Digital program analyzes supersonic flow field within bell-shaped rocket nozzles

Digital computer program computes and analyzes supersonic flow field in axisymmetric rocket nozzle for specified gas properties, nozzle geometry, and input or starting line. Method of characteristics is used for solution of set of hyperbolic partial differential equations

A Concept for Exploring Western Music Tonality in Physical Space

Musical theory about the structure and morphology of Western tonality is quite difficult to teach to young children, due to the relatively complex mathematical concepts behind tonality. Children usually grasp the concepts of musical harmony intuitively through listening to music examples. Placing the 12 notes of the well-tempered scale into a spatial arrangement, in which the proximity of these notes represents their mutual harmonic relationship, would allow to link physical motion through a spatial area with the exploration of music tonality. Music theorists have postulated the Circle of Fifth, the “Spiral Array”, and the “Tonnetz” as paradigms for spatial arrangements of music notes which allow mapping the distance between notes onto their “mutual consonance”. These approaches mostly have been of qualitative nature, leaving the actual numeric parameters of the spatial description undetermined. In this paper, these parameters have been determined, leading to a concrete numerical description of the planar Tonnetz. This allows the design of a physical space in which the music notes are distributed in space according to their musical consonance. Set up in an outdoor area, handheld devices (e.g. PDA) with integrated Global Positioning System can be used to play these notes at their actual physical location. This makes it possible for children to explore this musical space by moving through the real spatial area and experience the relationships of the notes through their proximity. Defining a range for each note as a circular area around each note location, consonant chords can be produced in those areas where those circles overlap. Using this concept, games can be developed in which the listeners have to perform certain tasks related to this musical space. This appears to be a promising approach for the music education of young children who can intuitively learn about music morphology without being explicitly taught about the complex theoretical mathematical background

Intra-industry trade and labour market adjustment: A reassessment using data on individual workers

We re-examine the relationship between intra-industry trade and labour reallocation, using individual-level data on manufacturing worker moves in the United Kingdom. The contribution of this analysis is twofold. First, we estimate the impact of intra-industry trade on worker moves between occupations as well as between industries. Second, we run individual-level regressions that allow us to control for worker heterogeneity. Our results suggest that intra-industry trade does have the stipulated attenuating effect on worker moves, both between occupations and between industries, but that this effect is relatively small compared to other determinants of labour reallocation

Active control of multi-dimensional random sound in ducts

Previous work has demonstrated how active control may be applied to the control of random noise in ducts. These implementations, however, have been restricted to frequencies where only plane waves are propagating in the duct. In spite of this, the need for this technology at low frequencies has progressed to the point where commercial products that apply these concepts are currently available. Extending the frequency range of this technology requires the extension of current single channel controllers to multi-variate control systems as well as addressing the problems inherent in controlling higher order modes. The application of active control in the multi-dimensional propagation of random noise in waveguides is examined. An adaptive system is implemented using measured system frequency response functions. Experimental results are presented illustrating attained suppressions of 15 to 30 dB for random noise propagating in multiple modes