Theoretical results are confirmed by a series of numerical rnexperiments, which are presented in the thesis, too.

Auditory motion direction encoding in auditory cortex and high-level visual cortex

The aim of this functional magnetic resonance imaging (fMRI) study was to identify human brain areas that are sensitive to the direction of auditory motion. Such directional sensitivity was assessed in a hypothesis-free manner by analyzing fMRI response patterns across the entire brain volume using a spherical-searchlight approach. In addition, we assessed directional sensitivity in three predefined brain areas that have been associated with auditory motion perception in previous neuroimaging studies. These were the primary auditory cortex, the planum temporale and the visual motion complex (hMT/V5+). Our whole-brain analysis revealed that the direction of sound-source movement could be decoded from fMRI response patterns in the right auditory cortex and in a high-level visual area located in the right lateral occipital cortex. Our region-of-interest-based analysis showed that the decoding of the direction of auditory motion was most reliable with activation patterns of the left and right planum temporale. Auditory motion direction could not be decoded from activation patterns in hMT/V5+. These findings provide further evidence for the planum temporale playing a central role in supporting auditory motion perception. In addition, our findings suggest a cross-modal transfer of directional information to high-level visual cortex in healthy humans.

A brief update on lung stereology

Lung stereology has a long and successful tradition. From mice to men, the application of new stereological methods at several levels (alveoli, parenchymal cells, organelles, proteins) has led to new insights into normal lung architecture, parenchymal remodelling in emphysema-like pathology, alveolar type II cell hyperplasia and hypertrophy and intracellular surfactant alterations as well as distribution of surfactant proteins. The Euler number of the network of alveolar openings, estimated using physical disectors at the light microscopic level, is an unbiased and direct estimate of alveolar number. Surfactant-producing alveolar type II cells can be counted and sampled for local size estimation with physical disectors at a high magnification light microscopic level. The number of their surfactant storage organelles, lamellar bodies, can be estimated using physical disectors at the EM level. By immunoelectron microscopy, surfactant protein distribution can be analysed with the relative labelling index. Together with the well-established classical stereological methods, these design-based methods now allow for a complete quantitative phenotype analysis in lung development and disease, including the structural characterization of gene-manipulated mice, at the light and electron microscopic level.

Effect of voluntary exercise on number and volume of cardiomyocytes and their mitochondria in the mouse left ventricle

Voluntary exercise (VE) has a beneficial influence on the heart and mean lifespan. The present study evaluates structural adaptations of cardiomyocytes and their mitochondria due to VE by new, unbiased stereological methods. Female, 7-9-week-old mice were randomly assigned to a control (CG, n = 7) or VE group (EG, n = 7). EG animals were housed in cages with free access to a running wheel and had a mean running distance of 6.7 (1.8) km per day. After 4 weeks, the hearts of all mice were processed for light and electron microscopy. We estimated the number and volume of cardiomyocytes by the disector method and the number and volume of mitochondria by estimation of the Euler number. In comparison to CG, VE did not have an effect on the myocardial volume of the left ventricle (CG: 93 (10), EG: 103 (17) (mm(3))), the number of cardiomyocytes (CG: 2.81 (0.27), EG: 2.82 (0.43) (x10(6))) and their number-weighted mean volume. However, the composition of the cardiomyocytes changed due to VE. The total volume of mitochondria (CG: 21.8 (4.9), EG: 32.2 (4.3) (mm(3)), P < 0.01) and the total number (CG: 3.76 (0.44), EG: 7.02 (1.13) (x10(10)), P < 0.001) were significantly higher in EG than in CG. The mean number-weighted mitochondrial volume was smaller in EG than in CG (P < 0.05). In summary, VE does not alter ventricular volume nor cardiomyocyte volume or number but the oxidative capacity of cardiomyocytes by an increased mitochondrial number and total volume in the left ventricle. These structural changes may participate in the beneficial effects of VE.

Contractile performance of adult ventricular rat cardiomyocytes is not directly jeopardized by NO/cGMP-dependent induction of pro-apoptotic pathways

The activation of NO/cGMP pathways can induce pro-apoptotic pathways in cardiomyocytes although only a small number of cardiomyocytes fulfill the criteria of apoptosis. The same pathways reduce the contractile performance of cardiomyocytes. In the present study, we tested the hypothesis that exposure of cells to NO/cGMP for 24 h decrease their contractile performance due to an activation of pro-apoptotic pathways. Experiments were performed on freshly isolated and cultured adult ventricular rat cardiomyocytes. Cells were incubated with 8-bromo-cyclo-GMP (100 nmol/L-1 micromol/L), the NO donor SNAP (1 nmol/L-100 micromol/L), or the guanylyl cyclase activator YC-1 (3 micromol/L). Cell shortening, contraction and relaxation velocities, and diastolic cell lengths were determined at beating frequencies of 0.5, 1, and 2 Hz 24 h later. The activation of pro-apoptotic pathways was determined by staining of cardiomyocytes with an antibody directed against active caspase-3 and quantification of the number of apoptotic cells (annexin staining). Caspase-3 activation and an increase in the number of apoptotic cells was observed, but only at the highest concentrations tested (8-bromo-cyclo-GMP: 1-10 mmol/L; SNAP: 1-100 micromol/L). At these concentrations, none of the drugs decreased the mean cell shortening of cardiomyocytes. However, at concentrations lower than those required for induction of apoptotic cell death, the diastolic cell lengths and sarcomere lengths increased but cell shortening decreased. In conclusion, low concentrations of either NO or cGMP cause a desensitization of myofibrils, as indicated by elongated cell shapes, increased sarcomere lengths and reduced load-free cell shortening. High concentrations of NO/cGMP induce caspase-3 activation and increase the number of cells fulfilling the criteria of apoptotic cell death but did not impair cell function. Therefore, induction of apoptotic cell death per se seems not to contribute to the loss of contractile efficiency on the cellular level.

Effect of mesh distortion on the accuracy of high order vorticity-velocity CFD approaches

The numerical solution of the incompressible Navier-Stokes equations offers an alternative to experimental analysis of fluid-structure interaction (FSI). We would save a lot of time and effort and help cut back on costs, if we are able to accurately model systems by these numerical solutions. These advantages are even more obvious when considering huge structures like bridges, high rise buildings or even wind turbine blades with diameters as large as 200 meters. The modeling of such processes, however, involves complex multiphysics problems along with complex geometries. This thesis focuses on a novel vorticity-velocity formulation called the Kinematic Laplacian Equation (KLE) to solve the incompressible Navier-stokes equations for such FSI problems. This scheme allows for the implementation of robust adaptive ordinary differential equations (ODE) time integration schemes, allowing us to tackle each problem as a separate module. The current algortihm for the KLE uses an unstructured quadrilateral mesh, formed by dividing each triangle of an unstructured triangular mesh into three quadrilaterals for spatial discretization. This research deals with determining a suitable measure of mesh quality based on the physics of the problems being tackled. This is followed by exploring methods to improve the quality of quadrilateral elements obtained from the triangles and thereby improving the overall mesh quality. A series of numerical experiments were designed and conducted for this purpose and the results obtained were tested on different geometries with varying degrees of mesh density.

Modeling contaminant behavior in Lake Superior : a comparison of PCBs, PBDEs, and mercury

A mass‐balance model for Lake Superior was applied to polychlorinated biphenyls (PCBs), polybrominated diphenyl ethers (PBDEs), and mercury to determine the major routes of entry and the major mechanisms of loss from this ecosystem as well as the time required for each contaminant class to approach steady state. A two‐box model (water column, surface sediments) incorporating seasonally adjusted environmental parameters was used. Both numerical (forward Euler) and analytical solutions were employed and compared. For validation, the model was compared with current and historical concentrations and fluxes in the lake and sediments. Results for PCBs were similar to prior work showing that air‐water exchange is the most rapid input and loss process. The model indicates that mercury behaves similarly to a moderately‐chlorinated PCB, with air‐water exchange being a relatively rapid input and loss process. Modeled accumulation fluxes of PBDEs in sediments agreed with measured values reported in the literature. Wet deposition rates were about three times greater than dry particulate deposition rates for PBDEs. Gas deposition was an important process for tri‐ and tetra‐BDEs (BDEs 28 and 47), but not for higher‐brominated BDEs. Sediment burial was the dominant loss mechanism for most of the PBDE congeners while volatilization was still significant for tri‐ and tetra‐BDEs. Because volatilization is a relatively rapid loss process for both mercury and the most abundant PCBs (tri‐ through penta‐), the model predicts that similar times (from 2 ‐ 10 yr) are required for the compounds to approach steady state in the lake. The model predicts that if inputs of Hg(II) to the lake decrease in the future then concentrations of mercury in the lake will decrease at a rate similar to the historical decline in PCB concentrations following the ban on production and most uses in the U.S. In contrast, PBDEs are likely to respond more slowly if atmospheric concentrations are reduced in the future because loss by volatilization is a much slower process for PBDEs, leading to lesser overall loss rates for PBDEs in comparison to PCBs and mercury. Uncertainties in the chemical degradation rates and partitioning constants of PBDEs are the largest source of uncertainty in the modeled times to steady‐state for this class of chemicals. The modeled organic PBT loading rates are sensitive to uncertainties in scavenging efficiencies by rain and snow, dry deposition velocity, watershed runoff concentrations, and uncertainties in air‐water exchange such as the effect of atmospheric stability.

Numerical solutions of elliptic inverse problems via the equation error method

To estimate a parameter in an elliptic boundary value problem, the method of equation error chooses the value that minimizes the error in the PDE and boundary condition (the solution of the BVP having been replaced by a measurement). The estimated parameter converges to the exact value as the measured data converge to the exact value, provided Tikhonov regularization is used to control the instability inherent in the problem. The error in the estimated solution can be bounded in an appropriate quotient norm; estimates can be derived for both the underlying (infinite-dimensional) problem and a finite-element discretization that can be implemented in a practical algorithm. Numerical experiments demonstrate the efficacy and limitations of the method.

Effect of high order interpolation in the stability and efficiency of the time-integration process in vorticity-velocity CFD algorithms

The numerical solution of the incompressible Navier-Stokes Equations offers an effective alternative to the experimental analysis of Fluid-Structure interaction i.e. dynamical coupling between a fluid and a solid which otherwise is very complex, time consuming and very expensive. To have a method which can accurately model these types of mechanical systems by numerical solutions becomes a great option, since these advantages are even more obvious when considering huge structures like bridges, high rise buildings, or even wind turbine blades with diameters as large as 200 meters. The modeling of such processes, however, involves complex multiphysics problems along with complex geometries. This thesis focuses on a novel vorticity-velocity formulation called the KLE to solve the incompressible Navier-stokes equations for such FSI problems. This scheme allows for the implementation of robust adaptive ODE time integration schemes and thus allows us to tackle the various multiphysics problems as separate modules. The current algorithm for KLE employs a structured or unstructured mesh for spatial discretization and it allows the use of a self-adaptive or fixed time step ODE solver while dealing with unsteady problems. This research deals with the analysis of the effects of the Courant-Friedrichs-Lewy (CFL) condition for KLE when applied to unsteady Stoke’s problem. The objective is to conduct a numerical analysis for stability and, hence, for convergence. Our results confirmthat the time step ∆t is constrained by the CFL-like condition ∆t ≤ const. hα, where h denotes the variable that represents spatial discretization.

Problems in the classical calculus of variations

This dissertation concerns convergence analysis for nonparametric problems in the calculus of variations and sufficient conditions for weak local minimizer of a functional for both nonparametric and parametric problems. Newton's method in infinite-dimensional space is proved to be well-defined and converges quadratically to a weak local minimizer of a functional subject to certain boundary conditions. Sufficient conditions for global converges are proposed and a well-defined algorithm based on those conditions is presented and proved to converge. Finite element discretization is employed to achieve an implementable line-search-based quasi-Newton algorithm and a proof of convergence of the discretization of the algorithm is included. This work also proposes sufficient conditions for weak local minimizer without using the language of conjugate points. The form of new conditions is consistent with the ones in finite-dimensional case. It is believed that the new form of sufficient conditions will lead to simpler approaches to verify an extremal as local minimizer for well-known problems in calculus of variations.

Optimal current control for sub-unity power factor correction

Switching mode power supplies (SMPS) are subject to low power factor and high harmonic distortions. Active power-factor correction (APFC) is a technique to improve the power factor and to reduce the harmonic distortion of SMPSs. However, this technique results in double frequency output voltage variation which can be reduced by using a large output capacitance. Using large capacitors increases the cost and size of the converter. Furthermore, the capacitors are subject to frequent failures mainly caused by evaporation of the electrolytic solution which reduce the converter reliability. This thesis presents an optimal control method for the input current of a boost converter to reduce the size of the output capacitor. The optimum current waveform as a function of weighing factor is found by using the Euler Lagrange equation. A set of simulations are performed to determine the ideal weighing which gives the lowest possible output voltage variation as the converter still meets the IEC-61000-3-2 class-A harmonics requirements with a power factor of 0.8 or higher. The proposed method is verified by the experimental work. A boost converter is designed and it is run for different power levels, 100 W, 200 W and 400 W. The desired output voltage ripple is 10 V peak to peak for the output voltage of 200 Vdc. This ripple value corresponds to a ± 2.5% output voltage ripple. The experimental and the simulation results are found to be quite matching. A significant reduction in capacitor size, as high as 50%, is accomplished by using the proposed method.

Verfahren und Anlage zum automatisierten Kommissionieren von in Beuteln verpackten Gütern

Automatisiertes Kommissionieren von biegeschlaffen Teilen stellt seit jeher ein besonderes Problem für die Handhabungstechnik dar, und es sind bisher verschiedenartigste sondermaschinenbauliche Lösungen hervorgebracht worden. Auch für das Kommissionieren von in Folien verpackten Artikeln gibt es einige L��sungen. Diese sind aber hinsichtlich ihrer Anwendung für in Beuteln verpackte Güter eingeschränkt. Ein neuartiges, am Fraunhofer-IML entwickeltes Verfahren verspricht Abhilfe. Der folgende Beitrag stellt dieses Verfahren im Detail vor und zeigt vergangene und zukünftige Untersuchungsfelder auf, die im Rahmen der Entwicklung bearbeitet wurden bzw. werden und sich insbesondere mit der Dimensionierung der Gerätschaften und Hilfsmittel beschäftigen.

Estimating Gesture Accuracy in Motion-Based Health Games

This manuscript details a technique for estimating gesture accuracy within the context of motion-based health video games using the MICROSOFT KINECT. We created a physical therapy game that requires players to imitate clinically significant reference gestures. Player performance is represented by the degree of similarity between the performed and reference gestures and is quantified by collecting the Euler angles of the player's gestures, converting them to a three-dimensional vector, and comparing the magnitude between the vectors. Lower difference values represent greater gestural correspondence and therefore greater player performance. A group of thirty-one subjects was tested. Subjects achieved gestural correspondence sufficient to complete the game's objectives while also improving their ability to perform reference gestures accurately.