Bounded Imaginary Powers of Differential Operators on Manifolds with Conical Singularities

We study the minimal and maximal closed extension of a differential operator A on a manifold B with conical singularities, when A acts as an unbounded operator on weighted L^p-spaces over B, 1 < p < \infty. Under suitable ellipticity assumptions we can define a family of complex powers A^z. We also obtain sufficient information on the resolvent of A to show the boundedness of the purely imaginary powers. Examples concern unique solvability and maximal regularity for the solution of the Cauchy problem for the Laplacian on conical manifolds as well as certain quasilinear diffusion equations.Comment: 27 pages, 3 figures (revised version 23/04/'02

Further analysis of field effects on liquids and solidification

Numerical calculations of the magnitude of external field effects on liquids are presented to describe how external fields can influence the substructure of the field. Quantitative estimates of magnetic and gravitational effects are reported on melts of metals and semiconductors. The results are condensed in tables which contain the input data for calculation of the field effects on diffusion coefficient, solidification rate and for calculation of field forces on individual molecules in the melt

Realizations of Differential Operators on Conic Manifolds with Boundary

We study the closed extensions (realizations) of differential operators subject to homogeneous boundary conditions on weighted L_p-Sobolev spaces over a manifold with boundary and conical singularities. Under natural ellipticity conditions we determine the domains of the minimal and the maximal extension. We show that both are Fredholm operators and give a formula for the relative index.Comment: 41 pages, 1 figur

On the Fredholm property of bisingular pseudodifferential operators

For operators belonging either to a class of global bisingular pseudodifferential operators on $R^m \times R^n$ or to a class of bisingular pseudodifferential operators on a product $M \times N$ of two closed smooth manifolds, we show the equivalence of their ellipticity (defined by the invertibility of certain associated homogeneous principal symbols) and their Fredholm mapping property in associated scales of Sobolev spaces. We also prove the spectral invariance of these operator classes and then extend these results to the even larger classes of Toeplitz type operators.Comment: 21 pages. Expanded sections 3 and 4. Corrected typos. Added reference

Comment on `Hawking radiation from fluctuating black holes'

Takahashi & Soda (2010 Class. Quantum Grav. v27 p175008, arXiv:1005.0286) have recently considered the effect (at lowest non-trivial order) of dynamical, quantized gravitational fluctuations on the spectrum of scalar Hawking radiation from a collapsing Schwarzschild black hole. However, due to an unfortunate choice of gauge, the dominant (even divergent) contribution to the coefficient of the spectrum correction that they identify is a pure gauge artifact. I summarize the logic of their calculation, comment on the divergences encountered in its course and comment on how they could be eliminated, and thus the calculation be completed.Comment: 12 pages, 1 fig; feynmp, amsref

Correlating the nanostructure of Al-oxide with deposition conditions and dielectric contributions of two-level systems in perspective of superconducting quantum circuits

This work is concerned with Al/Al-oxide(AlO$_{x}$)/Al-layer systems which are important for Josephson-junction-based superconducting devices such as quantum bits. The device performance is limited by noise, which has been to a large degree assigned to the presence and properties of two-level tunneling systems in the amorphous AlO$_{x}$ tunnel barrier. The study is focused on the correlation of the fabrication conditions, nanostructural and nanochemical properties and the occurrence of two-level tunneling systems with particular emphasis on the AlO$_{x}$-layer. Electron-beam evaporation with two different processes and sputter deposition were used for structure fabrication, and the effect of illumination by ultraviolet light during Al-oxide formation is elucidated. Characterization was performed by analytical transmission electron microscopy and low-temperature dielectric measurements. We show that the fabrication conditions have a strong impact on the nanostructural and nanochemical properties of the layer systems and the properties of two-level tunneling systems. Based on the understanding of the observed structural characteristics, routes are derived towards the fabrication of Al/AlO$_{x}$/Al-layers systems with improved properties.Comment: 28 pages, 4 figure

Gauged O(n) spin models in one dimension

We consider a gauged O(n) spin model, n >= 2, in one dimension which contains both the pure O(n) and RP(n-1) models and which interpolates between them. We show that this model is equivalent to the non-interacting sum of the O(n) and Ising models. We derive the mass spectrum that scales in the continuum limit, and demonstrate that there are two universality classes, one of which contains the O(n) and RP(n-1) models and the other which has a tuneable parameter but which is degenerate in the sense that it arises from the direct sum of the O(n) and Ising models.Comment: 9 pages, no figures, LaTeX sourc

Dietary variability of western gorillas (Gorilla gorilla gorilla)

Spatial and temporal variability in the availability of food resources will lead to variation in a species’ diet, which can then influence patterns of space use, sociality, and life history characteristics. Despite such potential impacts, little information is available about dietary variability for some species with large geographical ranges. Here we quantify the diet and nutritional content of plants consumed by western lowland gorillas (Gorilla gorilla gorilla) in Loango National Park, Gabon over a 2.6 year period and make comparisons with two study sites located 800 km away. The major foods consumed by the Loango gorillas differed greatly from the other two study sites, but gorillas at all three locations spent a similar proportion of feeding time consuming herbaceous vegetation and tree leaves (~ 50%) and fruit (35%). The Loango gorillas spent approximately 10% of feeding time eating nuts, which were not consumed at the other two study sites. Gorillas at those sites spent about 5% of feeding time eating insects, which were not consumed by Loango gorillas. Even though the species composition of the diet differed among the three sites, the nutritional composition of the major food items differed very little, suggesting that western gorillas consume foods of similar nutritional values to meet their dietary needs. This study shows the flexibility of diet of a species with a wide geographic distribution, which has implications for understanding variation in life history characteristics and can be useful for conservation management plans