Applications of DFT to the theory of twentieth-century harmony

Music theorists have only recently, following groundbreaking work by Quinn, recognized the potential for the DFT on pcsets, initially proposed by Lewin, to serve as the foundation of a theory of harmony for the twentieth century. This paper investigates pcset “arithmetic” – subset structure, transpositional combination, and interval content – through the lens of the DFT. It discusses relationships between interval classes and DFT magnitudes, considers special properties of dyads, pcset products, and generated collections, and suggest methods of using the DFT in analysis, including interpreting DFT magnitudes, using phase spaces to understand subset structure, and interpreting the DFT of Lewin’s interval function. Webern’s op. 5/4 and Bartok’s String Quartet 4, iv, are discussed.Accepted manuscrip

Decontextualizing contextual inversion

Contextual inversion, introduced as an analytical tool by David Lewin, is a concept of wide reach and value in music theory and analysis, at the root of neo-Riemannian theory as well as serial theory, and useful for a range of analytical applications. A shortcoming of contextual inversion as it is currently understood, however, is, as implied by the name, that the transformation has to be defined anew for each application. This is potentially a virtue, requiring the analyst to invest the transformational system with meaning in order to construct it in the first place. However, there are certainly instances where new transformational systems are continually redefined for essentially the same purposes. This paper explores some of the most common theoretical bases for contextual inversion groups and considers possible definitions of inversion operators that can apply across set class types, effectively decontextualizing contextual inversions.Accepted manuscrip

Modelling of Electroluminescence in Polymers Using a Bipolar Charge Transport Model

Electroluminescence (EL) in polymeric materials is thought to occur due to the energy dissipation process from the recombination of opposite polarity charge carriers. It is considered as an indication of storage and transport of charge carriers in cable insulation subject to electrical stresses and may indicate the change in charge movement due to aging or degradation processes. Under ac electric fields, the interaction of opposite polarity charge carriers at the interface of polymer/conductor is enhanced compared with dc conditions, and seems to contribute a lot to the electroluminescence rather than the charge behaviours in the bulk of polymers. The dynamics of charge carriers both at the interface of polymer/conductor and in the bulk of polymers is investigated through a simulation work using a bipolar charge transport model. Figure 1 compares experimental electroluminescence results with simulated data from the recombination of injected charge carriers. The paper will give more details on EL model and comparison under various waveforms and frequencies

Condition Monitoring of Power Cables

A National Grid funded research project at Southampton has investigated possible methodologies for data acquisition, transmission and processing that will facilitate on-line continuous monitoring of partial discharges in high voltage polymeric cable systems. A method that only uses passive components at the measuring points has been developed and is outlined in this paper. More recent work, funded through the EPSRC Supergen V, UK Energy Infrastructure (AMPerES) grant in collaboration with UK electricity network operators has concentrated on the development of partial discharge data processing techniques that ultimately may allow continuous assessment of transmission asset health to be reliably determined

Thermal performance of high voltage power cables

The UK high voltage electricity transmission network continues to face annual rises in demand, with ever greater volumes of power supplied to load centres throughout the country. To operate this network effectively, it is vital to accurately calculate the maximum allowable electric current which can be safely carried by each component in the power system. In high voltage power cables, this limit is defined by the maximum operating temperature of the cable insulation. Specify this current rating to be too low and the cable asset will never be used to its full potential; conversely setting the rating to be too high risks damage to the asset as the excessive heating can cause premature failure. Thus the rating calculation must be optimised to maintain security of supply by minimising the risk of cable failure, while also maximising the returns from capital investment on the power network. This project has employed a variety of mathematical techniques to improve the methods by which current ratings are calculated. Modern computational techniques such as finite element analysis (e.g Figure 1) and computational fluid dynamics are used to create more advanced circuit rating techniques. These have been compared and refined with input gained from field data. By eliminating simplifications from existing methods, it has been possible to identify ways of increasing the utilisation of the existing network. In addition the new techniques allow examination of the potential benefits of future developments in cable technology. Benefits are being derived from this work on both a day to day and strategic planning levels. For instance, by re-evaluating the current rating method for cables installed in tunnels, it has proved possible to consider the benefits from co-locating more cables in one tunnel to best use these expensive assets. The application of this method has allowed the quantification of the benefits which might be available from next generation cable technologies, enabling the prioritisation of future research effort in cable materials. Upon completion, the knowledge gained from this work is to be used to revise the international standard on calculating current ratings in cable tunnels. Techniques such as these underpin the concept of smart grids with improved operational flexibility and capability. Simultaneously the requirement to build expensive new components into the network is limited, whilst still meeting the need to supply ever increasing volumes of power across the country

Non-perturbative embedding of local defects in crystalline materials

We present a new variational model for computing the electronic first-order density matrix of a crystalline material in presence of a local defect. A natural way to obtain variational discretizations of this model is to expand the difference Q between the density matrix of the defective crystal and the density matrix of the perfect crystal, in a basis of precomputed maximally localized Wannier functions of the reference perfect crystal. This approach can be used within any semi-empirical or Density Functional Theory framework.Comment: 13 pages, 4 figure

Next-to-leading Log Resummation of Scalar and Pseudoscalar Higgs Boson Differential Cross-Sections at the LHC and Tevatron

The region of small transverse momentum in q qbar- and gg-initiated processes must be studied in the framework of resummation to account for the large, logarithmically-enhanced contributions to physical observables. In this paper, we will calculate the fixed order next-to-leading order (NLO) perturbative total and differential cross-sections for both a Standard Model (SM) scalar Higgs boson and the Minimal Supersymmetric Standard Model's (MSSM) pseudoscalar Higgs boson in the Heavy Quark Effective Theory (HQET) where the mass of the top quark is taken to be infinite. Resummation coefficients B^2_g, C^2_gg for the total cross-section resummation for the pseudoscalar case are given, as well as C^1_gg for the differential cross-section.Comment: 18 pages, REVTeX4, 5 eps figures. v2: Typos corrected, references added, a discussion of uncertainties was adde

Coulomb Charging Effects for Finite Channel Number

We consider quantum fluctuations of the charge on a small metallic grain caused by virtual electron tunneling to a nearby electrode. The average electron number and the effective charging energy are determined by means of perturbation theory in the tunneling Hamiltonian. In particular we discuss the dependence of charging effects on the number N of tunneling channels. Earlier results for N>>1 are found to be approached rather rapidly with increasing N.Comment: 6 pages, 5 figure

Evaluation of a ln tan integral arising in quantum field theory

We analytically evaluate a dilogarithmic integral that is prototypical of volumes of ideal tetrahedra in hyperbolic geometry. We additionally obtain new representations of the Clausen function Cl_2 and the Catalan constant G=Cl_2(\pi/2), as well as new relations between sine and Clausen function values.Comment: 24 pages, no figure