An Introduction to Hyperbolic Barycentric Coordinates and their Applications

Barycentric coordinates are commonly used in Euclidean geometry. The adaptation of barycentric coordinates for use in hyperbolic geometry gives rise to hyperbolic barycentric coordinates, known as gyrobarycentric coordinates. The aim of this article is to present the road from Einstein's velocity addition law of relativistically admissible velocities to hyperbolic barycentric coordinates along with applications.Comment: 66 pages, 3 figure

Dimensional effects in photoelectron spectra of Ag deposits on GaAs(110) surfaces

It is shown that the peak structure observed in angle-resolved photoelectron spectra of metallic deposits can only be unambiguously associated to single electronic states if the deposit has a two dimensional character (finite along one spatial direction). In one and zero dimensions the density of states shows peaks related to bunches of single electron states (the finer structure associated to the latter may not always be experimentally resolved). The characteristics of the peak structure strongly depend on the band dispersion in the energy region where they appear. Results for the density of states and photoemission yield for Ag crystallites on GaAs(110) are presented and compared with experimental photoelectron spectra.Comment: Uuencoded gz-compressed postcript file including text and three figures; Send comments to [email protected]

Selective dip-coating of chemically micropatterned surfaces

We characterize the selective deposition of liquid microstructures on chemically heterogeneous surfaces by means of dip coating processes. The maximum deposited film thickness depends critically on the speed of withdrawal as well as the pattern size, geometry, and angular orientation. For vertically oriented hydrophilic strips, we derive a hydrodynamic scaling relation for the deposited film thickness which agrees very well with interferometric measurements of dip-coated liquid lines. Due to the lateral confinement of the liquid, our scaling relation differs considerably from the classic Landau–Levich formula for chemically homogeneous surfaces. Dip coating is a simple method for creating large area arrays of liquid microstructures for applications involving chemical analysis and synthesis, biochemical assays, or wet printing of liquid polymer or ink patterns

Mach-Zehnder fiber interferometer test of the anisotropy of the speed of light

Two optical fiber Mach-Zehnder interferometers were constructed in an environment with a temperature stabilization of better than 1 mK per day. One interferometer with a length of 12 m optical fiber in each arm with the main direction of the arms perpendicular to each other. Another with a length of 2 m optical fiber in each arm where the main direction of the arms are parallel as a control. In each arm 1 m of fiber was wound around a ring made of piezo material enabling the control of the length of the arms by means of a voltage. The influence of the temperature on the optical phase difference between the interferometer arms was measured. It is attributed to the temperature change induced variation of the interaction region of the optical fiber couplers. Further, the influence of rotation of the interferometers at the Earth surface on the observed phase differences was determined. For one interferometer (with the long and perpendicular arms) it was found that the phase difference depends on the azimuth of the interferometer. For the other one (with the short and parallel arms) no relevant dependence on the azimuth has been measured.Comment: Errata: data of interferometers were interchange

Density of states "width parity" effect in d-wave superconducting quantum wires

We calculate the density of states (DOS) in a clean mesoscopic d-wave superconducting quantum wire, i.e. a sample of infinite length but finite width $N$. For open boundary conditions, the DOS at zero energy is found to be zero if $N$ is even, and nonzero if $N$ is odd. At finite chemical potential, all chains are gapped but the qualtitative differences between even and odd $N$ remain.Comment: 7 pages, 8 figures, new figures and extended discussio

Polynomial SUSY in Quantum Mechanics and Second Derivative Darboux Transformation

We give the classification of second-order polynomial SUSY Quantum Mechanics in one and two dimensions. The particular attention is paid to the irreducible supercharges which cannot be built by repetition of ordinary Darboux transformations. In two dimensions it is found that the binomial superalgebra leads to the dynamic symmetry generated by a central charge operator.Comment: 10 pages, LaTeX, preprint SPbU-IP-94-0

Jet disc coupling in black hole binaries

In the last decade multi-wavelength observations have demonstrated the importance of jets in the energy output of accreting black hole binaries. The observed correlations between the presence of a jet and the state of the accretion flow provide important information on the coupling between accretion and ejection processes. After a brief review of the properties of black hole binaries, I illustrate the connection between accretion and ejection through two particularly interesting examples. First, an INTEGRAL observation of Cygnus X-1 during a 'mini-' state transition reveals disc jet coupling on time scales of orders of hours. Second, the black hole XTEJ1118+480 shows complex correlations between the X-ray and optical emission. Those correlations are interpreted in terms of coupling between disc and jet on time scales of seconds or less. Those observations are discussed in the framework of current models.Comment: Invited talk at the Fifth Stromlo Symposium: Disks, Winds & Jets - from Planets to Quasars. Accepted for publication in Astrophysics & Space Scienc

Gauge invariant reduction to the light-front

The problem of constructing gauge invariant currents in terms of light-cone bound-state wave functions is solved by utilising the gauging of equations method. In particular, it is shown how to construct perturbative expansions of the electromagnetic current in the light-cone formalism, such that current conservation is satisfied at each order of the perturbation theory.Comment: 12 pages, revtex

US acculturation and poor sleep among an intergenerational cohort of adult Latinos in Sacramento, California

Acculturation may shape the disproportionate burden of poor sleep among Latinos in the United States. Existing studies are limited by unidimensional acculturation proxies that are incapable of capturing cultural complexities across generations. Understanding how acculturation relates to sleep may lead to the identification of modifiable intervention targets. We used multivariable regression and latent class methods to examine cross-sectional associations between a validated multidimensional scale of US acculturation and self-reported poor sleep measures. We analyzed an intergenerational cohort: first-generation (GEN1) older Latinos (Sacramento Area Latino Study on Aging; N = 1,716; median age: 69.5) and second-generation (GEN2) middle-aged offspring and relatives of GEN1 (Niños Lifestyle and Diabetes Study; N = 670; median age: 54.0) in Sacramento, California. GEN1 with high US acculturation, compared with high acculturation towards another origin/ancestral country, had less restless sleep (prevalence ratio [PR] [95% confidence interval (CI)]: 0.67 [0.54, 0.84]) and a higher likelihood of being in the best sleep class than the worst (OR [95% CI]: 1.62 [1.09, 2.40]), but among nonmanual occupations, high intergenerational US acculturation was associated with more general fatigue (PR [95% CI: 1.86 [1.11, 3.10]). GEN2 with high intergenerational US acculturation reported shorter sleep (PR [95% CI]: 2.86 [1.02, 7.99]). High US acculturation shaped sleep differentially by generation, socioeconomic context, and intergenerational acculturative status. High US acculturation was associated with better sleep among older, lower socioeconomic Latinos, but with shorter sleep duration among middle-aged, higher socioeconomic Latinos; results also differed by parental acculturation status. Upon replication, future studies should incorporate prospective and intergenerational designs to uncover sociobehavioral pathways by which acculturation may shape sleep to ultimately inform intervention efforts

GRB 081028 and its late-time afterglow re-brightening

‘The definitive version is available at www3.interscience.wiley.com '. Copyright Royal Astronomical SocietySwift captured for the first time a smoothly rising X-ray re-brightening of clear non-flaring origin after the steep decay in a long gamma-ray burst (GRB): GRB 081028. A rising phase is likely present in all GRBs but is usually hidden by the prompt tail emission and constitutes the first manifestation of what is later to give rise to the shallow decay phase. Contemporaneous optical observations reveal a rapid evolution of the injection frequency of a fast cooling synchrotron spectrum through the optical band, which disfavours the afterglow onset (start of the forward shock emission along our line of sight when the outflow is decelerated) as the origin of the observed re-brightening. We investigate alternative scenarios and find that the observations are consistent with the predictions for a narrow jet viewed off-axis. The high on-axis energy budget implied by this interpretation suggests different physical origins of the prompt and (late) afterglow emission. Strong spectral softening takes place from the prompt to the steep decay phase: we track the evolution of the spectral peak energy from the γ-rays to the X-rays and highlight the problems of the high latitude and adiabatic cooling interpretations. Notably, a softening of both the high and low spectral slopes with time is also observed. We discuss the low on-axis radiative efficiency of GRB 081028 comparing its properties against a sample of Swift long GRBs with secure Eγ,iso measurements.Peer reviewe