Approximation Algorithms for Generalized MST and TSP in Grid Clusters

We consider a special case of the generalized minimum spanning tree problem (GMST) and the generalized travelling salesman problem (GTSP) where we are given a set of points inside the integer grid (in Euclidean plane) where each grid cell is $1 \times 1$. In the MST version of the problem, the goal is to find a minimum tree that contains exactly one point from each non-empty grid cell (cluster). Similarly, in the TSP version of the problem, the goal is to find a minimum weight cycle containing one point from each non-empty grid cell. We give a $(1+4\sqrt{2}+\epsilon)$ and $(1.5+8\sqrt{2}+\epsilon)$-approximation algorithm for these two problems in the described setting, respectively. Our motivation is based on the problem posed in [7] for a constant approximation algorithm. The authors designed a PTAS for the more special case of the GMST where non-empty cells are connected end dense enough. However, their algorithm heavily relies on this connectivity restriction and is unpractical. Our results develop the topic further

Josephson supercurrent in a topological insulator without a bulk shunt

A Josephson supercurrent has been induced into the three-dimensional topological insulator Bi1.5Sb0.5Te1.7Se1.3. We show that the transport in Bi1.5Sb0.5Te1.7Se1.3 exfoliated flakes is dominated by surface states and that the bulk conductivity can be neglected at the temperatures where we study the proximity induced superconductivity. We prepared Josephson junctions with widths in the order of 40 nm and lengths in the order of 50 to 80 nm on several Bi1.5Sb0.5Te1.7Se1.3 flakes and measured down to 30 mK. The Fraunhofer patterns unequivocally reveal that the supercurrent is a Josephson supercurrent. The measured critical currents are reproducibly observed on different devices and upon multiple cooldowns, and the critical current dependence on temperature as well as magnetic field can be well explained by diffusive transport models and geometric effects

Looking for a Pulse: A Search for Rotationally Modulated Radio Emission from the Hot Jupiter, τ Boötis b

Hot Jupiters have been proposed as a likely population of low-frequency radio sources due to electron cyclotron maser emission of similar nature to that detected from the auroral regions of magnetized solar system planets. Such emission will likely be confined to specific ranges of orbital/rotational phase due to a narrowly beamed radiation pattern. We report on GMRT 150 MHz radio observations of the hot Jupiter τ Boötis b, consisting of 40 hr carefully scheduled to maximize coverage of the planet's 79.5 hr orbital/rotational period in an effort to detect such rotationally modulated emission. The resulting image is the deepest yet published at these frequencies and leads to a 3σ upper limit on the flux density from the planet of 1.2 mJy, two orders of magnitude lower than predictions derived from scaling laws based on solar system planetary radio emission. This represents the most stringent upper limits for both quiescent and rotationally modulated radio emission from a hot Jupiter yet achieved and suggests that either (1) the magnetic dipole moment of τ Boötis b is insufficient to generate the surface field strengths of >50 G required for detection at 150 MHz or (2) Earth lies outside the beaming pattern of the radio emission from the planet

The normal state Fermi surface of pristine and Pb-doped Bi2212 from ARPES measurements and its photon energy independence

We address the question as to whether the topology of the normal state Fermi surface of Bi2212 - as seen in angle resolved photoemission - depends on the photon energy used to measure it. High resolution photoemission spectra and Fermi surface maps from pristine and Pb-doped Bi2212 are presented, recorded using both polarised and unpolarised radiation of differing energies. The data show clearly that no main band crosses the Fermi surface along the GMZ direction in reciprocal space, even for a photon energy of 32 eV, thus ruling out the existence of a G-centred, electron-like Fermi surface in this archetypal high Tc superconductor. The true topology of the normal state Fermi surface remains that of hole-like barrels centred at the X,Y points of the Brillouin zone.Comment: 4 pages (revtex), 4 figures (jpg

New Measurement of the Cosmic-Ray Positron Fraction from 5 to 15 GeV

We present a new measurement of the cosmic-ray positron fraction at energies between 5 and 15 GeV with the balloon-borne HEAT-pbar instrument in the spring of 2000. The data presented here are compatible with our previous measurements, obtained with a different instrument. The combined data from the three HEAT flights indicate a small positron flux of non-standard origin above 5 GeV. We compare the new measurement with earlier data obtained with the HEAT-e+- instrument, during the opposite epoch of the solar cycle, and conclude that our measurements do not support predictions of charge sign dependent solar modulation of the positron abundance at 5 GeV.Comment: accepted for publication in PR

Phases in Strongly Coupled Electronic Bilayer Liquids

The strongly correlated liquid state of a bilayer of charged particles has been studied via the HNC calculation of the two-body functions. We report the first time emergence of a series of structural phases, identified through the behavior of the two-body functions.Comment: 5 pages, RevTEX 3.0, 4 ps figures; Submitted to Phys. Rev. Let

Periodic Bursts of Coherent Radio Emission from an Ultracool Dwarf

We report the detection of periodic (p = 1.96 hours) bursts of extremely bright, 100% circularly polarized, coherent radio emission from the M9 dwarf TVLM 513-46546. Simultaneous photometric monitoring observations have established this periodicity to be the rotation period of the dwarf. These bursts, which were not present in previous observations of this target, confirm that ultracool dwarfs can generate persistent levels of broadband, coherent radio emission, associated with the presence of kG magnetic fields in a large-scale, stable configuration. Compact sources located at the magnetic polar regions produce highly beamed emission generated by the electron cyclotron maser instability, the same mechanism known to generate planetary coherent radio emission in our solar system. The narrow beams of radiation pass our line of sight as the dwarf rotates, producing the associated periodic bursts. The resulting radio light curves are analogous to the periodic light curves associated with pulsar radio emission highlighting TVLM 513-46546 as the prototype of a new class of transient radio source.Comment: 12 pages, 3 figures, accepted for publication in ApJ Letter

Phase-resolved Crab Studies with a Cryogenic TES Spectrophotometer

We are developing time- and energy-resolved near-IR/optical/UV photon detectors based on sharp superconducting-normal transition edges in thin films. We report observations of the Crab pulsar made during prototype testing at the McDonald 2.7m telescope with a fiber-coupled transition-edge sensor (TES) system. These data show substantial (d[alpha]~0.3), rapid variations in the spectral index through the pulse profile, with a strong phase-varying IR break across our energy band. These variations correlate with X-ray spectral variations, but no single synchrotron population can account for the full Spectral Energy Distribution (SED). We also describe test spectrophotopolarimetry observations probing the energy dependence of the polarization sweep; this may provide a new key to understanding the radiating particle population.Comment: 12 pages, 10 figures -- to appear in ApJ V56

Collective Modes in Strongly Coupled Elecronic Bilayer Liquids

We present the first reliable calculation of the collective mode structure of a strongly coupled electronic bilayer. The calculation is based on a classical model through the $3^{rd}$ frequency-moment-sum-rule preserving Quasi Localized Charge Approximation, using the recently calculated Hypernetted Chain pair correlation functions. The spectrum shows an energy gap at $k=0$ and the absence of a previously conjectured dynamical instability.Comment: 4 pages, 4 .ps figure