Geometry and dynamics of vortex sheets in 3 dimensions

We consider the properties and dynamics of vortex sheets from a geometrical, coordinate-free, perspective. Distribution-valued forms (de Rham currents) are used to represent the fluid velocity and vorticity due to the vortex sheets. The smooth velocities on either side of the sheets are solved in terms of the sheet strengths using the language of double forms. The classical results regarding the continuity of the sheet normal component of the velocity and the conservation of vorticity are exposed in this setting. The formalism is then applied to the case of the self-induced velocity of an isolated vortex sheet. We develop a simplified expression for the sheet velocity in terms of representative curves. Its relevance to the classical Localized Induction Approximation (LIA) to vortex filament dynamics is discusse

Twisted Electromagnetic Modes and Sagnac Ring-Lasers

A new approximation scheme, designed to solve the covariant Maxwell equations inside a rotating hollow slender conducting cavity (modelling a ring-laser), is constructed. It is shown that for well-defined conditions there exist TE and TM modes with respect to the longitudinal axis of the cavity. A twisted mode spectrum is found to depend on the integrated Frenet torsion of the cavity and this in turn may affect the Sagnac beat frequency induced by a non-zero rotation of the cavity. The analysis is motivated by attempts to use ring-lasers to measure terrestrial gravito-magnetism or the Lense-Thirring effect produced by the rotation of the Earth.Comment: LaTeX 31 pages, 3 Figure

A primer on exterior differential calculus

A pedagogical application-oriented introduction to the cal­culus of exterior differential forms on differential manifolds is presented. Stokes' theorem, the Lie derivative, linear con­nections and their curvature, torsion and non-metricity are discussed. Numerous examples using differential calculus are given and some detailed comparisons are made with their tradi­tional vector counterparts. In particular, vector calculus on R3 is cast in terms of exterior calculus and the traditional Stokes' and divergence theorems replaced by the more powerful exterior expression of Stokes' theorem. Examples from classical continuum mechanics and spacetime physics are discussed and worked through using the language of exterior forms. The numerous advantages of this calculus, over more traditional ma­chinery, are stressed throughout the article

Software Developers Want Changes in Patent and Copyright Law

Most software developers do not oppose all software copyrights. There is broad support for basic copyright protection of computer programs which prohibits directly copying computer programs without the author\u27s permission. Nearly all commercial software is copyrighted, and most programmers agree that such protection is necessary in order for software development to be profitable. However, software patents and look and feel copyrights go well beyond this to prohibit other programmers from independently writing even programs that are similar to the protected program. Such constraints are strongly resented by many in the software development community who long for the good old days when they were free to write whatever programs they wanted without fear of lawsuits

Efficiency considerations and the allocation of new deal funds: an examination of the public goods explanation of expenditure patterns

The uneven state-level distribution of New Deal spending has been frequently studied and a variety of economic and political models have been developed. In their article, “Does the Distribution of New Deal Spending Reflect an Optimal Provision of Public Goods?,†(Economics Bulletin, Vol. 8, No. 3, 2007. pp 1-5) Bateman and Taylor propose that much of the disparity in state-level New Deal expenditures can be explained if the creation of public goods and the spillover effects are included in economic models. Using the available wealth of data on New Deal programs, expenditures by agencies within the New Deal are examined and correlation statistics provided to test this hypothesis against the 1930 US census population density figures.New Deal, public good, spillover effects, Public Works Administration, PWA, Civil Works Administration, CWA

Irrigation and drainage performance assessment: practical guidelines

Irrigation management / Drainage / Performance evaluation / Performance indexes / Evapotranspiration / Precipitation / Water balance / Participatory rural appraisal / Databases / Simulation

Checking ID-cards for the sale of restricted goods : age decisions bias face decisions

Matching unfamiliar faces is highly error-prone, and most studies highlight the implications for real-world ID-checking. Here we study a particular instance of ID-checking: proof of age for buying restricted goods such as alcohol. In this case, checkers must establish that an identity document is carried by its legitimate owner (i.e., that the ID photo matches the face of the bearer) and that the ID proves the bearer to be old enough to make the purchase. Across three experiments, using two common forms of photo-ID (i.e., driving licenses, PASS+ cards) we show that observers produce very high error rates when age requirements are met, but faces mismatch. This bias away from detecting a face mismatch remained evident in experienced cashiers—though to a somewhat attenuated level. We discuss interactions between face matching and other tasks, and the practical consequences of a bias which favours those using photo-ID with fraudulent intent

Viewers base estimates of face matching accuracy on their own familiarity: Explaining the photo-ID paradox

Matching two different images of a face is a very easy task for familiar viewers, but much harder for unfamiliar viewers. Despite this, use of photo-ID is widespread, and people appear not to know how unreliable it is. We present a series of experiments investigating bias both when performing a matching task and when predicting other people’s performance. Participants saw pairs of faces and were asked to make a same/different judgement, after which they were asked to predict how well other people, unfamiliar with these faces, would perform. In four experiments we show different groups of participants familiar and unfamiliar faces, manipulating this in different ways: celebrities in experiments 1 to 3 and personally familiar faces in experiment 4. The results consistently show that people match images of familiar faces more accurately than unfamiliar faces. However, people also reliably predict that the faces they themselves know will be more accurately matched by different viewers. This bias is discussed in the context of current theoretical debates about face recognition, and we suggest that it may underlie the continued use of photo-ID, despite the availability of evidence about its unreliability

Mapping warm molecular hydrogen with Spitzer's Infrared Array Camera (IRAC)

Photometric maps, obtained with Spitzer's Infrared Array Camera (IRAC), can provide a valuable probe of warm molecular hydrogen within the interstellar medium. IRAC maps of the supernova remnant IC443, extracted from the Spitzer archive, are strikingly similar to spectral line maps of the H2 pure rotational transitions that we obtained with the Infrared Spectrograph (IRS) instrument on Spitzer. IRS spectroscopy indicates that IRAC Bands 3 and 4 are indeed dominated by the H2 v=0-0 S(5) and S(7) transitions, respectively. Modeling of the H2 excitation suggests that Bands 1 and 2 are dominated by H2 v=1-0 O(5) and v=0-0 S(9). Large maps of the H2 emission in IC433, obtained with IRAC, show band ratios that are inconsistent with the presence of gas at a single temperature. The relative strengths of IRAC Bands 2, 3, and 4 are consistent with pure H2 emission from shocked material with a power-law distribution of gas temperatures. CO vibrational emissions do not contribute significantly to the observed Band 2 intensity. Assuming that the column density of H2 at temperatures T to T+dT is proportional to T raised to the power -b for temperatures up to 4000 K, we obtained a typical estimate of 4.5 for b. The power-law index, b, shows variations over the range 3 to 6 within the set of different sight-lines probed by the maps, with the majority of sight-lines showing b in the range 4 to 5. The observed power-law index is consistent with the predictions of simple models for paraboloidal bow shocks.Comment: 27 pages, including 11 figures. Accepted for publication in Ap