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Mathematical Analysis of Random Noise-Conclusion
About: This article is published in Bell System Technical Journal.The article was published on 1945-01-01 and is currently open access. It has received 807 citations till now.
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TL;DR: In this article, the authors derived a simplified model for the (2+1) exceeding probability distribution of ocean waves based on the Gaussian random field approach, with a particular interest in rogue waves.
8 citations
TL;DR: In this article, the effect of random magnetic fields on the dissociation of ultracold molecules with Feshbach resonances is studied analytically, and the authors uncover the robustness against noise of some characteristics of the process, in particular, of the dependence of the mean atomic kinetic energy on system parameters.
Abstract: The effect of random magnetic fields on the dissociation of ultracold molecules with Feshbach resonances is studied analytically. The dissociation spectrum and the evolution of the molecule fraction are obtained for a general form of the magnetic-field ramp and different noise properties relevant to standard experimental conditions. The results uncover the robustness against noise of some characteristics of the dissociation process, in particular, of the dependence of the mean atomic kinetic energy on the system parameters. Implications for the applicability of a method proposed to determine the width of the Feshbach resonances from the measurement of the dissociation spectrum are analyzed. Moreover, we discuss how the presence of fluctuations can affect the use of particular ramp shapes to tailor the properties of the generated atomic distribution.
8 citations
01 Sep 2016
TL;DR: In this paper, the classic time domain approach is taken as a reference for the comparison of different methods for the Fatigue Damage Spectrum (FDS) calculation in case of Sine-on-Random vibration environments.
Abstract: In many real-life environments, certain mechanical and electronic components may be subjected to Sine-on-Random vibrations, i.e. excitations composed of random vibrations superimposed on deterministic (sinusoidal) contributions, in particular sine tones due to some rotating parts of the system (e.g. helicopters, engine-mounted components,...). These components must be designed to withstand the fatigue damage induced by the "composed" vibration environment, and qualification tests are advisable for the most critical ones. In the case of an accelerated qualification test, a proper test tailoring which starts from the real environment (measured vibration signals) and which preserves not only the accumulated fatigue damage but also the "nature" of the excitation (i.e. sinusoidal components plus random process) is important to obtain reliable results. In this paper, the classic time domain approach is taken as a reference for the comparison of different methods for the Fatigue Damage Spectrum (FDS) calculation in case of Sine-on-Random vibration environments. Then, a methodology to compute a Sine-on-Random specification based on a mission FDS is proposed.
8 citations
TL;DR: In this paper, the amplification process of broad-band continuum radiation by astronomical masers in the one-dimensional case was analyzed and the basic equations appropriate for the scalar maser and the random nature of the maser radiation field were derived from basic physical principles.
Abstract: In this paper, we re-analyse the amplification process of broad-band continuum radiation by astronomical masers in the one-dimensional case The basic equations appropriate for the scalar maser and the random nature of the maser radiation field are derived from basic physical principles Comparison with the standard radiation transfer equation allows us to examine the underlying assumptions involved in the current theory of astronomical masers Simulations are carried out to follow the amplification of different realizations of the broad-band background radiation by the maser The observable quantities such as intensity and spectral line profile are obtained by averaging over an ensemble of the emerging radiation corresponding to the amplified background radiation field Our simulations show that the fluctuations of the radiation field inside the astronomical maser deviate significantly from Gaussian statistics even when the maser is only partially saturated Coupling between different frequency modes and the population pulsing are shown to have increasing importance in the transport of maser radiation as the maser approaches saturation Our results suggest that the standard formulation of radiation transfer provides a satisfactory description of the intensity and the line narrowing effect in the unsaturated and partially saturated masers within the framework of the one-dimensional model However, the application of the same formulation to the strong saturation regime should be considered with caution
8 citations
TL;DR: In this article, the authors present a survey of the state of the art in bioinformatics.Section 2.2.1.Section 3.3.1] Section 4.
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