On the convergence of an iterative formulation of the electromagnetic scattering from an infinite grating of thin wires

Contraction theory is applied to an iterative formulation of electromagnetic scattering from periodic structures and a computational method for insuring convergence is developed. A short history of spectral (or k-space) formulation is presented with an emphasis on application to periodic surfaces. The mathematical background for formulating an iterative equation is covered using straightforward single variable examples including an extension to vector spaces. To insure a convergent solution of the iterative equation, a process called the contraction corrector method is developed. Convergence properties of previously presented iterative solutions to one-dimensional problems are examined utilizing contraction theory and the general conditions for achieving a convergent solution are explored. The contraction corrector method is then applied to several scattering problems including an infinite grating of thin wires with the solution data compared to previous works

Observation of correlated spin-orbit order in a strongly anisotropic quantum wire system

Quantum wires with spin-orbit coupling provide a unique opportunity to simultaneously control the coupling strength and the screened Coulomb interactions where new exotic phases of matter can be explored. Here we report on the observation of an exotic spin-orbit density wave in Pb-atomic wires on Si(557) surfaces by mapping out the evolution of the modulated spin-texture at various conditions with spin- and angle-resolved photoelectron spectroscopy. The results are independently quantified by surface transport measurements. The spin polarization, coherence length, spin dephasing rate, and the associated quasiparticle gap decrease simultaneously as the screened Coulomb interaction decreases with increasing excess coverage, providing a new mechanism for generating and manipulating a spin-orbit entanglement effect via electronic interaction. Despite clear evidence of spontaneous spin-rotation symmetry breaking and modulation of spin-momentum structure as a function of excess coverage, the average spin-polarization over the Brillouin zone vanishes, indicating that time-reversal symmetry is intact as theoretically predicted

Experimental demonstration of painting arbitrary and dynamic potentials for Bose-Einstein condensates

There is a pressing need for robust and straightforward methods to create potentials for trapping Bose-Einstein condensates which are simultaneously dynamic, fully arbitrary, and sufficiently stable to not heat the ultracold gas. We show here how to accomplish these goals, using a rapidly-moving laser beam that "paints" a time-averaged optical dipole potential in which we create BECs in a variety of geometries, including toroids, ring lattices, and square lattices. Matter wave interference patterns confirm that the trapped gas is a condensate. As a simple illustration of dynamics, we show that the technique can transform a toroidal condensate into a ring lattice and back into a toroid. The technique is general and should work with any sufficiently polarizable low-energy particles.Comment: Minor text changes and three references added. This is the final version published in New Journal of Physic

On Matrices, Automata, and Double Counting

Matrix models are ubiquitous for constraint problems. Many such problems have a matrix of variables M, with the same constraint defined by a finite-state automaton A on each row of M and a global cardinality constraint gcc on each column of M. We give two methods for deriving, by double counting, necessary conditions on the cardinality variables of the gcc constraints from the automaton A. The first method yields linear necessary conditions and simple arithmetic constraints. The second method introduces the cardinality automaton, which abstracts the overall behaviour of all the row automata and can be encoded by a set of linear constraints. We evaluate the impact of our methods on a large set of nurse rostering problem instances

High resolution sub-millimetre mapping of starburst galaxies: Comparison with CO emission

Researchers present first results from a program of submillimeter continuum mapping of starburst galaxies, and comparison of their dust and CO emission. This project was prompted by surprising results from the first target, the nearby starburst M82, which shows in the dust continuum a morphology quite unlike that of its CO emission, in contrast to what might be expected if both CO and dust are accurately tracing the molecular hydrogen. Possible explanations for this striking difference are discussed. In the light of these results, the program has been extended to include sub-mm mapping of the nearby, vigorously star forming spirals, M83 and Maffei 2. The latter were also observed extensively in CO, in order to study excitation conditions in its central regions. The James Clerk Maxwell Telescope was used in these studies

The Asymmetric Thick Disk: A Star Count and Kinematic Analysis. II The Kinematics

We report a kinematic signature associated with the observed asymmetry in the distribution of thick disk/inner halo stars interior to the Solar circle described in Paper I. In that paper we found a statistically significant excess (20% to 25 %) of stars in quadrant I (l ~ 20 deg to 55 deg) both above and below the plane (b ~ +/- 25 deg to +/- 45 deg) compared to the complementary region in quadrant IV. We have measured Doppler velocities for 741 stars, selected according to the same magnitude and color criteria, in the direction of the asymmetry and in the corresponding fields in quadrant IV. We have also determined spectral types and metallicities measured from the same spectra. We not only find an asymmetric distribution in the V_LSR velocities for the stars in the two regions, but the angular rate of rotation, w, for the stars in quadrant I reveals a slower effective rotation rate compared to the corresponding quadrant IV stars. We use our [Fe/H] measurements to separate the stars into the three primary population groups, halo, thick disk, and disk, and conclude that it is primarily the thick disk stars that show the slower rotation in quadrant I. A solution for the radial, tangential and vertical components of the V_LSR velocities, reveals a significant lag of ~ 80 to 90 km/s in the direction of Galactic rotation for the thick disk stars in quadrant I, while in quadrant IV, the same population has only a ~ 20 km/s lag. The results reported here support a rotational lag among the thick disk stars due to a gravitational interaction with the bar as the most likely explanation for the asymmetry in both the star counts and the kinematics. The affected thick disk stars, however, may be associated with the recently discovered Canis Major debris stream or a similar merger event (abridged).Comment: Accepted for publication in the Astronomical Journa

Contact-induced apical asymmetry drives the thigmotropic responses of Candida albicans hyphae

Acknowledgements We thank Marco Thiel for assistance with data interpretation, Peter Sudbery for the provision of strains and Jeremy Craven for useful discussions. This work was supported by a BBSRC-DTG to D. D. T., NIH award DK083592 to F. J. B. and P. A. J., and a Royal Society URF UF080611 and MRC NIRG 90671 to A. C. B.Non peer reviewedPublisher PD

Discriminating cool-water from warm-water carbonates and their diagenetic environments using element geochemistry: the Oligocene Tikorangi Formation (Taranaki Basin) and the dolomite effect

Fields portrayed within bivariate element plots have been used to distinguish between carbonates formed in warm- (tropical) water and cool- (temperate) water depositional settings. Here, element concentrations (Ca, Mg, Sr, Na, Fe, and Mn) have been determined for the carbonate fraction of bulk samples from the late Oligocene Tikorangi Formation, a subsurface, mixed dolomite-calcite, cool-water limestone sequence in Taranaki Basin, New Zealand. While the occurrence of dolomite is rare in New Zealand Cenozoic carbonates, and in cool-water carbonates more generally, the dolomite in the Tikorangi carbonates is shown to have a dramatic effect on the "traditional" positioning of cool-water limestone fields within bivariate element plots. Rare undolomitised, wholly calcitic carbonate samples in the Tikorangi Formation have the following average composition: Mg 2800 ppm; Ca 319 100 ppm; Na 800 ppm; Fe 6300 ppm; Sr 2400 ppm; and Mn 300 ppm. Tikorangi Formation dolomite-rich samples (>15% dolomite) have average values of: Mg 53 400 ppm; Ca 290 400 ppm; Na 4700 ppm; Fe 28 100 ppm; Sr 5400 ppm; and Mn 500 ppm. Element-element plots for dolomite-bearing samples show elevated Mg, Na, and Sr values compared with most other low-Mg calcite New Zealand Cenozoic limestones. The increased trace element contents are directly attributable to the trace element-enriched nature of the burial-derived dolomites, termed here the "dolomite effect". Fe levels in the Tikorangi Formation carbonates far exceed both modern and ancient cool-water and warm-water analogues, while Sr values are also higher than those in modern Tasmanian cool-water carbonates, and approach modern Bahaman warm-water carbonate values. Trace element data used in conjunction with more traditional petrographic data have aided in the diagenetic interpretation of the carbonate-dominated Tikorangi sequence. The geochemical results have been particularly useful for providing more definitive evidence for deep burial dolomitisation of the deposits under the influence of marine-modified pore fluids

Decay modes of two repulsively interacting bosons

We study the decay of two repulsively interacting bosons tunneling through a delta potential barrier by direct numerical solution of the time-dependent Schr\"odinger equation. The solutions are analyzed according to the regions of particle presence: both particles inside the trap (in-in), one particle in and one particle out (in-out), and both particles outside (out-out). It is shown that the in-in probability is dominated by exponential decay, and its decay rate is predicted very well from outgoing boundary conditions. Up to a certain range of interaction strength the decay of in-out probability is dominated by the single particle decay mode. The decay mechanisms are adequately described by simple models.Comment: 18 pages, 13 figure