Dimensional analysis using toric ideals: Primitive invariants

© 2014 Atherton et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.Classical dimensional analysis in its original form starts by expressing the units for derived quantities, such as force, in terms of power products of basic units M, L, T etc. This suggests the use of toric ideal theory from algebraic geometry. Within this the Graver basis provides a unique primitive basis in a well-defined sense, which typically has more terms than the standard Buckingham approach. Some textbook examples are revisited and the full set of primitive invariants found. First, a worked example based on convection is introduced to recall the Buckingham method, but using computer algebra to obtain an integer K matrix from the initial integer A matrix holding the exponents for the derived quantities. The K matrix defines the dimensionless variables. But, rather than this integer linear algebra approach it is shown how, by staying with the power product representation, the full set of invariants (dimensionless groups) is obtained directly from the toric ideal defined by A. One candidate for the set of invariants is a simple basis of the toric ideal. This, although larger than the rank of K, is typically not unique. However, the alternative Graver basis is unique and defines a maximal set of invariants, which are primitive in a simple sense. In addition to the running example four examples are taken from: a windmill, convection, electrodynamics and the hydrogen atom. The method reveals some named invariants. A selection of computer algebra packages is used to show the considerable ease with which both a simple basis and a Graver basis can be found.The third author received funding from Leverhulme Trust Emeritus Fellowship (1-SST-U445) and United Kingdom EPSRC grant: MUCM EP/D049993/1

Effects of moisture in infrared thermography of resin matrix composites

Several multiply graphite polyimide composite specimens were examined by real-time infrared thermography in order to study the effects of moisture on their thermograms. Heat was injected from one side and IR emission detected on the opposite side using AGA Thermovision System-680. No differences between the thermograms of dry and water containing specimens were detected for defect-free specimens. However, the presence of trapped water in defective specimens modified the thermographic contrast significantly. It is concluded that: (1) IR thermography can be used to detect moisture in defective composites, and (2) because of the possibility of moisture camouflaging defects, IR thermography for subsurface defect detection should be supplemented by other techniques - such as acoustical imaging and X-radiography

Critical Ultrasonics Near the Superfluid Transition : Finite Size Effects

The suppression of order parameter fluctuations at the boundaries causes the ultrasonic attenuation near the superfluid transition to be lowered below the bulk value. We calculate explicitly the first deviation from the bulk value for temperatures above the lambda point. This deviation is significantly larger than for static quantities like the thermodynamic specific heat or other transport properties like the thermal conductivity. This makes ultrasonics a very effective probe for finite size effects.Comment: 10 pages (LaTeX), 1 figure (PostScript

Cues and knowledge structures used by mental-health professionals when making risk assessments

Background: Research into mental-health risks has tended to focus on epidemiological approaches and to consider pieces of evidence in isolation. Less is known about the particular factors and their patterns of occurrence that influence clinicians’ risk judgements in practice. Aims: To identify the cues used by clinicians to make risk judgements and to explore how these combine within clinicians’ psychological representations of suicide, self-harm, self-neglect, and harm to others. Method: Content analysis was applied to semi-structured interviews conducted with 46 practitioners from various mental-health disciplines, using mind maps to represent the hierarchical relationships of data and concepts. Results: Strong consensus between experts meant their knowledge could be integrated into a single hierarchical structure for each risk. This revealed contrasting emphases between data and concepts underpinning risks, including: reflection and forethought for suicide; motivation for self-harm; situation and context for harm to others; and current presentation for self-neglect. Conclusions: Analysis of experts’ risk-assessment knowledge identified influential cues and their relationships to risks. It can inform development of valid risk-screening decision support systems that combine actuarial evidence with clinical expertise

Using XML and XSLT for flexible elicitation of mental-health risk knowledge

Current tools for assessing risks associated with mental-health problems require assessors to make high-level judgements based on clinical experience. This paper describes how new technologies can enhance qualitative research methods to identify lower-level cues underlying these judgements, which can be collected by people without a specialist mental-health background. Methods and evolving results: Content analysis of interviews with 46 multidisciplinary mental-health experts exposed the cues and their interrelationships, which were represented by a mind map using software that stores maps as XML. All 46 mind maps were integrated into a single XML knowledge structure and analysed by a Lisp program to generate quantitative information about the numbers of experts associated with each part of it. The knowledge was refined by the experts, using software developed in Flash to record their collective views within the XML itself. These views specified how the XML should be transformed by XSLT, a technology for rendering XML, which resulted in a validated hierarchical knowledge structure associating patient cues with risks. Conclusions: Changing knowledge elicitation requirements were accommodated by flexible transformations of XML data using XSLT, which also facilitated generation of multiple data-gathering tools suiting different assessment circumstances and levels of mental-health knowledge

Tracking the reflexivity of the (dis)engaged citizen: some methodological reflections

The relationship between governments and citizens in many contemporary democracies is haunted by uncertainty and sociologists face the task of listening effectively to citizens’ own reflections on this uncertain relationship. This article reflects on the qualitative methodology of a recently completed UK project which used a combination of diary and multiple interviews/ focus groups to track over a fieldwork period of up to a year citizens’ reflections on their relationship to a public world and the contribution to this of their media consumption. In particular, the article considers how the project’s multiple methods enabled multiple angles on the inevitable artificiality and performative dimension of the diary process, resulting in rich data on people’s complex reflections on the uncertain position of the contemporary citizen

The time scale for the transition to turbulence in a high Reynolds number, accelerated flow

An experiment is described in which an interface between materials of different density is subjected to an acceleration history consisting of a strong shock followed by a period of deceleration. The resulting flow at this interface, initiated by the deposition of strong laser radiation into the initially well characterized solid materials, is unstable to both the Richtmyer–Meshkov (RM) and Rayleigh–Taylor (RT) instabilities. These experiments are of importance in their ability to access a difficult experimental regime characterized by very high energy density (high temperature and pressure) as well as large Reynolds number and Mach number. Such conditions are of interest, for example, in the study of the RM/RT induced mixing that occurs during the explosion of a core-collapse supernova. Under these experimental conditions, the flow is in the plasma state and given enough time will transition to turbulence. By analysis of the experimental data and a corresponding one-dimensional numerical simulation of the experiment, it is shown that the Reynolds number is sufficiently large (Re>105)(Re>105) to support a turbulent flow. An estimate of three key turbulence length scales (the Taylor and Kolmogorov microscales and a viscous diffusion scale), however, shows that the temporal duration of the present flow is insufficient to allow for the development of a turbulent inertial subrange. A methodology is described for estimating the time required under these conditions for the development of a fully turbulent flow. © 2003 American Institute of Physics.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70243/2/PHPAEN-10-3-614-1.pd

Flux Exclusion Superconducting Quantum Metamaterial: Towards Quantum-level Switching

Nonlinear and switchable metamaterials achieved by artificial structuring on the subwavelength scale have become a central topic in photonics research. Switching with only a few quanta of excitation per metamolecule, metamaterial's elementary building block, is the ultimate goal, achieving which will open new opportunities for energy efficient signal handling and quantum information processing. Recently, arrays of Josephson junction devices have been proposed as a possible solution. However, they require extremely high levels of nanofabrication. Here we introduce a new quantum superconducting metamaterial which exploits the magnetic flux quantization for switching. It does not contain Josephson junctions, making it simple to fabricate and scale into large arrays. The metamaterial was manufactured from a high-temperature superconductor and characterized in the low intensity regime, providing the first observation of the quantum phenomenon of flux exclusion affecting the far-field electromagnetic properties of the metamaterial