Lyapunov functions for a non-linear model of the X-ray bursting of the microquasar GRS 1915+105

This paper introduces a biparametric family of Lyapunov functions for a non-linear mathematical model based on the FitzHugh-Nagumo equations able to reproduce some main features of the X-ray bursting behaviour exhibited by the microquasar GRS 1915+105. These functions are useful to investigate the properties of equilibrium points and allow us to demonstrate a theorem on the global stability. The transition between bursting and stable behaviour is also analyzed.Comment: Published on International Journal of Non-Linear Mechanics, vol. 88, pp. 142-14

Comparison of the INRIM and PTB lattice-spacing standards

To base the kilogram definition on the atomic mass of the silicon 28 atom, the present relative uncertainty of the silicon 28 lattice parameter must lowered to 3E-9. To achieve this goal, a new experimental apparatus capable of a centimetre measurement-baseline has been made at the INRIM. The comparison between the determinations of the lattice parameter of crystals MO*4 of INRIM and WASO4.2a of PTB is intended to verify the measurement capabilities and to assess the limits of this experiment.Comment: 10 pages, 8 figures, submitted to Metrologi

Remarks on the misunderstood use of the term biodiversity

The term diversity is intended to denote species richness understood as the number of species and individuals; it was explicitly discussed at length by Hutchinson in 1959 and by many other scientists in the following decades. The term biodiversity, certainly derived from diversity, was born in the 1980s. The difference between the two terms is substantial, diversity is a part of the whole, as biodiversity is understood as diversity of organisms at the level of species, individuals, genes, interactions and ecological processes among them and at the level of ecosystems. Thus, it is correct to write ‘plant diversity’ or ‘animal diversity’, but not ‘plant biodiversity’ or ‘animal biodiversity’. Biodiversity is unique, it includes all living things, it is equal to a fundamental law of life, the maintenance of adequate levels of biodiversity is a necessity for the very life of our Planet. An illustration of biodiversity seen in the form of mosaic tesserae is tentatively presente

The complex time behaviour of the microquasar GRS 1915+105 in the \rho-class observed with BeppoSAX. III: The hard X-ray delay and limit cycle mapping

The microquasar GRS1915+105 was observed by BeppoSAX in October 2000 for about ten days while the source was in \rho-mode, which is characterized by a quasi-regular type I bursting activity. This paper presents a systematic analysis of the delay of the hard and soft X-ray emission at the burst peaks. The lag, also apparent from the comparison of the [1.7-3.4] keV light curves with those in the [6.8-10.2] keV range, is evaluated and studied as a function of time, spectral parameters, and flux. We apply the limit cycle mapping technique, using as independent variables the count rate and the mean photon rate. The results using this technique were also cross-checked using a more standard approach with the cross-correlation methods. Data are organized in runs, each relative to a continuous observation interval. The detected hard-soft delay changes in the course of the pointing from about 3 s to about 10 s and presents a clear correlation with the baseline count rate.Comment: accepted for publication in A&

Determining the Physical Properties of the B Stars I. Methodology and First Results

We describe a new approach to fitting the UV-to-optical spectra of B stars to model atmospheres and present initial results. Using a sample of lightly reddened stars, we demonstrate that the Kurucz model atmospheres can produce excellent fits to either combined low dispersion IUE and optical photometry or HST FOS spectrophotometry, as long as the following conditions are fulfilled: 1) an extended grid of Kurucz models is employed, 2) the IUE NEWSIPS data are placed on the FOS absolute flux system using the Massa & Fitzpatrick (1999) transformation, and 3) all of the model parameters and the effects of interstellar extinction are solved for simultaneously. When these steps are taken, the temperatures, gravities, abundances and microturbulence velocities of lightly reddened B0-A0 V stars are determined to high precision. We also demonstrate that the same procedure can be used to fit the energy distributions of stars which are reddened by any UV extinction curve which can be expressed by the Fitzpatrick & Massa (1990) parameterization scheme. We present an initial set of results and verify our approach through comparisons with angular diameter measurements and the parameters derived for an eclipsing B star binary. We demonstrate that the metallicity derived from the ATLAS 9 fits to main sequence B stars is essentially the Fe abundance. We find that a near zero microturbulence velocity provides the best-fit to all but the hottest or most luminous stars (where it may become a surrogate for atmospheric expansion), and that the use of white dwarfs to calibrate UV spectrophotometry is valid.Comment: 17 pages, including 2 pages of Tables and 6 pages of Figures. Astrophysical Jounral, in pres

Wavefront errors in a two-beam interferometer

This paper deals with the impact of wavefront errors, due to the optical aberrations of a two-beam interferometer, on the period of the travelling fringe observed by integrating the interference pattern. A Monte Carlo simulation of the interferometer operation showed that the fringe-period estimate is unbiased if evaluated on the basis of the angular spectrum of the beam entering the interferometer, but the wavefront errors increase the uncertainty