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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 consider fluctuations in the distribution of critical points, saddle points, minima and maxima of random Gaussian fields and calculate the asymptotic limits of the two point correlation function for various critical point densities, for both long and short range.
Abstract: We consider fluctuations in the distribution of critical points?saddle points, minima and maxima?of random Gaussian fields. We calculate the asymptotic limits of the two point correlation function for various critical-point densities, for both long and short range. We perform the calculation for any dimension of the field, provide explicit formulae for two and three dimensions and verify our results with numerical calculations.
3 citations
01 May 2002-Nuclear Instruments & Methods in Physics Research Section A-accelerators Spectrometers Detectors and Associated Equipment
TL;DR: In this paper, a three-dimensional space-frequency model for the excitation of electromagnetic radiation in a free-electron laser is presented, which is applied in a numerical particle code WB3D simulating the interaction of a free electron laser operating in the linear and non-linear regimes.
Abstract: A three-dimensional, space-frequency model for the excitation of electromagnetic radiation in a free-electron laser is presented. The approach is applied in a numerical particle code WB3D simulating the interaction of a free-electron laser operating in the linear and non-linear regimes. Solution of the electromagnetic excitation equations in the frequency domain inherently takes into account dispersive effects arising from the cavity and the gain medium. Moreover, it facilitates the consideration of statistical features of the electron beam and the excited radiation necessary for the study of spontaneous emission, synchrotron amplified spontaneous emission (SASE), super-radiance and noise. We employ the code to study the statistical and spectral characteristics of the radiation generated in a pulsed beam free-electron laser operating in the millimeter wavelengths. The evolution of the radiation spectrum, excited when a Gaussian-shaped bunch with a random distribution of electrons is passing through the wiggler, was investigated.
3 citations
TL;DR: In this paper, the authors proposed a method that reduces the computational cost of MCs of a linear system with a separable performance function; that is, a function that can be decomposed into parts and calculated independently.
Abstract: Reliability analysis of a structure under random vibratory loads involves estimation of the probability of the response exceeding a limit The classical, brute force approach to such analysis is the Monte Carlo method However, due to its slow convergence rate, it is often impractical for large-scale engineering structures In many engineering applications, such as offshore platforms under wave loads, the excitation is represented by Power Spectral Density (PSD) functions Random time histories of the excitation are generated using a linear combination of sinusoids that are consistent with the PSD of input load This paper proposes a method that reduces the computational cost of MCs of a linear system with a separable performance function; that is, a function that can be decomposed into parts and calculated independently The method generates sinusoidal functions of the excitation, finds the system response to each sinusoid, and stores the responses in a database Then it samples with replacement the sinusoids of the response from the database, finds the system response to the superposition of these sinusoids and checks for failure This procedure yields a very large number of values of the failure indicator function even from a database with a modest number of sinusoids because it uses sampling with replacement The efficiency of the proposed approach is demonstrated by estimating the probability of the first excursion in a ten-bar truss model In this example, the method predicts the probability of failure using less than 02 % of the calculated values of the failure indicator function than the standard MCs
3 citations
TL;DR: In this article, a stochastic model motivated by length fluctuations of a type of appendage of an eukaryotic cell called flagellum (also called cilium) is developed.
Abstract: Long cell protrusions, which are effectively one-dimensional, are highly dynamic subcellular structures. Length of many such protrusions keep fluctuating about the mean value even in the the steady state. We develop here a stochastic model motivated by length fluctuations of a type of appendage of an eukaryotic cell called flagellum (also called cilium). Exploiting the techniques developed for the calculation of level-crossing statistics of random excursions of stochastic process, we have derived analytical expressions of passage times for hitting various thresholds, sojourn times of random excursions beyond the threshold and the extreme lengths attained during the lifetime of these model flagella. We identify different parameter regimes of this model flagellum that mimic those of the wildtype and mutants of a well known flagellated cell. By analysing our model in these different parameter regimes, we demonstrate how mutation can alter the level-crossing statistics even when the steady state length remains unaffected by the same mutation. Comparison of the theoretically predicted level crossing statistics, in addition to mean and variance of the length, in the steady state with the corresponding experimental data can be used in near future as stringent tests for the validity of the models of flagellar length control. The experimental data required for this purpose, though never reported till now, can be collected, in principle, using a method developed very recently for flagellar length fluctuations.
3 citations
Enel1
TL;DR: The divergence from Kimura's theory is due to the approximations necessary to reduce the analytical problem within the Markov processes sphere, the intrinsic difference between the wave height and twice the envelope amplitude, the variability of actual wave periods and the bias of the statistics employed for run length as mentioned in this paper.
3 citations