4,033 research outputs found
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
Issues and Options for the Multilateral Regulation of GM Foods
As genetically modified food commodities have entered markets in recent years, domestic regulators have attempted to manage consumer, environmental and citizen concerns about these new products. One result has been incomplete and at times inconsistent domestic regulation, which has created international conflicts about market access. A number of international institutions have attempted in recent years to bridge the gulf between exporters and importers. This paper reviews recent international developments and offers options for different strategies for reducing the current tensions in international markets.Food Consumption/Nutrition/Food Safety,
End-Use Certificates for Wheat: Trade-Distorting Administrative Barriers?
International Relations/Trade,
Geochemical and spectral characterization of naturally altered rock surfaces
The possibility of using the visible-near infrared region for compositional analysis of remotely sensed rock surfaces is studied. This would allow mapping rock type both on the Earth's surface and on other planetary surfaces. Reflectance spectroscopy, economic geology, optical depth determination, and X-ray diffraction mineralogy are discussed
Flow field prediction and analysis, project fire final report
Flow field, and convective and radiative heating predictions for NASA Fire project reentry package trajectorie
Some Practical Hints Concerning the Care of Newborn Children: Notes of a Lecture at the Harvard Medical School
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Engaging Citizens with Televised Election Debates through Online Interactive Replays
In this paper we tackle the crisis of political trust and public engagement with politics by investigating new methods and tools to watch and take part in televised political debates. The paper presents relevant research at the intersection of citizenship, technologies and government/democracy, and describes the motivation, requirements and design of Democratic Replay, an online interactive video replay platform that offers a persistent, customisable digital space for: (a) members of the public to express their views as they watch online videos of political events; and (b) enabling for a richer collective understanding of what goes on in these complex media events
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