Nb3Sn wire shape and cross sectional area inhomogeneity in Rutherford cables

During Rutherford cable production the wires are plastically deformed and their initially round shape is distorted. Using X-ray absorption tomography we have determined the 3D shape of an unreacted Nb3Sn 11 T dipole Rutherford cable, and of a reacted and impregnated Nb3Sn cable double stack. State-of-the-art image processing was applied to correct for tomographic artefacts caused by the large cable aspect ratio, for the segmentation of the individual wires and subelement bundles inside the wires, and for the calculation of the wire cross sectional area and shape variations. The 11 T dipole cable cross section oscillates by 2% with a frequency of 1.24 mm (1/80 of the transposition pitch length of the 40 wire cable). A comparatively stronger cross sectional area variation is observed in the individual wires at the thin edge of the keystoned cable where the wire aspect ratio is largest.Comment: 6 pages, 11 figures, presented at EUCAS 201

Magnetization of noncircular quantum dots

We calculate the magnetization of quantum dots deviating from circular symmetry for noninteracting electrons or electrons interacting according to the Hartree approximation. For few electrons the magnetization is found to depend on their number, and the shape of the dot. The magnetization is an ideal probe into the many-electron state of a quantum dot.Comment: 11 RevTeX pages with 6 included Postscript figure

Incommensurate ground state of double-layer quantum Hall systems

Double-layer quantum Hall systems possess interlayer phase coherence at sufficiently small layer separations, even without interlayer tunneling. When interlayer tunneling is present, application of a sufficiently strong in-plane magnetic field $B_\parallel > B_c$ drives a commensurate-incommensurate (CI) transition to an incommensurate soliton-lattice (SL) state. We calculate the Hartree-Fock ground-state energy of the SL state for all values of $B_\parallel$ within a gradient approximation, and use it to obtain the anisotropic SL stiffness, the Kosterlitz-Thouless melting temperature for the SL, and the SL magnetization. The in-plane differential magnetic susceptibility diverges as $(B_\parallel - B_c)^{-1}$ when the CI transition is approached from the SL state.Comment: 12 pages, 7 figures, to be published in Physical Review

Ernst equation and spheroidal coordinates with a cosmological constant term

We discuss solution generating techniques treating stationary and axially symmetric metrics in the presence of a cosmological constant. Using the recently found extended form of Ernst's complex equation, which takes into account the cosmological constant term, we propose an extension of spheroidal coordinates adapted to asymptotically de-Sitter and anti de-Sitter static spacetimes. In the absence of a cosmological constant we show in addition that any higher dimensional metric parametrised by a single angular momentum can be given by a 4 dimensional solution and Weyl potentials parametrising the extra Killing directions. We explicitly show how a stationary, and a static axially symmetric spacetime solution in 4 dimensions, can be {\it added} together to give a 5 dimensional stationary and axisymmetric solution.Comment: 9 pages, no figures, some additional results to gr-qc/0610091. Prepared for 12th Conference on Recent Developments in Gravity (NEB XII), Nafplio, Greece, 29 Jun - 2 Jul 200

Exact relativistic treatment of stationary counter-rotating dust disks I: Boundary value problems and solutions

This is the first in a series of papers on the construction of explicit solutions to the stationary axisymmetric Einstein equations which describe counter-rotating disks of dust. These disks can serve as models for certain galaxies and accretion disks in astrophysics. We review the Newtonian theory for disks using Riemann-Hilbert methods which can be extended to some extent to the relativistic case where they lead to modular functions on Riemann surfaces. In the case of compact surfaces these are Korotkin's finite gap solutions which we will discuss in this paper. On the axis we establish for general genus relations between the metric functions and hence the multipoles which are enforced by the underlying hyperelliptic Riemann surface. Generalizing these results to the whole spacetime we are able in principle to study the classes of boundary value problems which can be solved on a given Riemann surface. We investigate the cases of genus 1 and 2 of the Riemann surface in detail and construct the explicit solution for a family of disks with constant angular velocity and constant relative energy density which was announced in a previous Physical Review Letter.Comment: 32 pages, 1 figure, to appear in Phys. Rev.

Analytical approximation of the exterior gravitational field of rotating neutron stars

It is known that B\"acklund transformations can be used to generate stationary axisymmetric solutions of Einstein's vacuum field equations with any number of constants. We will use this class of exact solutions to describe the exterior vacuum region of numerically calculated neutron stars. Therefore we study how an Ernst potential given on the rotation axis and containing an arbitrary number of constants can be used to determine the metric everywhere. Then we review two methods to determine those constants from a numerically calculated solution. Finally, we compare the metric and physical properties of our analytic solution with the numerical data and find excellent agreement even for a small number of parameters.Comment: 9 pages, 10 figures, 3 table

OBDD-Based Representation of Interval Graphs

A graph $G = (V,E)$ can be described by the characteristic function of the edge set $\chi_E$ which maps a pair of binary encoded nodes to 1 iff the nodes are adjacent. Using \emph{Ordered Binary Decision Diagrams} (OBDDs) to store $\chi_E$ can lead to a (hopefully) compact representation. Given the OBDD as an input, symbolic/implicit OBDD-based graph algorithms can solve optimization problems by mainly using functional operations, e.g. quantification or binary synthesis. While the OBDD representation size can not be small in general, it can be provable small for special graph classes and then also lead to fast algorithms. In this paper, we show that the OBDD size of unit interval graphs is $O(\ | V \ | /\log \ | V \ |)$ and the OBDD size of interval graphs is $O(\ | V \ | \log \ | V \ |)$which both improve a known result from Nunkesser and Woelfel (2009). Furthermore, we can show that using our variable order and node labeling for interval graphs the worst-case OBDD size is$\Omega(\ | V \ | \log \ | V \ |)$. We use the structure of the adjacency matrices to prove these bounds. This method may be of independent interest and can be applied to other graph classes. We also develop a maximum matching algorithm on unit interval graphs using$O(\log \ | V \ |)$operations and a coloring algorithm for unit and general intervals graphs using$O(\log^2 \ | V \ |)$ operations and evaluate the algorithms empirically.Comment: 29 pages, accepted for 39th International Workshop on Graph-Theoretic Concepts 201

The angular momentum and mass formulas for rotating stationary quasi-black holes

We consider the quasi-black hole limit of a stationary body when its boundary approaches its own gravitational radius, i.e., its quasi-horizon. It is shown that there exists a perfect correspondence between the different mass contributions and the mass formula for quasi-black and black holes in spite of difference in derivation and meaning of the formulas in both cases. For extremal quasi-black holes the finite surface stresses give zero contribution to the total mass. Conclusions similar to those for the properties of mass are derived for the angular momentum.Comment: 14 page

Symmetries and Asymmetries of B -> K* mu+ mu- Decays in the Standard Model and Beyond

The rare decay B -> K* (-> K pi) mu+ mu- is regarded as one of the crucial channels for B physics as the polarization of the K* allows a precise angular reconstruction resulting in many observables that offer new important tests of the Standard Model and its extensions. These angular observables can be expressed in terms of CP-conserving and CP-violating quantities which we study in terms of the full form factors calculated from QCD sum rules on the light-cone, including QCD factorization corrections. We investigate all observables in the context of the Standard Model and various New Physics models, in particular the Littlest Higgs model with T-parity and various MSSM scenarios, identifying those observables with small to moderate dependence on hadronic quantities and large impact of New Physics. One important result of our studies is that new CP-violating phases will produce clean signals in CP-violating asymmetries. We also identify a number of correlations between various observables which will allow a clear distinction between different New Physics scenarios.Comment: 56 pages, 18 figures, 14 tables. v5: Missing factor in eqs. (3.31-32) and fig. 6 corrected. Minor misprints in eq. (2.10) and table A corrected. Conclusions unchange

Magnetization of a two-dimensional electron gas with a second filled subband

We have measured the magnetization of a dual-subband two-dimensional electron gas, confined in a GaAs/AlGaAs heterojunction. In contrast to two-dimensional electron gases with a single subband, we observe non-1/B-periodic, triangularly shaped oscillations of the magnetization with an amplitude significantly less than $1 \mu_{\mathrm{B}}^*$ per electron. All three effects are explained by a field dependent self-consistent model, demonstrating the shape of the magnetization is dominated by oscillations in the confining potential. Additionally, at 1 K, we observe small oscillations at magnetic fields where Landau-levels of the two different subbands cross.Comment: 4 pages, 4 figure