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[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)
Journal
[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
Journal
[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.
Journal
[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 NR 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 NR/N = p has a distribution scaling as exp ( − βN2ψR(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 ψR(p) are explicitly derived. This function displays a third order phase transition at the critical (minimum) value pR∗=1−R2, associated to a phase transition of the Coulomb gas. We deduce that, in the central regime, the fluctuations of the index NR around its typical value pR∗N scale as N1/3. (fast track communications)
Journal
Journal of Physics. A, Mathematical and Theoretical (Online); ISSN 1751-8121; 
; v. 47(4); [8 p.]
; v. 47(4); [8 p.]
[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)
Journal
Laser Physics Letters (Internet); ISSN 1612-202X; ; v. 13(4); [10 p.]
; v. 13(4); [10 p.]
[en] A review of recent advances in the area of hysteretic nonlinearities driven by di.usion processes is presented. The analysis of these systems is based on the Preisach formalism for the description of hysteresis to represent complex nonlinearities as a weighted superposition of rectangular loops. The mathematical theory of di.usion processes on graphs is then applied to solve problems for stochastically driven hysteresis loops. Closed form expressions for the expected value and spectral density of the output are obtained, and sample computations for these quantities are presented. Because of the universality of the Preisach model, this approach can be used to investigate stochastic aspects in hysteretic systems of various physical origins
Journal
Journal of Physics. Conference Series (Online); ISSN 1742-6596; ; v. 22(1); p. 139-147
; v. 22(1); p. 139-147
[en] We carry out a detailed numerical investigation of stochastic resonance in underdamped systems in the nonperturbative regime. We point out that an important distinction between stochastic resonance in overdamped and underdamped systems lies in the lack of dependence of the amplitude of the noise-averaged trajectory on the noise strength, in the latter case. We provide qualitative explanations for the observed behaviour and show that signatures such as the initial decay and long-time oscillatory behaviour of the temporal correlation function and peaks in the noise and phase averaged power spectral density, clearly indicate the manifestation of resonant behaviour in noisy, underdamped bistable systems in the weak to moderate noise regime
Journal
[en] We expose an interesting connection between the distribution of local spectral density of states arising in the theory of disordered systems and the notion of superstatistics introduced by Beck and Cohen and recently incorporated in random matrix theory. The latter represents the matrix-element joint probability density function as an average of the corresponding quantity in the standard random-matrix theory over a distribution of level densities. We show that this distribution is in reasonable agreement with the numerical calculation for a disordered wire, which suggests to use the results of theory of disordered conductors in estimating the parameter distribution of the superstatistical random-matrix ensemble
Journal
[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)
Journal
Journal of Optics (Online); ISSN 2040-8986; ; v. 18(10); [10 p.]
; v. 18(10); [10 p.]
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