Algebraic methods for parameterized codes and invariants of vanishing ideals over finite fields

Let K be a finite field with q elements and let X be a subset of a projective space P^{s-1}, over the field K, which is parameterized by Laurent monomials. Let I(X) be the vanishing ideal of X. Some of the main contributions of this paper are in determining the structure of I(X) and some of their invariants. It is shown that I(X) is a lattice ideal. We introduce the notion of a parameterized code arising from X and present algebraic methods to compute and study its dimension, length and minimum distance. For a parameterized code arising from a connected graph we are able to compute its length and to make our results more precise. If the graph is non-bipartite, we show an upper bound for the minimum distance. We also study the underlying geometric structure of X.Comment: Finite Fields Appl., to appea

Electronic coupling between Bi nanolines and the Si(001) substrate: An experimental and theoretical study

Atomic nanolines are one dimensional systems realized by assembling many atoms on a substrate into long arrays. The electronic properties of the nanolines depend on those of the substrate. Here, we demonstrate that to fully understand the electronic properties of Bi nanolines on clean Si(001) several different contributions must be accounted for. Scanning tunneling microscopy reveals a variety of different patterns along the nanolines as the imaging bias is varied. We observe an electronic phase shift of the Bi dimers, associated with imaging atomic p-orbitals, and an electronic coupling between the Bi nanoline and neighbouring Si dimers, which influences the appearance of both. Understanding the interplay between the Bi nanolines and Si substrate could open a novel route to modifying the electronic properties of the nanolines.Comment: 6 pages (main), 2 pages (SI), accepted by Phys. Rev.

Structure of self-assembled Mn atom chains on Si(001)

Mn has been found to self-assemble into atomic chains running perpendicular to the surface dimer reconstruction on Si(001). They differ from other atomic chains by a striking asymmetric appearance in filled state scanning tunneling microscopy (STM) images. This has prompted complicated structural models involving up to three Mn atoms per chain unit. Combining STM, atomic force microscopy and density functional theory we find that a simple necklace-like chain of single Mn atoms reproduces all their prominent features, including their asymmetry not captured by current models. The upshot is a remarkably simpler structure for modelling the electronic and magnetic properties of Mn atom chains on Si(001).Comment: 5 pages, 4 figure

Discovery of the Neutron Star Spin Frequency in EXO 0748-676

We report the results of a search for burst oscillations during thermonuclear X-ray bursts from the low mass X-ray binary (LMXB) EXO 0748-676. With the proportional counter array (PCA) onboard the Rossi X-ray Timing Explorer (RXTE) we detected a 45 Hz oscillation in the average power spectrum of 38 thermonuclear X-ray bursts from this source. We computed power spectra with 1 Hz frequency resolution for both the rising and decaying portions of 38 X-ray bursts from the public RXTE archive. We averaged the 1 Hz power spectra and detected a significant signal at 45 Hz in the decaying phases of the bursts. The signal is detected at a significance level of 4 x 10^-8. No similar signal was detected in the rising intervals. A fit to the oscillation peak at 0.25 Hz resolution gives a frequency of 44.7 +/- 0.06 Hz and an oscillation quality factor of Q = 80 +/- 18. The average signal amplitude is 3% (rms). The detection of 45 Hz burst oscillations from EXO 0748-676 provides compelling evidence that this is the neutron star spin frequency in this system. We use the inferred spin frequency to model the widths of absorption lines from the neutron star surface and show that the widths of the absorption lines from EXO 0748-676 recently reported by Cottam et al. are consistent with a 45 Hz spin frequency as long as the neutron star radius is in the range from about 9.5-15 km. With a known spin frequency, precise modelling of the line profiles from EXO 0748-676 holds great promise for constraining the dense matter equation of state.Comment: 13 pages, 5 figures, to be published in ApJ

Spatial dispersion in Casimir forces: A brief review

We present the basic principles of non-local optics in connection with the calculation of the Casimir force between half-spaces and thin films. At currently accessible distances $L$, non-local corrections amount to about half a percent, but they increase roughly as 1/L at smaller separations. Self consistent models lead to corrections with the opposite sign as models with abrupt surfaces.Comment: Proceedings of QFEXT05, Barcelona, Sept. 5-9, 200

Casimir-like tunneling-induced electronic forces

We study the quantum forces that act between two nearby conductors due to electronic tunneling. We derive an expression for these forces by calculating the flux of momentum arising from the overlap of evanescent electronic fields. Our result is written in terms of the electronic reflection amplitudes of the conductors and it has the same structure as Lifshitz's formula for the electromagnetically mediated Casimir forces. We evaluate the tunneling force between two semiinfinite conductors and between two thin films separated by an insulating gap. We discuss some applications of our results.Comment: 8 pages, 3 figs, submitted to Proc. of QFEXT'05, to be published in J. Phys.

Axially symmetric membranes with polar tethers

Axially symmetric equilibrium configurations of the conformally invariant Willmore energy are shown to satisfy an equation that is two orders lower in derivatives of the embedding functions than the equilibrium shape equation, not one as would be expected on the basis of axial symmetry. Modulo a translation along the axis, this equation involves a single free parameter c.If c\ne 0, a geometry with spherical topology will possess curvature singularities at its poles. The physical origin of the singularity is identified by examining the Noether charge associated with the translational invariance of the energy; it is consistent with an external axial force acting at the poles. A one-parameter family of exact solutions displaying a discocyte to stomatocyte transition is described.Comment: 13 pages, extended and revised version of Non-local sine-Gordon equation for the shape of axi-symmetric membrane

A Silvopastoral System in the North Atlantic Zone of Costa Rica: Combining Indigenous Timber Species with Dairy Pasture Swards

The objective of this study was to design, establish and monitor a silvo pastoral experiment on a dairy farm in the northern Atlantic region of Costa Rica. Indigenous timber species, Vochysia guatemalensis and Hyeronima alchorneoides were used together with or without the tropical pasture legume, Arachis pintoi in a split plot design with a 4 x 2 x 2 factorial arrangement. First year establishment was good for the tree component (2.3 to 10 % mortality) but poor for A. pintoi (4 to 5 % of sward). Poor legume establishment was attributed to lax grazing management and excess competition from existing Brachiaria sp. A. Pintoi was reestablished in July 1996 after an adjustment of stocking rate. This experimental project is planned for a 10 year period which corresponds to the expected rotation length for harvesting the indigenous timber species