The Algebra of Strand Splitting. II. A Presentation for the Braid Group on One Strand

Presentations are computed for a braided version BV of Thompson's group V and for V itself showing that there is an Artin group/Coxeter group relation between them. The presentation for V is obtained from that for BV by declaring all that all generators are involutions.Comment: 15 page

The Algebra of Strand Splitting. I. A Braided Version of Thompson's Group V

We construct a braided version of Thompson's group V.Comment: 27 page

MUSE Illuminates Channels for Lyman Continuum Escape in the Halo of SBS 0335-52E

We report on the discovery of ionised gas filaments in the circum-galactic halo of the extremely metal-poor compact starburst SBS 0335-052E in a 1.5h integration with the MUSE integral-field spectrograph. We detect these features in H${\alpha}$ and [OIII] emission down to surface-brightness levels of $5 \times 10^{-19}$erg s$^{-1}$cm$^{-2}$arcsec$^{-2}$. The filaments have projected diameters of 2.1 kpc and extend more than 9 kpc to the north and north-west from the main stellar body. We also detect extended nebular HeII $\lambda$4686 emission that brightens towards the north-west at the rim of a star-burst driven super-shell, suggestive of a locally enhanced UV radiation field due to shocks. We also present a velocity field of the ionised gas. The filaments appear to connect seamlessly in velocity space to the kinematical disturbances caused by the shell. Similar to high-$z$ star-forming galaxies, the ionised gas in this galaxy is dispersion dominated. We argue that the filaments were created via feedback from the starburst and that these ionised structures in the halo may act as escape channels for Lyman continuum radiation in this gas-rich system.Comment: Revised version after peer review. Accepted for publication in A&A letter

Phase Diagram of One-Dimensional Extended Hubbard Model at Half Filling

We reexamine the ground-state phase diagram of the one-dimensional half-filled Hubbard model with on-site and nearest-neighbor repulsive interactions. We calculate second-order corrections to coupling constants in the g-ology to show that the bond-charge-density-wave (BCDW) phase exists for weak couplings in between the charge density wave (CDW) and spin density wave (SDW) phases. We find that the umklapp scattering of parallel-spin electrons destabilizes the BCDW state and gives rise to a bicritical point where the CDW-BCDW and SDW-BCDW continuous-transition lines merge into the CDW-SDW first-order transition line.Comment: 4 pages, 3 figure

Invariant Peano curves of expanding Thurston maps

We consider Thurston maps, i.e., branched covering maps $f\colon S^2\to S^2$ that are postcritically finite. In addition, we assume that $f$ is expanding in a suitable sense. It is shown that each sufficiently high iterate $F=f^n$ of $f$ is semi-conjugate to $z^d\colon S^1\to S^1$, where $d$ is equal to the degree of $F$. More precisely, for such an $F$ we construct a Peano curve $\gamma\colon S^1\to S^2$ (onto), such that $F\circ \gamma(z) = \gamma(z^d)$ (for all $z\in S^1$).Comment: 63 pages, 12 figure

Mechanism of CDW-SDW Transition in One Dimension

The phase transition between charge- and spin-density-wave (CDW, SDW) phases is studied in the one-dimensional extended Hubbard model at half-filling. We discuss whether the transition can be described by the Gaussian and the spin-gap transitions under charge-spin separation, or by a direct CDW-SDW transition. We determine these phase boundaries by level crossings of excitation spectra which are identified according to discrete symmetries of wave functions. We conclude that the Gaussian and the spin-gap transitions take place separately from weak- to intermediate-coupling region. This means that the third phase exists between the CDW and the SDW states. Our results are also consistent with those of the strong-coupling perturbative expansion and of the direct evaluation of order parameters.Comment: 5 pages(REVTeX), 5 figures(EPS), 1 table, also available from http://wwwsoc.nacsis.ac.jp/jps/jpsj/1999/p68a/p68a42/p68a42h/p68a42h.htm

Umklapp scattering of pairs in BCS superconductivity theory

The BCS theory of superconductivity is extended to recognize pairing of electrons by both normal and umklapp scattering. Application of the variational approach shows that coexistence of normal and umklapp scattering frustrates superconductivity.Comment: 9 pages, 5 figures. to be published in Journal of Physics: Condensed Matte

Techniques for measuring atmospheric aerosols at the High Resolution Fly's Eye experiment

We describe several techniques developed by the High Resolution Fly's Eye experiment for measuring aerosol vertical optical depth, aerosol horizontal attenuation length, and aerosol phase function. The techniques are based on measurements of side-scattered light generated by a steerable ultraviolet laser and collected by an optical detector designed to measure fluorescence light from cosmic-ray air showers. We also present a technique to cross-check the aerosol optical depth measurement using air showers observed in stereo. These methods can be used by future air fluorescence experiments.Comment: Accepted for publication in Astroparticle Physics Journal 16 pages, 9 figure

Magnetic Fluctuations in a Charge Ordered State of the One-Dimensional Extended Hubbard Model with a Half-Filled Band

Magnetic properties in a charge ordered state are examined for the extended Hubbard model at half-filling. Magnetic excitations, magnetic susceptibilities and a nuclear spin relaxation rate are calculated with taking account of fluctuations around the mean-field solution. The relevance of the present results to the observation in the 1:1 organic conductors, (TTM-TTP)I$_3$, is discussed.Comment: 4 pages, 3 figures, to be published in J. Phys. Soc. Jpn. Vol.71 (2002) No.