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

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

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

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

Dependence on temperature and GC content of bubble length distributions in DNA

We present numerical results on the temperature dependence of the distribution of bubble lengths in DNA segments of various guanine-cytosine (GC) concentrations. Base-pair openings are described by the Peyrard-Bishop-Dauxois model and the corresponding thermal equilibrium distributions of bubbles are obtained through Monte Carlo calculations for bubble sizes up to the order of a hundred base pairs. The dependence of the parameters of bubble length distribution on temperature and the GC content is investigated. We provide simple expressions which approximately describe these relations. The variation of the average bubble length is also presented. We find a temperature dependence of the exponent c that appears in the distribution of bubble lengths. If an analogous dependence exists in the loop entropy exponent of real DNA, it may be relevant to understand overstretching in force-extension experiments.Comment: 8 pages, 6 figures. Published on The Journal of Chemical Physic

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

A Comparison between Electroluminescence Models and Experimental Results

Electrical insulation ages and degrades until its eventual failure under electrical stress. One cause of this relates to the movement and accumulation of charge within the insulation. The emission of a low level of light from polymeric materials while under electrical stressing occurs before the onset of currently detectable material degradation. This light is known as electroluminescence (EL) and under an ac electric field is thought to relate to the interaction of charge in close proximity to the electrode-polymer interface. Understanding the cause of this light emission gives a very high-resolution method of monitoring charge interaction and its influence on material ageing. A possible cause of this light emission is the bipolar charge recombination theory. This theory involves the injection, trapping and recombination of charge carriers during each half cycle of the applied field [1]. This work compares two models that to simulate the EL emission according to this bipolar charge recombination theory. Model 1 assumes a fixed space charge region and all injected charge is uniformly distributed in this region with charges able to either become trapped or to recombine with opposite polarity charge carriers [2]. This recombination relates directly the excitation needed for the emission of a photon of light as measured in experiments. Model 2 develops on this by accounting for the transport and extraction of charge with an exponential distribution of trap levels rather than a uniform distribution [3]. Figure 1 shows a good correlation between the two models and experimental data. The full paper will describe the models in more detail and present results comparing the simulated and experimental results under various applied waveforms. Model 1 and model 2 both provide a good correlation with experimental data but model 2 allows a greater understanding of the space charge profile in the region close to the electrodes as well as the shape of the conduction current. Further work involves developing these models to support changes in the charge trapping profiles due to material ageing and supporting simulated results with measured conduction current