Interplay of superconductivity and magnetism in strong coupling

A model is introduced describing the interplay between superconductivity and spin-ordering. It is characterized by on-site repulsive electron-electron interactions, causing antiferromagnetism, and nearest-neighbor attractive interactions, giving rise to d-wave superconductivity. Due to a special choice for the lattice, this model has a strong-coupling limit where the superconductivity can be described by a bosonic theory, similar to the strongly coupled negative U Hubbard model. This limit is analyzed in the present paper. A rich mean-field phase diagram is found and the leading quantum corrections to the mean-field results are calculated. The first-order line between the antiferromagnetic- and the superconducting phase is found to terminate at a tricritical point, where two second-order lines originate. At these lines, the system undergoes a transition to- and from a phase exhibiting both antiferromagnetic order and superconductivity. At finite temperatures above the spin-disordering line, quantum-critical behavior is found. For specific values of the model parameters, it is possible to obtain SO(5) symmetry involving the spin- and the phase-sector at the tricritical point. Although this symmetry is explicitly broken by the projection to the lower Hubbard band, it survives on the mean-field level, and modes related to a spontaneously broken SO(5) symmetry are present on the level of the random phase approximation in the superconducting phase.Comment: 16 pages Revtex, 5 figure

Theory of site-disordered magnets

In realistic spinglasses, such as CuMn, AuFe and EuSrS, magnetic atoms are located at random positions. Their couplings are determined by their relative positions. For such systems a field theory is formulated. In certain limits it reduces to the Hopfield model, the Sherrington-Kirkpatrick model, and the Viana-Bray model. The model has a percolation transition, while for RKKY couplings the ``concentration scaling'' T_g proportional to c occurs. Within the Gaussian approximation the Ginzburg-Landau expansion is considered in the clusterglass phase, that is to say, for not too small concentrations. Near special points, the prefactor of the cubic term, or the one of the replica-symmetry- breaking quartic term, may go through zero. Around such points new spin glass phases are found.Comment: 26 pages Revtex, 6 figure

A comparison of zinc levels in runoff from rubberized hot mix asphalt and conventional pavement

High levels of dissolved zinc in water bodies can be toxic to aquatic organisms. There are currently over 40 waterways in California that have on occasion been in exceedance of Clean Water Act minimum toxicity threshold standards for zinc. Recycled tires that contain 1-2% zinc by mass are commonly used in California paving formulations known as Rubberized Hot Mix Asphalt (RHMA). The addition of tires to RHMA increases the zinc content of the pavement in comparison to conventional HMA. This research assesses the zinc content and leaching rate of RHMA in field and laboratory settings to estimate its contribution of zinc to stormwater runoff relative to other significant sources. To compare stormwater runoff zinc concentrations between RHMA and Hot Mix Asphalt (HMA), two laboratory leaching studies and a field paired pavement sampling study were conducted. The first leaching study assessed zinc leaching from different sizes of passenger and truck tire crumb rubber that is similar to the tire crumb rubber added as an ingredient in RHMA. The results from this study indicate that passenger tire crumb has a higher zinc mass transfer rate than truck tire crumb and that smaller particles increase the zinc leaching rate for both types of tire crumb. After 61 days of leaching in distilled water, the percentages that were recovered in the leachate were 2 percent and 3 percent of the total zinc contained in the passenger and truck crumb rubber samples, respectively. The second leaching study observed dissolved zinc leaching from RHMA and HMA pavement cores by submerging duplicate samples of each type in distilled water and determining the zinc concentration in the leachate over time. Both the pavement cores show an initial pulse (40-45 µg/ft2/day) of zinc, that declines to near-zero mass transfer after ten days and contributes little or no zinc for the remaining duration of the 61-day (RHMA) and 41-day (HMA) experiments. The percent recovery of zinc within crumb rubber contained in the RHMA was 0.024% after 61 days. To assess differences in stormwater zinc concentrations between RHMA and HMA pavement, paired pavement runoff samples were collected from both types of pavement in close proximity to each other (at either side of the edge of a change in pavement type). The paired pavement sampling showed 27% higher median dissolved zinc concentrations and 40% higher median total zinc concentrations in stormwater runoff from RHMA compared to HMA across the entire 186 pavement runoff samples. Further analysis suggests that pavement surface characteristics such as age, aggregate gradation and void space can likely impact zinc concentrations in runoff between the two pavement types. This finding suggests that both the material composition and the physical structure of the pavement are important considerations for paired pavement sample comparison. An application of mass transfer rates found in the leaching studies in addition to literature values for galvanized metal leaching helped demonstrate potential ranges of environmental loading of zinc from precipitation (wet deposition), RHMA, tire wear, and galvanized metal. Tire wear particle leaching rates were assumed equal to those found in the tire crumb rubber leaching study, though tire wear particles are generally smaller in diameter than crumb rubber. The resulting analysis showed that theoretical environmental mass loading rates along a 1-mile stretch of highway during a 1-year period for 2-lane RHMA, precipitation, tire wear and galvanized metal guard rail are 0.5 lbs, 0.22 lbs, 1 - 9 lbs, and 17 - 87 lbs, respectively. This demonstrated the potential for tire wear and galvanized metal to contribute significantly higher zinc loads to the environment than RHMA. Further assessment of the impact that pavement aging and RHMA aggregate gradation might have on zinc concentrations in stormwater runoff would help refine this analysis