109 research outputs found

    Counting function fluctuations and extreme value threshold in multifractal patterns: the case study of an ideal 1/f1/f noise

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    To understand the sample-to-sample fluctuations in disorder-generated multifractal patterns we investigate analytically as well as numerically the statistics of high values of the simplest model - the ideal periodic 1/f1/f Gaussian noise. By employing the thermodynamic formalism we predict the characteristic scale and the precise scaling form of the distribution of number of points above a given level. We demonstrate that the powerlaw forward tail of the probability density, with exponent controlled by the level, results in an important difference between the mean and the typical values of the counting function. This can be further used to determine the typical threshold xmx_m of extreme values in the pattern which turns out to be given by xm(typ)=2clnlnM/lnMx_m^{(typ)}=2-c\ln{\ln{M}}/\ln{M} with c=3/2c=3/2. Such observation provides a rather compelling explanation of the mechanism behind universality of cc. Revealed mechanisms are conjectured to retain their qualitative validity for a broad class of disorder-generated multifractal fields. In particular, we predict that the typical value of the maximum pmaxp_{max} of intensity is to be given by lnpmax=αlnM+32f(α)lnlnM+O(1)-\ln{p_{max}} = \alpha_{-}\ln{M} + \frac{3}{2f'(\alpha_{-})}\ln{\ln{M}} + O(1), where f(α)f(\alpha) is the corresponding singularity spectrum vanishing at α=α>0\alpha=\alpha_{-}>0. For the 1/f1/f noise we also derive exact as well as well-controlled approximate formulas for the mean and the variance of the counting function without recourse to the thermodynamic formalism.Comment: 28 pages; 7 figures, published version with a few misprints corrected, editing done and references adde

    Chandra X-ray Observations of the Spiral Galaxy M81

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    A Chandra X-Ray Observatory ACIS-S imaging observation is used to study the population of X-ray sources in the nearby Sab galaxy M81 (NGC 3031). A total of 177 sources are detected with 124 located within the D25 isophote to a limiting X-ray luminosity of 3e36 ergs/cm2/s. Source positions, count rates, luminosities in the 0.3-8.0 keV band, limiting optical magnitudes, and potential counterpart identifications are tabulated. Spectral and timing analysis of the 36 brightest sources are reported including the low-luminosity active galactic nucleus, SN 1993J, and the Einstein-discovered ultra-luminous X-ray source X6.Comment: 27 pages, 17 figures, 2 tables, submitted to Ap

    Methodological Consideration in Color Research

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