Instability and Chaos in Non-Linear Wave Interaction: a simple model

We analyze stability of a system which contains an harmonic oscillator non-linearly coupled to its second harmonic, in the presence of a driving force. It is found that there always exists a critical amplitude of the driving force above which a loss of stability appears. The dependence of the critical input power on the physical parameters is analyzed. For a driving force with higher amplitude chaotic behavior is observed. Generalization to interactions which include higher modes is discussed. Keywords: Non-Linear Waves, Stability, Chaos.Comment: 16 pages, 4 figure

Using the Uncharged Kerr Black Hole as a Gravitational Mirror

We extend the study of the possibility to use the Schwarzschild black hole as a gravitational mirror to the more general case of an uncharged Kerr black hole. We use the null geodesic equation in the equatorial plane to prove a theorem concerning the conditions the impact parameter has to satisfy if there shall exist boomerang photons. We derive an equation for these boomerang photons and an equation for the emission angle. Finally, the radial null geodesic equation is integrated numerically in order to illustrate boomerang photons.Comment: 11 pages Latex, 3 Postscript figures, uufiles to compres

HF radar observations of high-aspect angle backscatter from the E-region

International audienceWe present evidence for the observation of high-aspect angle HF radar backscatter from the auroral electrojets, and describe the spectral characteristics of these echoes. Such backscatter is observed at very near ranges where ionospheric refraction is not sufficient to bring the sounding radio waves to orthogonality with the magnetic field; the frequency dependence of this propagation effect is investigated with the Stereo upgrade of the CUTLASS Iceland radar. We term the occurrence of such echoes the "high-aspect angle irregularity region" or HAIR. It is suggested that backscatter is observed at aspect angles as high as 30°, with an aspect sensitivity as low as 1dB deg–1. These echoes are distinguished from normal electrojet backscatter by having low Doppler shifts with an azimuthal dependence that appears more consistent with the direction of the convection electric field than with the expected electron drift direction. This is discussed in terms of the linear theory dispersion relation for electrojet waves. Key words. Ionosphere (ionospheric irregularities; plasma waves and instabilities; auroral ionosphere

Sphere rolling on the surface of a cone

We analyse the motion of a sphere that rolls without slipping on a conical surface having its axis in the direction of the constant gravitational field of the Earth. This nonholonomic system admits a solution in terms of quadratures. We exhibit that the only circular of the system orbit is stable and furthermore show that all its solutions can be found using an analogy with central force problems. We also discuss the case of motion with no gravitational field, that is, of motion on a freely falling cone.Comment: 12 pages, 2 figures, to be published in Eur J Phy

Fabrication and Characterization of Borosilicate Glasses Containing Alpha-Radionuclides and Silver From Conversion and Mixed-Oxide Facilities Proposed for Russia

Liquid and solid radioactive wastes are formed during conversion of plutonium metal to oxide and during fabrication of weapons-grade plutonium into mixed-oxide (MOX) fuel. In Russia, these wastes are to be processed for disposition by immobilization in either borosilicate glass or cement matrices depending upon the waste stream-specific radionuclide contents. Vitrification is planned for the liquid high-level waste raffinate stream containing the bulk of the Am-241 produced from Pu-241 decay. Previous work on the Russian MOX Fuel Fabrication Facility (R-MFFF) by the Public Joint Stock Corporation (TVEL) [1] showed that this waste stream may contain significant amounts of silver derived from the electrochemical dissolution of PuO2 using a Ag(II) catalyst. The work reported here further investigated silver solubility limits, which, if exceeded in a production glass melter, allow discrete silver grains to form in the glass and also deposit over time on the bottom of a joule-heated ceramic melter. In melters with immersed electrodes, such as the Russian EP-100 for phosphate glasses or the US Duratek DP-100 type melters for borosilicate glasses that are being considered for use at the Siberian Chemical Combine (SCC) Tomsk site, the undissolved silver could cause a short circuit and an unacceptable production melter failure. The silver solubility limit of 3.85 wt% Ag{sub 2}O in liquid, alpha-bearing wastes determined in this work will guide the production scale use of borosilicate glass compositions, and effectively increase the capacity of the ceramic melters and reduce the total volume of solidified vitrified wastes at SCC Tomsk that require storage prior to geologic disposal

Midlands Cadences: Narrative Voices in the Work of Alan Sillitoe

This paper will examine excerpts from a range of Alan Sillitoe’s prose fiction, most notably Saturday Night and Sunday Morning (1958) and short stories from the collection The Loneliness of the Long-Distance Runner (1958), via a comparative exploration of the texts’ representations of Midlands English demotic. Both texts enact Bakhtin’s notion of novelistic dialogism and find much expressive capital in the tension between discourses: between the oral and the written. Indeed, it could be argued that much of Sillitoe’s work functions as a direct challenge to dominant notions of the literary. The narrative discourse attempts to trace a link between the quotidian experience of the Midlands English working classes represented and the demotic language which they speak. His technique also explores the link between language and sensibility; i.e. verbal articulacy need not be a limit to expression of a character’s distinctive identity. In contrast to the more radical techniques of novelists like James Kelman and Irvine Welsh, all instances of phonetically-rendered demotic remain imprisoned by what Joyce called ‘perverted commas’ – as direct speech. However, the diegetic narrative discourse itself is redolent of registers rooted in 1950s English working class life. The texts also contain different methods of representing their protagonists’ consciousness through their own idiolect. In Saturday Night and Sunday Morning, this is evidenced by the use of the second person ‘you’. It functions simultaneously as a representation of Seaton’s consciousness in the oral register which he might choose to articulate it, and as a dialogic ‘sideways glance’ at the reader and assumed shared experience. The second is more redolent of internal monologue, using the first-person form (as seen in the homodiegetic narration of the second novel); crucially, though, it remains in Standard English, if explicitly orientated towards oral register. Sillitoe’s is a novelistic discourse which refuses to normalise itself to accord with the conventions of classic realism, and as such prefigures the ambitions of many contemporary writers who incline their narrative voices towards the oral – asserting the right of a character’s dialect/idiolect to be the principal register of the narrative. The paper will demonstrate this thesis through the ideas of Bakhtin, and through an analytical taxonomy derived from literary stylistics. It aims to propose a model which can be used to analyse and explore any fiction which has been labelled as ‘working class’, and asserts that such an approach leads to a more principled characterisation of working class fiction (based on its use of language) than current literary-critical discussions based simply on cultural/social context and biography

The Ks-band Tully-Fisher Relation - A Determination of the Hubble Parameter from 218 ScI Galaxies and 16 Galaxy Clusters

The value of the Hubble Parameter (H0) is determined using the morphologically type dependent Ks-band Tully-Fisher Relation (K-TFR). The slope and zero point are determined using 36 calibrator galaxies with ScI morphology. Calibration distances are adopted from direct Cepheid distances, and group or companion distances derived with the Surface Brightness Fluctuation Method or Type Ia Supernova. Distances are determined to 16 galaxy clusters and 218 ScI galaxies with minimum distances of 40.0 Mpc. From the 16 galaxy clusters a weighted mean Hubble Parameter of H0=84.2 +/-6 km s-1 Mpc-1 is found. From the 218 ScI galaxies a Hubble Parameter of H0=83.4 +/-8 km s-1 Mpc-1 is found. When the zero point of the K-TFR is corrected to account for recent results that find a Large Magellanic Cloud distance modulus of 18.39 +/-0.05 a Hubble Parameter of 88.0 +/-6 km s-1 Mpc-1 is found. A comparison with the results of the Hubble Key Project (Freedman et al 2001) is made and discrepancies between the K-TFR distances and the HKP I-TFR distances are discussed. Implications for Lamda-CDM cosmology are considered with H0=84 km s-1 Mpc-1. (Abridged)Comment: 37 pages including 12 tables and 7 figures. Final version accepted for publication in the Journal of Astrophysics & Astronom