Combining gravity with the forces of the standard model on a cosmological scale

We prove the existence of a spectral resolution of the Wheeler-DeWitt equation when the underlying spacetime is a Friedman universe with flat spatial slices and where the matter fields are comprised of the strong interaction, with \SU(3) replaced by a general \SU(n), $n\ge 2$, and the electro-weak interaction. The wave functions are maps from $\R[4n+10]$ to a subspace of the antisymmetric Fock space, and one noteworthy result is that, whenever the electro-weak interaction is involved, the image of an eigenfunction is in general not one dimensional, i.e., in general it makes no sense specifying a fermion and looking for an eigenfunction the range of which is contained in the one dimensional vector space spanned by the fermion.Comment: 53 pages, v6: some typos correcte

Alternative way to characterize a q-gaussian distribution by a robust heavy tail measurement

The q-Gaussians are a class of stable distributions which are present in many scientific fields, and that behave as heavy tailed distributions for an especific range of q values. The identification of these values, which are used in the description of systems, is sometimes a hard task. In this work the identification of a q-Gaussian distribution from empirical data was done by a measure of its tail weight using robust statistics. Numerical methods were used to generate artificial data, to find out the tail weight -- medcouple, and also to adjust the curve between medcouple and the q value. We showed that the medcouple value remains unchanged when the calculation is applied to data which have long memory. A routine was made to calculate the q value and its standard deviation, when applied to empirical data. It is possible to identify a q-Gaussian by the proposed methods with higher precision than in the literature for the same data sample, or as precise as found in the literature. However, in this case, it is required a smaller sample of data. We hope that this method will be able to open new ways for identifying physical phenomena that belongs to nonextensive frameworks.Comment: Added references. Corrected typos. Improved in introduction, conclusion, results unchange

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

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

Intrinsic time gravity and the Lichnerowicz-York equation

We investigate the effect on the Hamiltonian structure of general relativity of choosing an intrinsic time to fix the time slicing. 3-covariance with momentum constraint is maintained, but the Hamiltonian constraint is replaced by a dynamical equation for the trace of the momentum. This reveals a very simple structure with a local reduced Hamiltonian. The theory is easily generalised; in particular, the square of the Cotton-York tensor density can be added as an extra part of the potential while at the same time maintaining the classic 2 + 2 degrees of freedom. Initial data construction is simple in the extended theory; we get a generalised Lichnerowicz-York equation with nice existence and uniqueness properties. Adding standard matter fields is quite straightforward.Comment: 4 page

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

A logarithmic epiperimetric inequality for the obstacle problem

For the general obstacle problem, we prove by direct methods an epiperimetric inequality at regular and singular points, thus answering a question of Weiss (Invent. Math., 138 (1999), 23--50). In particular at singular points we introduce a new tool, which we call logarithmic epiperimetric inequality, which yields an explicit logarithmic modulus of continuity on the $C^1$ regularity of the singular set, thus improving previous results of Caffarelli and Monneau

Quantum walks with infinite hitting times

Hitting times are the average time it takes a walk to reach a given final vertex from a given starting vertex. The hitting time for a classical random walk on a connected graph will always be finite. We show that, by contrast, quantum walks can have infinite hitting times for some initial states. We seek criteria to determine if a given walk on a graph will have infinite hitting times, and find a sufficient condition, which for discrete time quantum walks is that the degeneracy of the evolution operator be greater than the degree of the graph. The set of initial states which give an infinite hitting time form a subspace. The phenomenon of infinite hitting times is in general a consequence of the symmetry of the graph and its automorphism group. Using the irreducible representations of the automorphism group, we derive conditions such that quantum walks defined on this graph must have infinite hitting times for some initial states. In the case of the discrete walk, if this condition is satisfied the walk will have infinite hitting times for any choice of a coin operator, and we give a class of graphs with infinite hitting times for any choice of coin. Hitting times are not very well-defined for continuous time quantum walks, but we show that the idea of infinite hitting-time walks naturally extends to the continuous time case as well.Comment: 28 pages, 3 figures in EPS forma