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Elastic bodies with random distribution of micro-cracks
Published in H. Furuta, M. Dogaki, M. Sakano, Reliability and Optimization of Structural Systems, 2018
G. Augusti, P.M. Mariano, F.L. Stazi, M. Gioffrè
where σ is the standard deviation of lm, c1 and c2 are parameters that are proportional to the correlation distance of the stochastic field along the axes x and y in the plane of Figure 2, respectively (see [40]).We assume that the correlation function has c1 = c2 =360, and σ =20. A plot of the associated scaled correlation function is given in Figure 3.
Sources of variability in AUC
Published in Dev P. Chakraborty, Observer Performance Methods for Diagnostic Imaging, 2017
The bootstrap and jackknife methods described in this chapter have wide applicability. Later they will be extended to estimating the covariance (essentially a scaled correlation) between two random variables. Also described was the DeLong method, applicable to the empirical AUC. Using a real dataset and simulators, all methods were shown to agree with each other, especially when the number of cases is large, Table 7.3 (row D, last column).
Phase separation kinetics of binary mixture in the influence of bond disorder: sensitivity to quench temperature
Published in Phase Transitions, 2023
Samiksha Shrivastava, Awaneesh Singh
When a homogeneous binary mixture was deep quenched, the influence of lower on the segregation kinetics was almost negligible; the system showed nearly perfect dynamical scaling with the pure case, displayed by the scaled correlation function and the structure factor. The domain evolution stayed within a transient growth regime even at an asymptotic time limit. The growth exponent, for the pure case, decreased even further; for due to some randomness at domain interfaces caused by the disorder. Thus, the growth exponent for a binary mixture, deep quenched at with and were much smaller than the usual Lifshitz-Slyozov (LS) growth exponent, .
Photon bunching from an equilateral triangle of atoms
Published in Journal of Modern Optics, 2023
In Figure 2, the polar plots of the correlation functions computed in steady state are shown. The atoms are positioned at , and . Frame (a) depicts the one-time normalized correlation function of the second order, . The effect of strong superbunching can be readily noticed as shows large values along the directions of and in the form of two needle-like peaks. Frame (b) shows the angular distribution of the corresponding scaled correlation function of the first order, . One can notice that the first-order correlation function is minimum at the directions of and , see Equation (19). This clearly means that a reduced single-photon emission in certain directions implies an enhanced correlated two-photon emission in these directions. The criterion of super bunching given by does not necessarily result from increased correlations between pairs of photons, but can be a result of a prominent decrease of single-photon emission [17]. Very large values of signify that the likelihood of registering two single photons is reduced compared to the probability of recording pairs of photons at the same instant of time. In Figure 3, the two mentioned types of the correlation functions have been plotted using a logarithmic scale so that the angular variation depicting the peaks in one and the dips in the other is more evident.
LIDAR systems operating in a non-Kolmogorov turbulent atmosphere
Published in Waves in Random and Complex Media, 2019
I. Toselli, F. Wang, O. Korotkova
It is well visible the completely different trend of the plots shown in Figures 9 and 10, therefore any conclusion should be given relatively to the approach used to present the results. However, we note that the scaled correlation function for the mean on-axis irradiance shown in Figure 7 is not affected by the unit dependency.