Counting function for a sphere of anisotropic quartz

We calculate the leading Weyl term of the counting function for a mono-crystalline quartz sphere. In contrast to other studies of counting functions, the anisotropy of quartz is a crucial element in our investigation. Hence, we do not obtain a simple analytical form, but we carry out a numerical evaluation. To this end we employ the Radon transform representation of the Green's function. We compare our result to a previously measured unique data set of several tens of thousands of resonances.Comment: 16 pages, 11 figure

Pattern Dynamics of Vortex Ripples in Sand: Nonlinear Modeling and Experimental Validation

Vortex ripples in sand are studied experimentally in a one-dimensional setup with periodic boundary conditions. The nonlinear evolution, far from the onset of instability, is analyzed in the framework of a simple model developed for homogeneous patterns. The interaction function describing the mass transport between neighboring ripples is extracted from experimental runs using a recently proposed method for data analysis, and the predictions of the model are compared to the experiment. An analytic explanation of the wavelength selection mechanism in the model is provided, and the width of the stable band of ripples is measured.Comment: 4 page

Abelian Conformal Field theories and Determinant Bundles

The present paper is the first in a series of papers, in which we shall construct modular functors and Topological Quantum Field Theories from the conformal field theory developed in [TUY]. The basic idea is that the covariant constant sections of the sheaf of vacua associated to a simple Lie algebra over Teichm\"uller space of an oriented pointed surface gives the vectorspace the modular functor associates to the oriented pointed surface. However the connection on the sheaf of vacua is only projectively flat, so we need to find a suitable line bundle with a connection, such that the tensor product of the two has a flat connection. We shall construct a line bundle with a connection on any family of pointed curves with formal coordinates. By computing the curvature of this line bundle, we conclude that we actually need a fractional power of this line bundle so as to obtain a flat connection after tensoring. In order to functorially extract this fractional power, we need to construct a preferred section of the line bundle. We shall construct the line bundle by the use of the so-called $bc$-ghost systems (Faddeev-Popov ghosts) first introduced in covariant quantization [FP]. We follow the ideas of [KNTY], but decribe it from the point of view of [TUY].Comment: A couple of typos correcte

Relationships between a roller and a dynamic pressure distribution in circular hydraulic jumps

We investigated numerically the relation between a roller and the pressure distribution to clarify the dynamics of the roller in circular hydraulic jumps. We found that a roller which characterizes a type II jump is associated with two high pressure regions after the jump, while a type I jump (without the roller) is associated with only one high pressure region. Our numerical results show that building up an appropriate pressure field is essential for a roller.Comment: 10 pages, 7 PS files. To appear in PR

Haematologic and Clinical Chemical values in 3 and 6 months old Göttingen minipigs

Blood samples were collected from sixty healthy Göttingen minipigs. fifteen males and fifteen females at the age of three months and fifteen males and fifteen females at the age of six months. The samples were taken at the breeder’s facilities. The samples were analysed for nineteen haematological and twenty~six clinical chemical parameters. Means, standard deviations and lowest and highest values are presented. In general the parameters were comparable with those reponed for other breeds of miniature and domestic swine. The white blood cell count, the percentages of neutrophils and monocytes and serum globulin levels were lower in these microbiologically defined minipigs compared with conventionally rearedpigs and minipigs. Three litter mates had a complex of abnormally high serum creatine kinase, lactate dehydrogenase, uspartate aminotransterase and alanine aminotmnsferase levels

The Stability Balloon for Two-dimensional Vortex Ripple Patterns

Patterns of vortex ripples form when a sand bed is subjected to an oscillatory fluid flow. Here we describe experiments on the response of regular vortex ripple patterns to sudden changes of the driving amplitude a or frequency f. A sufficient decrease of f leads to a "freezing" of the pattern, while a sufficient increase of f leads to a supercritical secondary "pearling" instability. Sufficient changes in the amplitude a lead to subcritical secondary "doubling" and "bulging" instabilities. Our findings are summarized in a "stability balloon" for vortex ripple pattern formation.Comment: 4 pages, 5 figure

Gaussian random waves in elastic media

Similar to the Berry conjecture of quantum chaos we consider elastic analogue which incorporates longitudinal and transverse elastic displacements with corresponding wave vectors. Based on that we derive the correlation functions for amplitudes and intensities of elastic displacements. Comparison to numerics in a quarter Bunimovich stadium demonstrates excellent agreement.Comment: 4 pages, 4 figure

The UV filtering potential of drop-casted layers of frustules of three diatom species

Abstract Diatoms are in focus as biological materials for a range of photonic applications. Many of these applications would require embedding a multitude of diatoms in a matrix (e.g. paint, crème or lacquer); however, most studies on the photonic and spectral properties of diatoms frustules (silica walls) have been carried out on single cells. In this study, for the first time, we test the spectral properties of layers of frustules of three diatom species (Coscinodiscus granii, Thalassiosira punctifera and Thalassiosira pseudonana), with special focus on transmission and reflectance in the UV range. The transmittance efficiency in the UV A and B range was: T. pseudonana (56–59%) >C. granii (53–54%) >T. punctifera (18–21%) for the rinsed frustules. To investigate the underlying cause of these differences, we performed X-ray scattering analysis, measurement of layer thickness and microscopic determination of frustule nanostructures. We further tested dried intact cells in the same experimental setup. Based on these data we discuss the relative importance of crystal structure properties, nanostructure and quantity of material on the spectral properties of diatom layers. Characterization of the UV protection performance of layers of diatom frustules is of central relevance for their potential use as innovative bio-based UV filters