Pairing symmetry of the one-band Hubbard model in the paramagnetic weak-coupling limit: a numerical RPA study

We study the spin-fluctuation-mediated superconducting pairing gap in a weak-coupling approach to the Hubbard model for a two dimensional square lattice in the paramagnetic state. Performing a comprehensive theoretical study of the phase diagram as a function of filling, we find that the superconducting gap exhibits transitions from p-wave at very low electron fillings to d_{x^2-y^2}-wave symmetry close to half filling in agreement with previous reports. At intermediate filling levels, different gap symmetries appear as a consequence of the changes in the Fermi surface topology and the associated structure of the spin susceptibility. In particular, the vicinity of a van Hove singularity in the electronic structure close to the Fermi level has important consequences for the gap structure in favoring the otherwise sub-dominant triplet solution over the singlet d-wave solution. By solving the full gap equation, we find that the energetically favorable triplet solutions are chiral and break time reversal symmetry. Finally, we also calculate the detailed angular gap structure of the quasi-particle spectrum, and show how spin-fluctuation-mediated pairing leads to significant deviations from the first harmonics both in the singlet d_{x^2-y^2} gap as well as the chiral triplet gap solution.Comment: 11 pages 11 figure

Anatomy, morphology and evolution of the patella in squamate lizards and tuatara (Sphenodon punctatus)

The patella (kneecap) is the largest and best-known of the sesamoid bones, postulated to confer biomechanical advantages including increasing joint leverage and reinforcing the tendon against compression. It has evolved several times independently in amniotes, but despite apparently widespread occurrence in lizards, the patella remains poorly characterised in this group and is, as yet, completely undescribed in their nearest extant relative Sphenodon (Rhynchocephalia). Through radiography, osteological and fossil studies we examined patellar presence in diverse lizard and lepidosauromorph taxa, and using computed tomography, dissection and histology we investigated in greater depth the anatomy and morphology of the patella in 16 lizard species and 19 Sphenodon specimens. We have found the first unambiguous evidence of a mineralised patella in Sphenodon, which appears similar to the patella of lizards and shares several gross and microscopic anatomical features. Although there may be a common mature morphology, the squamate patella exhibits a great deal of variability in development (whether from a cartilage anlage or not, and in the number of mineralised centres) and composition (bone, mineralised cartilage or fibrotendinous tissue). Unlike in mammals and birds, the patella in certain lizards and Sphenodon appears to be a polymorphic trait. We have also explored the evolution of the patella through ancestral state reconstruction, finding that the patella is ancestral for lizards and possibly Lepidosauria as a whole. Clear evidence of the patella in rhynchocephalian or stem lepidosaurian fossil taxa would clarify the evolutionary origin(s) of the patella, but due to the small size of this bone and the opportunity for degradation or loss we could not definitively conclude presence or absence in the fossils examined. The pattern of evolution in lepidosaurs is unclear but our data suggest that the emergence of this sesamoid may be related to the evolution of secondary ossification centres and/or changes in knee joint conformation, where enhancement of extensor muscle leverage would be more beneficial.Sophie Regnault, Marc E. H. Jones, Andrew A. Pitsillides, John R. Hutchinso

Superclustering at Redshift Z=0.54

We present strong evidence for the existence of a supercluster at a redshift of z=0.54 in the direction of Selected Area 68. From the distribution of galaxies with spectroscopic redshifts we find that there is a large over-density of galaxies (a factor of four over the number expected in an unclustered universe) within the redshift range 0.530 < z < 0.555. By considering the spatial distribution of galaxies within this redshift range (using spectroscopic and photometric redshifts) we show that the galaxies in SA68 form a linear structure passing from the South-West of the survey field through to the North-East (with a position angle of approximately 35 deg East of North). This position angle is coincident with the positions of the X-ray clusters CL0016+16, RX J0018.3+1618 and a new X-ray cluster, RX J0018.8+1602, centered near the radio source 54W084. All three of these sources are at a redshift of approximately z=0.54 and have position angles, derived from their X-ray photon distributions, consistent with that measured for the supercluster. Assuming a redshift of 0.54 for the distribution of galaxies and a FWHM dispersion in redshift of 0.020 this represents a coherent structure with a radial extent of 31 Mpc, transverse dimension of 12 Mpc, and a thickness of approximately 4 Mpc. The detection of this possible supercluster demonstrates the power of using X-ray observations, combined with multicolor observations, to map the large scale distribution of galaxies at intermediate redshifts.Comment: 12 pages, 3 figures, Latex, aaspp4.sty, accepted for publication in Ap J Letters. Figure 3 and followup observations can be found at http://tarkus.pha.jhu.edu/~ajc/papers/supercluster

Linear Momentum Density in Quasistatic Electromagnetic Systems

We discuss a couple of simple quasistatic electromagnetic systems in which the density of electromagnetic linear momentum can be easily computed. The examples are also used to illustrate how the total electromagnetic linear momentum, which may also be calculated by using the vector potential, can be understood as a consequence of the violation of the action-reaction principle, because a non-null external force is required to maintain constant the mechanical linear momentum. We show how one can avoid the divergence in the interaction linear electromagnetic momentum of a system composed by an idealization often used in textbooks (an infinite straight current) and a point charge.Comment: 22 pages, 5 figures, to appear in Eur. J. Phy

Cl 1205+44, a fossil group at z = 0.59

This is a report of Chandra, XMM-Newton, HST and ARC observations of an extended X-ray source at z = 0.59. The apparent member galaxies range from spiral to elliptical and are all relatively red (i'-Ks about 3). We interpret this object to be a fossil group based on the difference between the brightness of the first and second brightest cluster members in the i'-band, and because the rest-frame bolometric X-ray luminosity is about 9.2x10^43 h70^-2 erg s^-1. This makes Cl 1205+44 the highest redshift fossil group yet reported. The system also contains a central double-lobed radio galaxy which appears to be growing via the accretion of smaller galaxies. We discuss the formation and evolution of fossil groups in light of the high redshift of Cl 1205+44.Comment: 21 pages, 13 figures, minor corrections to match published ApJ versio