Singularities of equidistants and global centre symmetry sets of Lagrangian submanifolds

We define the Global Centre Symmetry set (GCS) of a smooth closed m-dimensional submanifold M of R^n, $n \leq 2m$, which is an affinely invariant generalization of the centre of a k-sphere in R^{k+1}. The GCS includes both the centre symmetry set defined by Janeczko and the Wigner caustic defined by Berry. We develop a new method for studying generic singularities of the GCS which is suited to the case when M is lagrangian in R^{2m} with canonical symplectic form. The definition of the GCS, which slightly generalizes one by Giblin and Zakalyukin, is based on the notion of affine equidistants, so, we first study singularities of affine equidistants of Lagrangian submanifolds, classifying all the stable ones. Then, we classify the affine-Lagrangian stable singularities of the GCS of Lagrangian submanifolds and show that, already for smooth closed convex curves in R^2, many singularities of the GCS which are affine stable are not affine-Lagrangian stable.Comment: 26 pages, 2 figure

Observation of a superconducting glass state in granular superconducting diamond

The magnetic field dependence of the superconductivity in nanocrystalline boron doped diamond thin films is reported. Evidence of a glass state in the phase diagram is presented, as demonstrated by electrical resistance and magnetic relaxation measurements. The position of the phase boundary in the H-T plane is determined from resistance data by detailed fitting to zero-dimensional fluctuation conductivity theory. This allows determination of the boundary between resistive and non-resistive behavior to be made with greater precision than the standard ad hoc onset/midpoint/offset criterion

Fluctuation spectroscopy as a probe of granular superconducting diamond films

We present resistance versus temperature data for a series of boron-doped nanocrystalline diamond films whose grain size is varied by changing the film thickness. Upon extracting the fluctuation conductivity near to the critical temperature we observe three distinct scaling regions -- 3D intragrain, quasi-0D, and 3D intergrain -- in confirmation of the prediction of Lerner, Varlamov and Vinokur. The location of the dimensional crossovers between these scaling regions allows us to determine the tunnelling energy and the Thouless energy for each film. This is a demonstration of the use of \emph{fluctuation spectroscopy} to determine the properties of a superconducting granular system

Evidence for an Early High-Energy Afterglow Observed with BATSE from GRB980923

In this Letter, we present the first evidence in the BATSE data for a prompt high-energy (25-300 keV) afterglow component from a gamma-ray burst (GRB), GRB980923. The event consists of rapid variabilty lasting ~40 s followed by a smooth power law emission tail lasting ~400 s. An abrupt change in spectral shape is found when the tail becomes noticeable. Our analysis reveals that the spectral evolution in the tail of the burst mimics that of a cooling synchrotron spectrum, similar to the spectral evolution of the low-energy afterglows for GRBs. This evidence for a separate emission component is consistent with the internal-external shock scenario in the relativistic fireball picture. In particular, it illustrates that the external shocks can be generated during the gamma-ray emission phase, as in the case of GRB990123.Comment: 4 pages, 4 figures, accepted for publication in Astrophysical Journal Letter

Design and development of a low temperature, inductance based high frequency ac susceptometer

We report on the development of an induction based low temperature high frequency ac susceptometer capable of measuring at frequencies up to 3.5 MHz and at temperatures between 2 K and 300 K. Careful balancing of the detection coils and calibration have allowed a sample magnetic moment resolution of $5\times10^{-10} Am^2$ at 1 MHz. We will discuss the design and characterization of the susceptometer, and explain the calibration process. We also include some example measurements on the spin ice material CdEr$_2$S$_4$ and iron oxide based nanoparticles to illustrate functionality

Probing the magnetic ground state of the molecular Dysprosium triangle

We present zero field muon spin lattice relaxation measurements of a Dysprosium triangle molecular magnet. The local magnetic fields sensed by the implanted muons indicate the coexistence of static and dynamic internal magnetic fields below $T^* ~35$ K. Bulk magnetization and heat capacity measurements show no indication of magnetic ordering below this temperature. We attribute the static fields to the slow relaxation of the magnetization in the ground state of Dy3. The fluctuation time of the dynamic part of the field is estimated to be ~0.55 $\mu$s at low temperaturesComment: 5 pages, 5 figures, accepted for publication in Phys. Rev.

Immunolocalization of KATP channel subunits in mouse and rat cardiac myocytes and the coronary vasculature.

BACKGROUND: Electrophysiological data suggest that cardiac KATP channels consist of Kir6.2 and SUR2A subunits, but the distribution of these (and other KATP channel subunits) is poorly defined. We examined the localization of each of the KATP channel subunits in the mouse and rat heart. RESULTS: Immunohistochemistry of cardiac cryosections demonstrate Kir6.1 protein to be expressed in ventricular myocytes, as well as in the smooth muscle and endothelial cells of coronary resistance vessels. Endothelial capillaries also stained positive for Kir6.1 protein. Kir6.2 protein expression was found predominantly in ventricular myocytes and also in endothelial cells, but not in smooth muscle cells. SUR1 subunits are strongly expressed at the sarcolemmal surface of ventricular myocytes (but not in the coronary vasculature), whereas SUR2 protein was found to be localized predominantly in cardiac myocytes and coronary vessels (mostly in smaller vessels). Immunocytochemistry of isolated ventricular myocytes shows co-localization of Kir6.2 and SUR2 proteins in a striated sarcomeric pattern, suggesting t-tubular expression of these proteins. Both Kir6.1 and SUR1 subunits were found to express strongly at the sarcolemma. The role(s) of these subunits in cardiomyocytes remain to be defined and may require a reassessment of the molecular nature of ventricular KATP channels. CONCLUSIONS: Collectively, our data demonstrate unique cellular and subcellular KATP channel subunit expression patterns in the heart. These results suggest distinct roles for KATP channel subunits in diverse cardiac structures