On two 10th order mock theta identities

We give short proofs of conjectural identities due to Gordon and McIntosh involving two 10th order mock theta functions.Comment: 5 pages, to appear in the Ramanujan Journa

Multiresolution analysis of active region magnetic structure and its correlation with the Mt. Wilson classification and flaring activity

Two different multi-resolution analyses are used to decompose the structure of active region magnetic flux into concentrations of different size scales. Lines separating these opposite polarity regions of flux at each size scale are found. These lines are used as a mask on a map of the magnetic field gradient to sample the local gradient between opposite polarity regions of given scale sizes. It is shown that the maximum, average and standard deviation of the magnetic flux gradient for alpha, beta, beta-gamma and beta-gamma-delta active regions increase in the order listed, and that the order is maintained over all length-scales. This study demonstrates that, on average, the Mt. Wilson classification encodes the notion of activity over all length-scales in the active region, and not just those length-scales at which the strongest flux gradients are found. Further, it is also shown that the average gradients in the field, and the average length-scale at which they occur, also increase in the same order. Finally, there are significant differences in the gradient distribution, between flaring and non-flaring active regions, which are maintained over all length-scales. It is also shown that the average gradient content of active regions that have large flares (GOES class 'M' and above) is larger than that for active regions containing flares of all flare sizes; this difference is also maintained at all length-scales.Comment: Accepted for publication in Solar Physic

Observed Effect of Magnetic Fields on the Propagation of Magnetoacoustic Waves in the Lower Solar Atmosphere

We study Hinode/SOT-FG observations of intensity fluctuations in Ca II H-line and G-band image sequences and their relation to simultaneous and co-spatial magnetic field measurements. We explore the G-band and H-line intensity oscillation spectra both separately and comparatively via their relative phase differences, time delays and cross-coherences. In the non-magnetic situations, both sets of fluctuations show strong oscillatory power in the 3 - 7 mHz band centered at 4.5 mHz, but this is suppressed as magnetic field increases. A relative phase analysis gives a time delay of H-line after G-band of 20\pm1 s in non-magnetic situations implying a mean effective height difference of 140 km. The maximum coherence is at 4 - 7 mHz. Under strong magnetic influence the measured delay time shrinks to 11 s with the peak coherence near 4 mHz. A second coherence maximum appears between 7.5 - 10 mHz. Investigation of the locations of this doubled-frequency coherence locates it in diffuse rings outside photospheric magnetic structures. Some possible interpretations of these results are offered.Comment: 19 pages, 6 figure

Boundary Liouville theory at c=1

The c=1 Liouville theory has received some attention recently as the Euclidean version of an exact rolling tachyon background. In an earlier paper it was shown that the bulk theory can be identified with the interacting c=1 limit of unitary minimal models. Here we extend the analysis of the c=1-limit to the boundary problem. Most importantly, we show that the FZZT branes of Liouville theory give rise to a new 1-parameter family of boundary theories at c=1. These models share many features with the boundary Sine-Gordon theory, in particular they possess an open string spectrum with band-gaps of finite width. We propose explicit formulas for the boundary 2-point function and for the bulk-boundary operator product expansion in the c=1 boundary Liouville model. As a by-product of our analysis we also provide a nice geometric interpretation for ZZ branes and their relation with FZZT branes in the c=1 theory.Comment: 37 pages, 1 figure. Minor error corrected, slight change in result (1.6

Spatial competition and agglomeration in the visitor attraction sector

This paper provides a theoretical and empirical contribution to understanding spatial competition by examining visitor attractions in two contrasting clusters of lower and higher levels of agglomeration of businesses in Cornwall, the UK. The study found that competition is mainly for customers and labour and is related differently to the levels of agglomeration, spatial proximity and thematic product similarity between visitor attractions at the local compared to the regional scale. Location can be used differently for employing ‘weak’ and ‘strong’ competitive strategies. The study contributes to the knowledge on the spatiality of competition and the locational strategies of service businesses

The Hamiltonian limit of (3+1)D SU(3) lattice gauge theory on anisotropic lattices

The extreme anisotropic limit of Euclidean SU(3) lattice gauge theory is examined to extract the Hamiltonian limit, using standard path integral Monte Carlo (PIMC) methods. We examine the mean plaquette and string tension and compare them to results obtained within the Hamiltonian framework of Kogut and Susskind. The results are a significant improvement upon previous Hamiltonian estimates, despite the extrapolation procedure necessary to extract observables. We conclude that the PIMC method is a reliable method of obtaining results for the Hamiltonian version of the theory. Our results also clearly demonstrate the universality between the Hamiltonian and Euclidean formulations of lattice gauge theory. It is particularly important to take into account the renormalization of both the anisotropy, and the Euclidean coupling $\beta_E$, in obtaining these results.Comment: 10 pages, 11 figure

Multiwavelength studies of MHD waves in the solar chromosphere: An overview of recent results

The chromosphere is a thin layer of the solar atmosphere that bridges the relatively cool photosphere and the intensely heated transition region and corona. Compressible and incompressible waves propagating through the chromosphere can supply significant amounts of energy to the interface region and corona. In recent years an abundance of high-resolution observations from state-of-the-art facilities have provided new and exciting ways of disentangling the characteristics of oscillatory phenomena propagating through the dynamic chromosphere. Coupled with rapid advancements in magnetohydrodynamic wave theory, we are now in an ideal position to thoroughly investigate the role waves play in supplying energy to sustain chromospheric and coronal heating. Here, we review the recent progress made in characterising, categorising and interpreting oscillations manifesting in the solar chromosphere, with an impetus placed on their intrinsic energetics.Comment: 48 pages, 25 figures, accepted into Space Science Review