Superconductivity in the two dimensional Hubbard Model.

Quasiparticle bands of the two-dimensional Hubbard model are calculated using the Roth two-pole approximation to the one particle Green's function. Excellent agreement is obtained with recent Monte Carlo calculations, including an anomalous volume of the Fermi surface near half-filling, which can possibly be explained in terms of a breakdown of Fermi liquid theory. The calculated bands are very flat around the (pi,0) points of the Brillouin zone in agreement with photoemission measurements of cuprate superconductors. With doping there is a shift in spectral weight from the upper band to the lower band. The Roth method is extended to deal with superconductivity within a four-pole approximation allowing electron-hole mixing. It is shown that triplet p-wave pairing never occurs. Singlet d_{x^2-y^2}-wave pairing is strongly favoured and optimal doping occurs when the van Hove singularity, corresponding to the flat band part, lies at the Fermi level. Nearest neighbour antiferromagnetic correlations play an important role in flattening the bands near the Fermi level and in favouring superconductivity. However the mechanism for superconductivity is a local one, in contrast to spin fluctuation exchange models. For reasonable values of the hopping parameter the transition temperature T_c is in the range 10-100K. The optimum doping delta_c lies between 0.14 and 0.25, depending on the ratio U/t. The gap equation has a BCS-like form and (2*Delta_{max})/(kT_c) ~ 4.Comment: REVTeX, 35 pages, including 19 PostScript figures numbered 1a to 11. Uses epsf.sty (included). Everything in uuencoded gz-compressed .tar file, (self-unpacking, see header). Submitted to Phys. Rev. B (24-2-95

Modeling the Subsurface Structure of Sunspots

While sunspots are easily observed at the solar surface, determining their subsurface structure is not trivial. There are two main hypotheses for the subsurface structure of sunspots: the monolithic model and the cluster model. Local helioseismology is the only means by which we can investigate subphotospheric structure. However, as current linear inversion techniques do not yet allow helioseismology to probe the internal structure with sufficient confidence to distinguish between the monolith and cluster models, the development of physically realistic sunspot models are a priority for helioseismologists. This is because they are not only important indicators of the variety of physical effects that may influence helioseismic inferences in active regions, but they also enable detailed assessments of the validity of helioseismic interpretations through numerical forward modeling. In this paper, we provide a critical review of the existing sunspot models and an overview of numerical methods employed to model wave propagation through model sunspots. We then carry out an helioseismic analysis of the sunspot in Active Region 9787 and address the serious inconsistencies uncovered by \citeauthor{gizonetal2009}~(\citeyear{gizonetal2009,gizonetal2009a}). We find that this sunspot is most probably associated with a shallow, positive wave-speed perturbation (unlike the traditional two-layer model) and that travel-time measurements are consistent with a horizontal outflow in the surrounding moat.Comment: 73 pages, 19 figures, accepted by Solar Physic

To what extent do frameworks of reading development and the phonics screening check support the assessment of reading development in England?

The purpose of this article is to question the suitability of the phonics screening check in relation to models and theories of reading development. The article questions the appropriateness of the check by drawing on theoretical frameworks which underpin typical reading development. I examine the Simple View of Reading developed by Gough and Tunmer and Ehri’s model of reading development. The article argues that the assessment of children’s development in reading should be underpinned and informed by a developmental framework which identifies the sequential skills in reading development

Local Helioseismology of Sunspots: Current Status and Perspectives (Invited Review)

Mechanisms of the formation and stability of sunspots are among the longest-standing and intriguing puzzles of solar physics and astrophysics. Sunspots are controlled by subsurface dynamics hidden from direct observations. Recently, substantial progress in our understanding of the physics of the turbulent magnetized plasma in strong-field regions has been made by using numerical simulations and local helioseismology. Both the simulations and helioseismic measurements are extremely challenging, but it becomes clear that the key to understanding the enigma of sunspots is a synergy between models and observations. Recent observations and radiative MHD numerical models have provided a convincing explanation to the Evershed flows in sunspot penumbrae. Also, they lead to the understanding of sunspots as self-organized magnetic structures in the turbulent plasma of the upper convection zone, which are maintained by a large-scale dynamics. Local helioseismic diagnostics of sunspots still have many uncertainties, some of which are discussed in this review. However, there have been significant achievements in resolving these uncertainties, verifying the basic results by new high-resolution observations, testing the helioseismic techniques by numerical simulations, and comparing results obtained by different methods. For instance, a recent analysis of helioseismology data from the Hinode space mission has successfully resolved several uncertainties and concerns (such as the inclined-field and phase-speed filtering effects) that might affect the inferences of the subsurface wave-speed structure of sunspots and the flow pattern. It becomes clear that for the understanding of the phenomenon of sunspots it is important to further improve the helioseismology methods and investigate the whole life cycle of active regions, from magnetic-flux emergence to dissipation.Comment: 34 pages, 18 figures, submitted to Solar Physic