Estimates for the volume of a Lorentzian manifold

We prove new estimates for the volume of a Lorentzian manifold and show especially that cosmological spacetimes with crushing singularities have finite volume.Comment: 8 pages, a pdf version of the preprint can also be retrieved from http://www.math.uni-heidelberg.de/studinfo/gerhardt/LM-Volume.pdf v2: A further estimate has been added covering the case when the mean curvature is merely non-negative resp. non-positive (Theorem 1.1

Expansion of pinched hypersurfaces of the Euclidean and hyperbolic space by high powers of curvature

We prove convergence results for expanding curvature flows in the Euclidean and hyperbolic space. The flow speeds have the form $F^{-p}$, where $p>1$ and $F$ is a positive, strictly monotone and 1-homogeneous curvature function. In particular this class includes the mean curvature $F=H$. We prove that a certain initial pinching condition is preserved and the properly rescaled hypersurfaces converge smoothly to the unit sphere. We show that an example due to Andrews-McCoy-Zheng can be used to construct strictly convex initial hypersurfaces, for which the inverse mean curvature flow to the power $p>1$ loses convexity, justifying the necessity to impose a certain pinching condition on the initial hypersurface.Comment: 18 pages. We included an example for the loss of convexity and pinching. In the third version we dropped the concavity assumption on F. Comments are welcom

Tribology of Skin: Review and Analysis of Experimental Results for the Friction Coefficient of Human Skin

In this review, we discuss the current knowledge on the tribology of human skin and present an analysis of the available experimental results for skin friction coefficients. Starting with an overview on the factors influencing the friction behaviour of skin, we discuss the up-to-date existing experimental data and compare the results for different anatomical skin areas and friction measurement techniques. For this purpose, we also estimated and analysed skin contact pressures applied during the various friction measurements. The detailed analyses show that substantial variations are a characteristic feature of friction coefficients measured for skin and that differences in skin hydration are the main cause thereof, followed by the influences of surface and material properties of the contacting materials. When the friction coefficients of skin are plotted as a function of the contact pressure, the majority of the literature data scatter over a wide range that can be explained by the adhesion friction model. The case of dry skin is reflected by relatively low and pressure-independent friction coefficients (greater than 0.2 and typically around 0.5), comparable to the dry friction of solids with rough surfaces. In contrast, the case of moist or wet skin is characterised by significantly higher (typically >1) friction coefficients that increase strongly with decreasing contact pressure and are essentially determined by the mechanical shear properties of wet skin. In several studies, effects of skin deformation mechanisms contributing to the total friction are evident from friction coefficients increasing with contact pressure. However, the corresponding friction coefficients still lie within the range delimited by the adhesion friction model. Further research effort towards the analysis of the microscopic contact area and mechanical properties of the upper skin layers is needed to improve our so far limited understanding of the complex tribological behaviour of human ski

Quantum cosmological Friedman models with a massive Yang-Mills field

We prove the existence of a spectral resolution of the Wheeler-DeWitt equation when the matter field is provided by a massive Yang-Mills field. The resolution is achieved by first solving the free eigenvalue problem for the gravitational field and then the constrained eigenvalue problem for the Yang-Mills field. In the latter case the mass of the Yang-Mills field assumes the role of the eigenvalue.Comment: 16 pages, v3: typos corrected, final version, to appear in CQ

Fabrication, Characterisation and Tribological Investigation of Artificial Skin Surface Lipid Films

This article deals with the tribology of lipid coatings that resemble those found on human skin. In order to simulate the lipidic surface chemistry of human skin, an artificial sebum formulation that closely resembles human sebum was spray-coated onto mechanical skin models in physiologically relevant concentrations (5-100μg/cm2). Water contact angles and surface free energies (SFEs) showed that model surfaces with ≤25μg/cm2 lipids appropriately mimic the physico-chemical properties of dry, sebum-poor skin regions. In friction experiments with a steel ball, lipid-coated model surfaces demonstrated lubrication effects over a wide range of sliding velocities and normal loads. In friction measurements on model surfaces as a function of lipid-film thickness, a clear minimum in the friction coefficient (COF) was observed in the case of hydrophilic, high-SFE materials (steel, glass), with the lowest COF (≈0.5) against skin model surfaces being found at 25μg/cm2 lipids. For hydrophobic, low-SFE polymers, the COF was considerably lower (0.4 for PP, 0.16 for PTFE) and relatively independent of the lipid amount, indicating that both the mechanical and surface-chemical properties of the sliders strongly influence the friction behaviour of the skin-model surfaces. Lipid-coated skin models might be a valuable tool not only for tribologists but also for cosmetic chemists, in that they allow the objective study of friction, adhesion and wetting behaviour of liquids and emulsions on simulated skin-surface condition

Global existence problem in T3T^3-Gowdy symmetric IIB superstring cosmology

We show global existence theorems for Gowdy symmetric spacetimes with type IIB stringy matter. The areal and constant mean curvature time coordinates are used. Before coming to that, it is shown that a wave map describes the evolution of this system

Metamagnetism in the XXZ model with next-to-nearest-neighbor coupling

We investigate groundstate energies and magnetization curves in the one dimensional XXZ-model with next to nearest neighbour coupling $\alpha>0$ and anisotropy $\Delta$ ($-1 \le \Delta \le 1$) at T=0. In between the familiar ferro- and antiferromagnetic phase we find a transition region -- called metamagnetic phase -- where the magnetization curve is discontinuous at a critical field $B_c(\alpha,\Delta)$.Comment: LaTeX file (text) + 5 PS files (5 figures

Development of a backward-mode photoacoustic microscope using a Fabry-Perot sensor

Optical-resolution photoacoustic microscopy (PAM) has been shown to enable the acquisition of high resolution (μm) functional and anatomical images. For backward-mode operation, conventional piezoelectric ultrasound transducers need to be placed far away from the signal source due to their opacity and size. This can result in reduced acoustic sensitivity. Planar Fabry-Perot polymer film interferometer (FPI) sensors have the potential to overcome this limitation since they are transparent to the excitation wavelength, can be placed immediately adjacent to the signal source for high acoustic sensitivity, and offer a broadband frequency response (0 –50 MHz). In this study, we present a high frame rate, backward-mode OR-PAM system based on a planar FPI ultrasound sensor. A ns-pulsed laser provides excitation pulses (<200 nJ, maximum pulse repetition frequency = 200 kHz, 532 nm) to generate photoacoustic waves that are detected using a planar FPI sensor interrogated at 765-781 nm. For backwardmode operation and highest acoustic sensitivity, the excitation and interrogation beams are coaxially aligned and rasterscanned. The optical transfer function of the sensor, the spatial resolution and the detection sensitivity were determined to characterise the set-up. Images of a leaf phantom and first in vivo images of zebrafish larvae were acquired. This approach will enable fast 3D OR-PAM with high resolution and high sensitivity for functional and molecular imaging applications. FPI-based ultrasound detection also has the potential to enable dual-mode optical- and acousticresolution PAM and the integration of photoacoustic imaging with purely optical modalities such as multi-photon microscopy

Brane Formation and Cosmological Constraint on the Number of Extra Dimensions

Special relativity is generalized to extra dimensions and quantized energy levels of particles are obtained. By calculating the probability of particles' motion in extra dimensions at high temperature of the early universe, it is proposed that the branes may have not existed since the very beginning of the universe, but formed later. Meanwhile, before the formation, particles of the universe may have filled in the whole bulk, not just on the branes. This scenario differs from that in the standard big bang cosmology in which all particles are assumed to be in the 4D spacetime. So, in brane models, whether our universe began from a 4D big bang singularity is questionable. A cosmological constraint on the number of extra dimensions is also given which favors $N\geq 7$.Comment: 11 pages, no figures. To appear in IJT