[en] The integrated use of neural network and noise analysis technologies offers advantages not available by the use of either technology alone. The application of neural network technology to noise analysis offers an opportunity to expand the scope of problems where noise analysis is useful and unique ways in which the integration of these technologies can be used productively. The two-sensor technique, in which the responses of two sensors to an unknown driving source are related, is used to demonstration such integration. The relationship between power spectral densities (PSDs) of accelerometer signals is derived theoretically using noise analysis to demonstrate its uniqueness. This relationship is modeled from experimental data using a neural network when the system is working properly, and the actual PSD of one sensor is compared with the PSD of that sensor predicted by the neural network using the PSD of the other sensor as an input. A significant deviation between the actual and predicted PSDs indicate that system is changing (i.e., failing). Experiments carried out on check values and bearings illustrate the usefulness of the methodology developed. (Author)

[en] The quantum dynamics of an anharmonic oscillator coupled to a bath of up to 60 harmonic oscillators is investigated by a new multiconfigurational hybrid method for wave packet propagation. The method, originally proposed in [Burghardt, Meyer, and Cederbaum, J. Chem. Phys. 111, 2927 (1999)], represents a variant of the multiconfiguration time-dependent Hartree method including a moving basis of Gaussian functions. Energy relaxation and quantum decoherence induced by the zero-temperature oscillator bath are shown to be accurately described by the new method. Decoherence rates for a bath with a discretized ohmic spectral density are found to be consistent with golden-rule predictions for T=0

[en] It is reported that the rotationally symmetric distributions of the spectral density and the spectral degree of coherence of the scattered field in the far zone can be produced by appropriate choices of the effective radius and the correlation length of the scatterer, when a polychromatic plane light wave is incident upon a Gaussian-correlated, quasi-homogeneous, anisotropic medium. The necessary and sufficient conditions are presented. Our results are illustrated by numerical examples.

[en] In technical plants disturbances are possible which generate small narrow-band components in the measured signals. For the detection of these oscillatory signals the observation of the frequency spectra of the measured signals' noise components is particularly advantageous because they produce additional characteristic peaks. In this paper detection systems for the fast detection of suddenly appearing peaks in the power spectral density of noise signals are presented based on auto- and cross correlation techniques. General criteria were developed to enable the determination of the optimal detection system and its sensitivity for the different problems. Specially auto- and cross correlation measurements were compared in dependence of the signal coherence. Theoretical results were confirmed in a number of experiments. Special experimental and theoretical parameter studies were done for the optimal detection of sodium boiling in LMFBR's. Computations showed that local sodium boiling can be detected in nearly the whole core range of SNR-300 by detection systems based on the observation of the neutron flux fluctuations. (orig.)

[en] The model of a partially coherent four-petal Lorentz–Gauss beam generated by the Gaussian Schell-model source was first introduced. The cross-spectral density function of a partially coherent four-petal Lorentz–Gauss beam propagating in non-Kolmogorov turbulence was derived by using the extended Huygens–Fresnel integral. The spreading and coherence properties of a partially coherent four-petal Lorentz–Gauss beam propagating in non-Kolmogorov turbulence were studied. The results show that such a beam propagating in non-Kolmogorov turbulence with either larger , smaller , larger , or smaller will lose the four-petal profile distribution and evolve into a solid beam with Gaussian-like distribution more rapidly as the propagation distance increases. The results also show that the spectral degree of coherence of a partially coherent four-petal Lorentz–Gauss beam between two points and will decrease as the distance of two points increases in the far field. (paper)

[en] A stochastic beam generated by a recently introduced Gaussian Schell-model array (GSMA) source (2015 Opt. Lett. 40 5662) is investigated. We derive the analytical propagation formulae for the spectral density and the propagation factor in non-Kolmogorov turbulence by utilizing the extended Huygens–Fresnel principle and second-order moments of the Wigner distribution function. Numerical results show that the lattice patterns of GSMA beams, which keep propagation-invariant in free space, are destroyed by the turbulence at sufficiently large distances. The GSMA beams have significant advantage over the Gaussian Schell-model beam in the robustness of the destructive effect of non-Kolmogorov turbulence, especially for the GSMA beam with more lattice elements and bigger relative separation distance of each lattice element. The effects of beam parameters and non-Kolmogorov turbulence on the propagation factor are analyzed in detail. (paper)

[en] Using recently derived results about the difference of two cross-spectral densities, we consider a source whose correlation function is the difference of two mutually displaced Gaussian Schell-model cross-spectral densities. We examine the main features of this new cross-spectral density in terms of coherence and intensity distribution, both across the source plane and after free propagation. (paper)

[en] In Part I of this report we developed analytical expressions which represent exactly the energy density spectra of ''digitization processes'' that are essentially involved in spectral analysis of continuous signals. Besides, we related the spectral energy density of each digitization process to the parameters of the exact spectral energy density of the corresponding signal. On this basis, we briefly discussed the forms of distortions (or false structures) which are present in normally computed power spectra when the corresponding spectra of the digitization processes are not sufficiently decoupled from or nullified in the computed spectra. The biggest worry with regard to these distortions is not only that they may mask the actual information contained in the original signal, but also they may tempt the researcher to establish false characteristics about the signal involved. It is, in this context, that any reasonable method that could be used (even conditionally) to pinpoint false structures in computed power spectra would be both timely and useful. A simple, handy guidance through which some portions of computed energy density spectra which are dominated by the false structures mentioned above, can be located is presented herein. Equations are presented which give the various frequencies at which false peaks may be located in such ''contaminated'' portions of computed energy density spectra. The occurrence of frequency shifts in computed power spectra is also briefly discussed. (author)

[en] Complex systems, and in particular random neural networks, are often described by randomly interacting dynamical systems with no specific symmetry. In that context, characterizing the number of relevant directions necessitates fine estimates on the Ginibre ensemble. In this fast track communication, we compute analytically the probability distribution of the number of eigenvalues N_R with modulus greater than R (the index) of a large N × N random matrix in the real or complex Ginibre ensemble. We show that the fraction N_R/N = p has a distribution scaling as exp ( − βN²ψ_R(p)) with β = 2 (respectively β = 1) for the complex (resp. real) Ginibre ensemble. For any p ∈ [0, 1], the equilibrium spectral densities as well as the rate function ψ_R(p) are explicitly derived. This function displays a third order phase transition at the critical (minimum) value p_R^∗=1−R², associated to a phase transition of the Coulomb gas. We deduce that, in the central regime, the fluctuations of the index N_R around its typical value p_R^∗N scale as N^1/3. (fast track communications)

[en] We introduce a novel class of planar random source producing far fields with multi-ring-shaped average intensity patterns by modeling the source degree of coherence, and confirm that such sources are physically genuine. Further, we derive the analytical expressions for the cross-spectral density (CSD) function of the beam-like fields generated by the novel source propagating in free space and in a linear isotropic random medium, and analyze the evolution of the spectral density and the state of coherence. It is shown that at some distance from the source the spectral density of the propagating beam in free space takes on the shape-invariant multi-ring profile, and the number of rings and intensity profiles of the beams can be flexibly adjusted by changing the source parameters. However, in atmospheric turbulence, we find that at sufficiently large distances from the source, the multi-ring profiles are destroyed by the medium, even if it remains such for intermediate distances from the source. (letter)