The angular scale of homogeneity in the local Universe with the SDSS blue galaxies

ABSTRACT We probe the angular scale of homogeneity in the local Universe using blue galaxies from the SDSS survey as a cosmological tracer. Through the scaled counts in spherical caps, $\mathcal {N}(\lt \theta)$, and the fractal correlation dimension, $\mathcal {D}_{2}(\theta)$, we find an angular scale of transition to homogeneity for this sample of θH = 22.19° ± 1.02°. A comparison of this measurement with another obtained using a different cosmic tracer at a similar redshift range (z < 0.06), namely, the H i extragalactic sources from the ALFALFA catalogue, confirms that both results are in excellent agreement (taking into account the corresponding bias correction). We also perform tests to assess the robustness of our results. For instance, we test if the size of the surveyed area is large enough to identify the transition scale we search for, and also we investigate a reduced sample of blue galaxies, obtaining in both cases a similar angular scale for the transition to homogeneity. Our results, besides confirming the existence of an angular scale of transition to homogeneity in different cosmic tracers present in the local Universe, show that the observed angular scale θH agrees well with what is expected in the ΛCDM scenario. Although we cannot prove spatial homogeneity within the approach followed, our results provide one more evidence of it, strengthening the validity of the Cosmological Principle.

Damage Detection Method Based on Fractal Correlation Dimension for Steel Truss Structure

Damage of steel truss structure can be determined by the sudden change of correlation dimension which was obtained from the structural vibration response through fractal theory. The streel truss structure was as exampled to verify this method. The results show that: this method can determine the damage location of the structure whether single damage or multi damage and can preliminarily judge the damage degree.