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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 paper, the Eulerian and Lagrangian correlation functions in low frequency electrostatic turbulence in strongly magnetized plasmas are studied in two spatial dimensions, where the ion velocity in the direction perpendicular to a homogeneous magnetic field is approximated by the E × B/B2-velocity.
Abstract: The Eulerian and Lagrangian correlation functions in low frequency electrostatic turbulence in strongly magnetized plasmas are studied in two spatial dimensions. In this limit the ion velocity in the direction perpendicular to a homogeneous magnetic field is approximated by the E × B/B2-velocity. For strictly flute type fluctuations a similar model is used also for the electron dynamics. Allowing, on the other hand, for a small B-parallel component of the perturbations an isothermal Boltzmann distribution for the electrons can be argued while the two dimensional ion description is retained. The present analysis is based on an approximation of the actual two-dimensional flow in terms of an autonomous flow consisting of many overlapping and mutually convecting vortices. Simple analytical expressions for the full space-time varying Eulerian correlation are derived solely in terms of plasma parameters. It is demonstrated that an extension of the arguments giving the foregoing results allows also for derivation of analytical expressions for the Lagrangian correlation function. The results are supported by a Monte Carlo simulation based on the model.
TL;DR: In this paper, the spectral properties of power spectral density (PSD) have been used to evaluate the fatigue damage under random loading, and a simple approximation procedure of high cycle fatigue damage for austenitic stainless steel and ferritic steel has been proposed.
Abstract: This paper shows the new design approach for random fatigue evaluation based on spectral characteristics. Fatigue damage under random loading is usually evaluated according to the following steps: 1. decomposition of random wave to stress amplitude using the rainflow cycle counting method (RFC) 2. evaluation of fatigue damage using Palmgren-Miner’s linear summation rule. In design process, the fluctuation of load is usually characterized through power spectral density (PSD). Therefore, the design process is expected to be generalized if the fatigue damage is directly evaluated from the PSD together with S-N diagram of the material. In fact many properties related to fatigue damage, such as distribution of extreme values, can be derived theoretically from geometrical properties of PSD. However, concerning the distribution of stress amplitude counted by RFC, it is rather difficult to derive it theoretically due to its complicated procedure. In this paper, upper bound of stress amplitude distribution is confirmed for many random waves generated by numerical simulation for many types of PSD. Expressing the upper bound distribution by closed form function using PSD characteristics leads us to the direct evaluation of fatigue damage with safety margin if the fatigue damage by particular stress amplitude is approximated using some series expansion form. Simple approximation procedure of high cycle fatigue damage for austenitic stainless steel and ferritic steel will be proposed in the paper. Finally, design evaluation procedure for the fatigue damage evaluation from PSD together with S-N diagram is summarized.Copyright © 2009 by ASME
01 Jan 2019
TL;DR: In this paper, the authors illustrate the experimental techniques that appeared around the end of the nineteenth century to measure aerodynamic actions, first of all the technology that represents the symbol of this discipline: the wind tunnel.
Abstract: The knowledge about aerodynamic actions is vitally important in many fields, such as those involving structures and transportation. Facing such issues, This chapter illustrates the experimental techniques that appeared around the end of the nineteenth century to measure aerodynamic actions, first of all the technology that represents the symbol of this discipline: the wind tunnel. It also describes the pioneering stage during which this device was aimed at every type of test, and then, the appearance of facilities specialized in various sectors, first of all those aiming to reproduce the atmospheric boundary layer, then those addressed to aircrafts, sailing boats, road and rail vehicles. The evolution of aerodynamic knowledge is overshadowed by the driving role of aeronautics. Relying on the huge impact of the first flights, it inspired an increasingly stricter relationship between theory and experimentation focusing on the study of wings and originating analytical methods and experimental techniques destined to impact on several sectors, first and above all wind actions and effects on structures and transportation.
TL;DR: In this paper, the authors derived explicit expressions of the probability density function for a non-stationary non-negative random process (a statistical Laguerre expansion type and a statistical Hermite expansion type) from the above two fundamental viewpoints of modeling a time series, in relation to the statistical method described in a previous paper by the authors.
TL;DR: In this paper, the moment generating function of the integrated light intensity of thermal radiation having multiple peak spectrum is obtained for two-peak and three-peak spectra where different peaks are in orthogonal states of polarisation.
Abstract: The moment generating function of the integrated light intensity of thermal radiation having multiple peak spectrum is obtained Cases of two-peak and three-peak spectra where different peaks are in orthogonal states of polarisation are considered The moment generating function is shown to be the product of two simpler generating functions