Spectral gaps for water waves above a corrugated bottom

In this paper, the essential spectrum of the linear problem on water waves in a water layer and in a channel with a gently corrugated bottom is studied. We show that, under a certain geometric condition, the essential spectrum has spectral gaps. In other words, there exist intervals in the positive real semi-axis that are free of the spectrum but have their endpoints in it. The position and the length of the gaps are found out by applying an asymptotic analysis to the model problem in the periodicity cell

Visualizing landscapes of the superconducting gap in heterogeneous superconductor thin films: geometric influences on proximity effects

The proximity effect is a central feature of superconducting junctions as it underlies many important applications in devices and can be exploited in the design of new systems with novel quantum functionality. Recently, exotic proximity effects have been observed in various systems, such as superconductor-metallic nanowires and graphene-superconductor structures. However, it is still not clear how superconducting order propagates spatially in a heterogeneous superconductor system. Here we report intriguing influences of junction geometry on the proximity effect for a 2D heterogeneous superconductor system comprised of 2D superconducting islands on top of a surface metal. Depending on the local geometry, the superconducting gap induced in the surface metal region can either be confined to the boundary of the superconductor, in which the gap decays within a short distance (~ 15 nm), or can be observed nearly uniformly over a distance of many coherence lengths due to non-local proximity effects.Comment: 17 pages, 4 figure

Effective Rheology of Bubbles Moving in a Capillary Tube

We calculate the average volumetric flux versus pressure drop of bubbles moving in a single capillary tube with varying diameter, finding a square-root relation from mapping the flow equations onto that of a driven overdamped pendulum. The calculation is based on a derivation of the equation of motion of a bubble train from considering the capillary forces and the entropy production associated with the viscous flow. We also calculate the configurational probability of the positions of the bubbles.Comment: 4 pages, 1 figur

AIB1 gene amplification and the instability of polyQ encoding sequence in breast cancer cell lines

BACKGROUND: The poly Q polymorphism in AIB1 (amplified in breast cancer) gene is usually assessed by fragment length analysis which does not reveal the actual sequence variation. The purpose of this study is to investigate the sequence variation of poly Q encoding region in breast cancer cell lines at single molecule level, and to determine if the sequence variation is related to AIB1 gene amplification. METHODS: The polymorphic poly Q encoding region of AIB1 gene was investigated at the single molecule level by PCR cloning/sequencing. The amplification of AIB1 gene in various breast cancer cell lines were studied by real-time quantitative PCR. RESULTS: Significant amplifications (5–23 folds) of AIB1 gene were found in 2 out of 9 (22%) ER positive cell lines (in BT-474 and MCF-7 but not in BT-20, ZR-75-1, T47D, BT483, MDA-MB-361, MDA-MB-468 and MDA-MB-330). The AIB1 gene was not amplified in any of the ER negative cell lines. Different passages of MCF-7 cell lines and their derivatives maintained the feature of AIB1 amplification. When the cells were selected for hormone independence (LCC1) and resistance to 4-hydroxy tamoxifen (4-OH TAM) (LCC2 and R27), ICI 182,780 (LCC9) or 4-OH TAM, KEO and LY 117018 (LY-2), AIB1 copy number decreased but still remained highly amplified. Sequencing analysis of poly Q encoding region of AIB1 gene did not reveal specific patterns that could be correlated with AIB1 gene amplification. However, about 72% of the breast cancer cell lines had at least one under represented (<20%) extra poly Q encoding sequence patterns that were derived from the original allele, presumably due to somatic instability. Although all MCF-7 cells and their variants had the same predominant poly Q encoding sequence pattern of (CAG)(3)CAA(CAG)(9)(CAACAG)(3)(CAACAGCAG)(2)CAA of the original cell line, a number of altered poly Q encoding sequences were found in the derivatives of MCF-7 cell lines. CONCLUSION: These data suggest that poly Q encoding region of AIB1 gene is somatic unstable in breast cancer cell lines. The instability and the sequence characteristics, however, do not appear to be associated with the level of the gene amplification

Space Telescope and Optical Reverberation Mapping Project. IX. Velocity–Delay Maps for Broad Emission Lines in NGC 5548

In this contribution, we achieve the primary goal of the active galactic nucleus (AGN) STORM campaign by recovering velocity–delay maps for the prominent broad emission lines (Lyα, C iv, He ii, and Hβ) in the spectrum of NGC 5548. These are the most detailed velocity–delay maps ever obtained for an AGN, providing unprecedented information on the geometry, ionization structure, and kinematics of the broad-line region. Virial envelopes enclosing the emission-line responses show that the reverberating gas is bound to the black hole. A stratified ionization structure is evident. The He ii response inside 5–10 lt-day has a broad single-peaked velocity profile. The Lyα, C iv, and Hβ responses extend from inside 2 to outside 20 lt-day, with double peaks at ±2500 km s−1 in the 10–20 lt-day delay range. An incomplete ellipse in the velocity–delay plane is evident in Hβ. We interpret the maps in terms of a Keplerian disk with a well-defined outer rim at R = 20 lt-day. The far-side response is weaker than that from the near side. The line-center delay $\tau =(R/c)(1-\sin i)\approx 5$ days gives the inclination i ≈ 45°. The inferred black hole mass is MBH ≈ 7 × 107 M⊙. In addition to reverberations, the fit residuals confirm that emission-line fluxes are depressed during the "BLR Holiday" identified in previous work. Moreover, a helical "Barber-Pole" pattern, with stripes moving from red to blue across the C iv and Lyα line profiles, suggests azimuthal structure rotating with a 2 yr period that may represent precession or orbital motion of inner-disk structures casting shadows on the emission-line region farther out

Alignment of the ALICE Inner Tracking System with cosmic-ray tracks

37 pages, 15 figures, revised version, accepted by JINSTALICE (A Large Ion Collider Experiment) is the LHC (Large Hadron Collider) experiment devoted to investigating the strongly interacting matter created in nucleus-nucleus collisions at the LHC energies. The ALICE ITS, Inner Tracking System, consists of six cylindrical layers of silicon detectors with three different technologies; in the outward direction: two layers of pixel detectors, two layers each of drift, and strip detectors. The number of parameters to be determined in the spatial alignment of the 2198 sensor modules of the ITS is about 13,000. The target alignment precision is well below 10 micron in some cases (pixels). The sources of alignment information include survey measurements, and the reconstructed tracks from cosmic rays and from proton-proton collisions. The main track-based alignment method uses the Millepede global approach. An iterative local method was developed and used as well. We present the results obtained for the ITS alignment using about 10^5 charged tracks from cosmic rays that have been collected during summer 2008, with the ALICE solenoidal magnet switched off.Peer reviewe