The tensor structure on the representation category of the Wp\mathcal{W}_p triplet algebra

We study the braided monoidal structure that the fusion product induces on the abelian category $\mathcal{W}_p$-mod, the category of representations of the triplet $W$-algebra $\mathcal{W}_p$. The $\mathcal{W}_p$-algebras are a family of vertex operator algebras that form the simplest known examples of symmetry algebras of logarithmic conformal field theories. We formalise the methods for computing fusion products, developed by Nahm, Gaberdiel and Kausch, that are widely used in the physics literature and illustrate a systematic approach to calculating fusion products in non-semi-simple representation categories. We apply these methods to the braided monoidal structure of $\mathcal{W}_p$-mod, previously constructed by Huang, Lepowsky and Zhang, to prove that this braided monoidal structure is rigid. The rigidity of $\mathcal{W}_p$-mod allows us to prove explicit formulae for the fusion product on the set of all simple and all projective $\mathcal{W}_p$-modules, which were first conjectured by Fuchs, Hwang, Semikhatov and Tipunin; and Gaberdiel and Runkel.Comment: 58 pages; edit: added references and revisions according to referee reports. Version to appear on J. Phys.

On the formation of current sheets in response to the compression or expansion of a potential magnetic field

The compression or expansion of a magnetic field that is initially potential is considered. It was recently suggested by Janse & Low [2009, ApJ, 690, 1089] that, following the volumetric deformation, the relevant lowest energy state for the magnetic field is another potential magnetic field that in general contains tangential discontinuities (current sheets). Here we examine this scenario directly using a numerical relaxation method that exactly preserves the topology of the magnetic field. It is found that of the magnetic fields discussed by Janse & Low, only those containing magnetic null points develop current singularities during an ideal relaxation, while the magnetic fields without null points relax toward smooth force-free equilibria with finite non-zero current.Comment: Accepted for publication in Ap

Microstructure control during twin roll casting of an AZ31 magnesium alloy

The existing twin roll casting technique for magnesium alloys suffers heterogeneity in both microstructure and chemistry and downstream processing is required to improve the strip quality, resulting in cost rise. In the present work, twin roll casting was carried out using an AZ31 magnesium alloy, with the application of intensive shearing melt conditioning prior to casting. The effect of process parameters such as pouring temperature and casting speed on microstructure control during casting and subsequent downstream processing was studied. Experimental results showed that the melt conditioning treatment allowed the production of AZ31 strips with uniform and refined microstructure free of centreline segregations. It was also shown that an optimized combination of pouring temperature and casting speed, in conjunction with a strip thickness control operation, resulted in uniformly distributed stored energies due to enhanced plastic deformation, which promoted recrystallization during casting and subsequent heat treatment. Strips prepared by twin roll casting and homogenization developed similar microstructural features to those prepared by twin roll casting followed by lengthy downstream processing by homogenization, hot rolling and annealing and displayed a weaker basal texture, exhibiting a potentially better formability.The EPSRC (UK

Unconventional superconducting pairing symmetry induced by phonons

The possibility of non-s-wave superconductivity induced by phonons is investigated using a simple model that is inspired by Sr$_2$RuO$_4$. The model assumes a two-dimensional electronic structure, a two-dimensional spin-fluctuation spectrum, and three-dimensional electron-phonon coupling. Taken separately, each interaction favors formation of spin-singlet pairs (of s symmetry for the phonon interaction and d$_{x^2-y^2}$ symmetry for the spin interaction), but in combination, a variety of more unusual singlet and triplet states are found, depending on the interaction parameters. This may have important implications for Sr$_2$RuO$_4$, providing a plausible explanation of how the observed spin fluctuations, which clearly favor d$_{x^2-y^2}$ pairing, may still be instrumental in creating a superconducting state with a different (e.g., p-wave) symmetry. It also suggests an interpretation of the large isotope effect observed in Sr$_2$RuO$_4$. These results indicate that phonons could play a key role in establishing the order-parameter symmetry in Sr$_2$RuO$_4$, and possibly in other unconventional superconductors.Comment: 6 pages, 5 figures, submitted to Phys. Rev.

Weak interactions and quasi-stable particle energy loss

We discuss the interplay between electromagnetic energy loss and weak interactions in the context of quasistable particle particle propagation through materials. As specific examples, we consider staus, where weak interactions may play a role, and taus, where they don't.Comment: 4 pages, 4 figures, to appear in the proceedings of the Second Workshop on TeV Particle Astrophysics (August 2006, Madison, WI

THE IMPACT OF SWINE PRODUCTION ON LAND VALUES IN ILLINOIS

Based on a spatiotemporal hedonic farmland price model and county-level data in Illinois from 1979 to 1999, we examined the impact of swine production on farmland values. Our results show that, in addition to the conventional determinants of farmland values, an increase in swine production intensity has a negative relationship with farmland values while an increase in swine operation scale had a positive association with farmland values at the county level in Illinois. We also estimate the impact of changes in the Illinois swine industry over the period 1980-1999 on farmland values at the state level and find that changes in swine inventory and scale of swine operations have led to changes in farmland prices from $-10.56 to$62.96 per acre. In general, the changes in Illinois swine industry increase farmland values in Illinois.Land Economics/Use,

Full Hydrodynamic Model of Nonlinear Electromagnetic Response in Metallic Metamaterials

Applications of metallic metamaterials have generated significant interest in recent years. Electromagnetic behavior of metamaterials in the optical range is usually characterized by a local-linear response. In this article, we develop a finite-difference time-domain (FDTD) solution of the hydrodynamic model that describes a free electron gas in metals. Extending beyond the local-linear response, the hydrodynamic model enables numerical investigation of nonlocal and nonlinear interactions between electromagnetic waves and metallic metamaterials. By explicitly imposing the current continuity constraint, the proposed model is solved in a self-consistent manner. Charge, energy and angular momentum conservation laws of high-order harmonic generation have been demonstrated for the first time by the Maxwell-hydrodynamic FDTD model. The model yields nonlinear optical responses for complex metallic metamaterials irradiated by a variety of waveforms. Consequently, the multiphysics model opens up unique opportunities for characterizing and designing nonlinear nanodevices.Comment: 11 pages, 14 figure

Locating regions in a sequence under density constraints

Several biological problems require the identification of regions in a sequence where some feature occurs within a target density range: examples including the location of GC-rich regions, identification of CpG islands, and sequence matching. Mathematically, this corresponds to searching a string of 0s and 1s for a substring whose relative proportion of 1s lies between given lower and upper bounds. We consider the algorithmic problem of locating the longest such substring, as well as other related problems (such as finding the shortest substring or a maximal set of disjoint substrings). For locating the longest such substring, we develop an algorithm that runs in O(n) time, improving upon the previous best-known O(n log n) result. For the related problems we develop O(n log log n) algorithms, again improving upon the best-known O(n log n) results. Practical testing verifies that our new algorithms enjoy significantly smaller time and memory footprints, and can process sequences that are orders of magnitude longer as a result.Comment: 17 pages, 8 figures; v2: minor revisions, additional explanations; to appear in SIAM Journal on Computin