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

Construction of an isotropic cellular automaton for a reaction-diffusion equation by means of a random walk

We propose a new method to construct an isotropic cellular automaton corresponding to a reaction-diffusion equation. The method consists of replacing the diffusion term and the reaction term of the reaction-diffusion equation with a random walk of microscopic particles and a discrete vector field which defines the time evolution of the particles. The cellular automaton thus obtained can retain isotropy and therefore reproduces the patterns found in the numerical solutions of the reaction-diffusion equation. As a specific example, we apply the method to the Belousov-Zhabotinsky reaction in excitable media

On the Quantum Phase Operator for Coherent States

In papers by Lynch [Phys. Rev. A41, 2841 (1990)] and Gerry and Urbanski [Phys. Rev. A42, 662 (1990)] it has been argued that the phase-fluctuation laser experiments of Gerhardt, B\"uchler and Lifkin [Phys. Lett. 49A, 119 (1974)] are in good agreement with the variance of the Pegg-Barnett phase operator for a coherent state, even for a small number of photons. We argue that this is not conclusive. In fact, we show that the variance of the phase in fact depends on the relative phase between the phase of the coherent state and the off-set phase $\phi_0$ of the Pegg-Barnett phase operator. This off-set phase is replaced with the phase of a reference beam in an actual experiment and we show that several choices of such a relative phase can be fitted to the experimental data. We also discuss the Noh, Foug\`{e}res and Mandel [Phys.Rev. A46, 2840 (1992)] relative phase experiment in terms of the Pegg-Barnett phase taking post-selection conditions into account.Comment: 8 pages, 8 figures. Typographical errors and misprints have been corrected. The outline of the paper has also been changed. Physica Scripta (in press

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

Self Organization and a Dynamical Transition in Traffic Flow Models

A simple model that describes traffic flow in two dimensions is studied. A sharp {\it jamming transition } is found that separates between the low density dynamical phase in which all cars move at maximal speed and the high density jammed phase in which they are all stuck. Self organization effects in both phases are studied and discussed.Comment: 6 pages, 4 figure

Importance of exposure route for behavioural responses in Lumbriculus variegatus Müller (Oligochaeta: Lumbriculida) in short-term exposures to Pb

Abstract Goal, Scope and Background Lumbriculus variegatus Müller (Oligochaeta), a common freshwater sediment-dweller, has frequently been used in toxicokinetic studies, although has been less used in ecotoxicity tests. Methods For the first time the Multispecies Freshwater Biomonitor® (MFB) was applied in a short-term whole-sediment toxicity test. The MFB automatically and quantitatively recorded the spontaneous locomotory behaviour of Lumbriculus variegatus in exposures with two compartments, water and sediment. The study questioned, whether the animals altered their locomotion depending on the compartment which was spiked with lead (Pb). Results and Discussion As in the exposures to Pb-contaminated water/clean sediment, the animals exposed to Pb-contaminated sediment/clean water showed higher activities in intermediate Pb-concentrations. This indicates, that spontaneous locomotory activity is affected by Pb-concentrations at sublethal levels regardless of whether the Pb-concentration is found in the water or in the sediment, because these animals use both environmental compartments simultaneously. However, within the same Pb-levels, the animals showed higher locomotory activity in contaminated water compared with contaminated sediment. This indicates a possible tendency to withdraw from (‘avoidance’) contaminated water into the clean sediment compartment, whereas there was no withdrawal from contaminated sediment into clean water. The latter might be explained by the fact that withdrawal from sediment to water might increase the risk of predation and drift in nature, whereas retracting to sediment might provide shelter. Conclusions The study showed that spontaneous locomotory responses of L. variegatus to Pb depend on whether the water or sediment is contaminated. The study also concluded that the Multispecies Freshwater Biomonitor® can be applied effectively in sediment toxicity testing. Recommendations and Perspectives More emphasis should be given to the interactions of water/sediment in sediment ecotoxicity tests to better simulate field conditions and increase ecological realism in risk assessment, especially as quantitative recording methods exisit