Periodic discrete conformal maps

A discrete conformal map (DCM) maps the square lattice to the Riemann sphere such that the image of every irreducible square has the same cross-ratio. This paper shows that every periodic DCM can be determined from spectral data (a hyperelliptic compact Riemann surface, called the spectral curve, equipped with some marked points). Each point of the map corresponds to a line bundle over the spectral curve so that the map corresponds to a discrete subgroup of the Jacobi variety. We derive an explicit formula for the generic maps using Riemann theta functions, describe the typical singularities and give a geometric interpretation of DCM's as a discrete version of the Schwarzian KdV equation. As such, the DCM equation is a discrete soliton equation and we describe the dressing action of a loop group on the set of DCM's. We also show that this action corresponds to a lattice of isospectral Darboux transforms for the finite gap solutions of the KdV equation.Comment: 41 pages, 10 figures, LaTeX2

Evolution in the iron abundance of the ICM

We present a Chandra analysis of the X-ray spectra of 56 clusters of galaxies at $z>0.3$, which cover a temperature range of $3> kT > 15$ keV. Our analysis is aimed at measuring the iron abundance in the ICM out to the highest redshift probed to date. We find that the emission-weighted iron abundance measured within $(0.15-0.3) R_{vir}$ in clusters below 5 keV is, on average, a factor of $\sim2$ higher than in hotter clusters, following $Z(T)\simeq 0.88 T^{-0.47} Z_\odot$, which confirms the trend seen in local samples. We made use of combined spectral analysis performed over five redshift bins at $0.3> z > 1.3$ to estimate the average emission weighted iron abundance. We find a constant average iron abundance $Z_{Fe}\simeq 0.25 Z_\odot$ as a function of redshift, but only for clusters at $z>0.5$. The emission-weighted iron abundance is significantly higher ($Z_{Fe}\simeq0.4 Z_\odot$) in the redshift range $z\simeq0.3-0.5$, approaching the value measured locally in the inner $0.15 R_{vir}$ radii for a mix of cool-core and non cool-core clusters in the redshift range $0.1<z<0.3$. The decrease in $Z_{Fe}$ with $z$ can be parametrized by a power law of the form $\sim(1+z)^{-1.25}$. The observed evolution implies that the average iron content of the ICM at the present epoch is a factor of $\sim2$ larger than at $z\simeq 1.2$. We confirm that the ICM is already significantly enriched ($Z_{Fe}\simeq0.25 Z_\odot$) at a look-back time of 9 Gyr. Our data provide significant constraints on the time scales and physical processes that drive the chemical enrichment of the ICM.Comment: 4 pages, 4 figures, to appear in the Proceedings of "The Extreme Universe in the Suzaku Era", Dicember 2006, Kyoto (Japan

Odd Parity and Line Nodes in Heavy Fermion Superconductors

Group theory arguments have demonstrated that a general odd parity order parameter cannot have line nodes in the presence of spin-orbit coupling. In this paper, it is shown that these arguments do not hold on the $k_z = \pi/c$ zone face of a hexagonal close packed lattice. In particular, three of the six odd parity representations vanish identically on this face. This has potential relevance to the heavy fermion superconductor $UPt_3$.Comment: 5 pages, revte

Double dispersion of the magnetic resonant mode in cuprates

The magnetic excitation spectra in the vicinity of the resonant peak, as observed by inelastic neutron scattering in cuprates, are studied within the memory-function approach. It is shown that at intermediate doping the superconducting gap induces a double dispersion of the peak, with an anisotropy rotated between the downward and upward branch. Similar behavior, but with a spin-wave dispersion at higher energies, is obtained for the low-doping case assuming a large pairing pseudogap.Comment: 4 LaTeX pages, 4 figure

Tracing the evolution in the iron content of the ICM

We present a Chandra analysis of the X-ray spectra of 56 clusters of galaxies at z>0.3, which cover a temperature range of 3>kT>15 keV. Our analysis is aimed at measuring the iron abundance in the ICM out to the highest redshift probed to date. We find that the emission-weighted iron abundance measured within (0.15-0.3)R_vir in clusters below 5 keV is, on average, a factor of ~2 higher than in hotter clusters, following Z(T)~0.88T^-(0.47)Z_o, which confirms the trend seen in local samples. We made use of combined spectral analysis performed over five redshift bins at 0.3>z>1.3 to estimate the average emission weighted iron abundance. We find a constant average iron abundance Z_Fe~0.25Z_o as a function of redshift, but only for clusters at z>0.5. The emission-weighted iron abundance is significantly higher (Z_Fe~0.4Z_o) in the redshift range z~0.3-0.5, approaching the value measured locally in the inner 0.15R_vir radii for a mix of cool-core and non cool-core clusters in the redshift range 0.1<z<0.3. The decrease in Z_Fe with redshift can be parametrized by a power law of the form ~(1+z)^(-1.25). The observed evolution implies that the average iron content of the ICM at the present epoch is a factor of ~2 larger than at z=1.2. We confirm that the ICM is already significantly enriched (Z_Fe~0.25Z_o) at a look-back time of 9 Gyr. Our data provide significant constraints on the time scales and physical processes that drive the chemical enrichment of the ICM.Comment: 6 pages, 6 figures, to appear in the Proceedings of "Heating vs. Cooling in Galaxies and Clusters of Galaxies", August 2006, Garching (Germany

Spin-memory loss at Co/Ru interfaces

We have determined the spin-memory-loss parameter, $\delta_{Co/Ru}$, by measuring the transmission of spin-triplet and spin-singlet Cooper pairs across Co/Ru interfaces in Josephson junctions and by Current-Perpendicular-to-Plane Giant Magnetoresistance (CPP-GMR) techniques. The probability of spin-memory loss at the Co/Ru interface is $(1-exp(-\delta_{Co/Ru}))$. From the CPP-MR, we obtain $\delta_{Co/Ru} = 0.34^{+0.04}_{-0.02}$ that is in good agreement with $\delta_{Co/Ru} = 0.35 \pm 0.08$ obtained from spin-triplet transmission. For spin-singlet transmission, we have $\delta_{Co/Ru} = 0.64 \pm 0.05$ that is different from that obtained from CPP-GMR and spin-triplet transmission. The source of this difference is not understood.Comment: 9 pages, 9 figure

Spin Triplet Supercurrent in Co/Ni Multilayer Josephson Junctions with Perpendicular Anisotropy

We have measured spin-triplet supercurrent in Josephson junctions of the form S/F'/F/F'/S, where S is superconducting Nb, F' is a thin Ni layer with in-plane magnetization, and F is a Ni/[Co/Ni]n multilayer with out-of-plane magnetization. The supercurrent in these junctions decays very slowly with F-layer thickness, and is much larger than in similar junctions not containing the two F' layers. Those two features are the characteristic signatures of spin-triplet supercurrent, which is maximized by the orthogonality of the magnetizations in the F and F' layers. Magnetic measurements confirm the out-of-plane anisotropy of the Co/Ni multilayers. These samples have their critical current optimized in the as-prepared state, which will be useful for future applications.Comment: 4 pages, 4 figures, formatted in RevTeX version 4. Submitted to Physical Review B on August 13th, 201

Radiation Pressure Supported Starburst Disks and AGN Fueling

We consider the structure of marginally Toomre-stable starburst disks under the assumption that radiation pressure on dust grains provides the dominant vertical support against gravity. This is particularly appropriate when the disk is optically thick to its own IR radiation, as in the central regions of ULIRGs. Because the disk radiates at its Eddington limit, the Schmidt-law for star formation changes in the optically-thick limit, with the star formation rate per unit area scaling as Sigma_g/kappa, where Sigma_g is the gas surface density and kappa is the mean opacity. We show that optically thick starburst disks have a characteristic flux and dust effective temperature of F ~ 10^{13} L_sun/kpc^2 and T_eff ~ 90K, respectively. We compare our predictions with observations and find good agreement. We extend our model from many-hundred parsec scales to sub-parsec scales and address the problem of fueling AGN. We assume that angular momentum transport proceeds via global torques rather than a local viscosity. We account for the radial depletion of gas due to star formation and find a strong bifurcation between two classes of disk models: (1) solutions with a starburst on large scales that consumes all of the gas with little fueling of a central AGN and (2) models with an outer large-scale starburst accompanied by a more compact starburst on 1-10 pc scales and a bright central AGN. The luminosity of the latter models is in many cases dominated by the AGN. We show that the vertical thickness of the starburst disk on pc scales can approach h ~ r, perhaps accounting for the nuclear obscuration in some Type 2 AGN. We also argue that the disk of young stars in the Galactic Center may be the remnant of such a compact nuclear starburst.Comment: 26 pages, 9 figures, emulateapj, accepted to ApJ, minor changes, discussion tightened, references adde

Production and Playback of Human Figure Motion 3D Virtual Environments

We describe a system for off-line production and real-time playback of motion for articulated human figures in 3D virtual environments. The key notions are (1) the logical storage of full body motion in posture graphs, which provides a simple motion access method for playback, and (2) mapping the motions of higher DOF figures using slaving to provide human models at several levels of detail, both in geometry and articulation, for later playback. We present our system in a context of a simple problem: Animating human figures in a distributed simulation, using DIS protocols for communication the human state information. We also discuss several related techniques for real-time animation of articulated figures in visual simulation

Real-Time Control of a Virtual Human Using Minimal Sensors

We track, in real-time, the position and posture of a human body, using a minimal number of 6 DOF sensors to capture full body standing postures. We use 4 sensors to create a good approximation of a human operator\u27s position and posture, and map it on to our articulated computer graphics human model. The unsensed joints are positioned by a fast inverse kinematics algorithm. Our goal is to realistically recreate human postures while minimally encumbering the operator