arXiv subjects
Publications and source records attributed to Michael Mayer.
The anisotropic, stress-dependent velocity of elastic waves in glass beads -- as observed by Y. Khidas and X. Jia, see [Phys. Rev. E, 81:021303, Feb. 2010] -- is shown to be well accounted for by ``granular solid hydrodynamics,'' a broad-range macroscopic theory of granular behavior. As the theory makes no reference to fabric anisotropy, the influence of which on sound is in doubt.
In 1948, W. Hoeffding introduced a large class of unbiased estimators called U-statistics, defined as the average value of a real-valued m-variate function h calculated at all possible sets of m points from a random sample. In the present paper, we investigate the corresponding robust analogue which we call U-quantile-statistics. We are concerned with the asymptotic behavior of the sample p-quantile of such function h instead of its average. Alternatively, U-quantile-statistics can be viewed as quantile estimators for a certain class of dependent random variables. Examples are given by a slightly modified Hodges-Lehmann estimator of location and the median interpoint distance among random points in space.
In 1948, W. Hoeffding introduced a large class of unbiased estimators called U-statistics, defined as the average value of a real-valued k-variate function h calculated at all possible sets of k points from a random sample. In the present paper we investigate the corresponding extreme value analogue, which we shall call U-max-statistics. We are concerned with the behavior of the largest value of such function h instead of its average. Examples of U-max-statistics are the diameter or the largest scalar product within a random sample. U-max-statistics of higher degrees are given by triameters and other metric invariants.
We prove a limit theorem for the the maximal interpoint distance (also called the diameter) for a sample of n i.i.d. points in the unit ball of dimension 2 or more. The exact form of the limit distribution and the required normalisation are derived using assumptions on the tail of the interpoint distance for two i.i.d. points. The results are specialised for the cases when the points have spherical symmetric distributions, in particular, are uniformly distributed in the whole ball and on its boundary.
We present newly calculated low-temperature opacities for gas with a primordial chemical composition. In contrast to earlier calculations which took a pure metal-free Hydrogen/Helium mixture, we take into account the small fractions of Deuterium and Lithium as resulting from Standard Big Bang Nucleosynthesis. Our opacity tables cover the density range -16 < log rho [g cm^{-3}] < -2 and temperature range of 1.8 < T [K] < 4.6, while previous tables were usually restricted to T > 10^3 K. We find that, while the presence of Deuterium does not significantly alter the opacity values, the presence of Lithium gives rise to major modifications of the opacities, at some points increasing it by approximately 2 orders of magnitude relative to pure Hydrogen/Helium opacities.
We present stationary models of protostellar population III (Pop III, for short) accretion discs, compare them to Pop I discs, and investigate the influence of the different chemical compositions on the occurence of gravitational, thermal and thermal-viscous instabilities in the discs. In particular in the cooler regions, we find major differences between Pop III and Pop I discs, both in the structure and stability behaviour. This is mainly due to the absence of most molecules and dust in Pop III, which are very efficient absorbers in Pop I discs.