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Analogous Method
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R K L Su – One of the best experts on this subject based on the ideXlab platform.
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a wasserstein distance based Analogous Method to predict distribution of non uniform corrosion on reinforcements in concrete
Construction and Building Materials, 2019Co-Authors: R K L SuAbstract:Abstract This paper presents an Analogous Method to predict the distribution of non-uniform corrosion on reinforcements in concrete by minimizing the Wasserstein distance. A comparison between the predicted and experimental results shows that the proposed Method is capable of predicting distributions of non-uniform corrosion modeled by Gaussian functions. The non-uniformity and the total area of the rust layer are selected as the key parameters to determine the distribution of non-uniform corrosion on reinforcements. Empirical equations of the non-uniformity and the total area of the rust layer versus degree of corrosion are proposed to validate the application of the Method for practical projects. The Method presented in this study fills a research gap in quantifying the distribution of non-uniform corrosion on reinforcements by realistically simulating crack propagation in concrete.
Ernst E Scheufens – One of the best experts on this subject based on the ideXlab platform.
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from fourier series to rapidly convergent series for zeta 3
Mathematics Magazine, 2011Co-Authors: Ernst E ScheufensAbstract:SummaryExact values of the Riemann zeta function ζ(s) for even values of s can be determined from Fourier series for periodic versions of even power functions, but there is not an Analogous Method for determining exact values of ζ(s) for odd values of s. After giving a brief historical overview of ζ(s) for integer values of s greater than one, and showing how we can determine ζ(2) and ζ(4) from Fourier series, we consider the Fourier series for a continuous and piecewise differentiable odd periodic function from which we can find a series with logarithmic terms for ζ(3). Using power series for logarithmic functions on this series, a rapidly convergent series for ζ(3) is obtained. Using a partial sum of this series we can compute ζ(3) with an error which is much smaller than the error obtained by using a similar partial sum of the infinite series defining ζ(3).
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From Fourier Series to Rapidly Convergent Series for Zeta(3)
Mathematics Magazine, 2011Co-Authors: Ernst E ScheufensAbstract:SummaryExact values of the Riemann zeta function ζ(s) for even values of s can be determined from Fourier series for periodic versions of even power functions, but there is not an Analogous Method …
Sergey Vyazovkin – One of the best experts on this subject based on the ideXlab platform.
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evaluation of activation energy of thermally stimulated solid state reactions under arbitrary variation of temperature
Journal of Computational Chemistry, 1997Co-Authors: Sergey VyazovkinAbstract:The thermal effect of a reaction makes the temperature inside the reaction system deviate from a prescribed heating program. To take into account the effect of such temperature deviations on kinetic evaluations, a computational Method applicable to an arbitrary variation in temperature has been developed. The Method combines the isoconversional principle of evaluating the activation energy with numerical integration of the equation, dα/dt = k[T(t)]f(α), over the actual variation of the temperature with the time, T(t). Details of the numerical algorithm are reported. A model example has been used to verify the reliability of this Method as compared to an Analogous Method which does not account for the deviations of the temperature from a prescribed program. The Method has been tested for tolerance for noise in the temperature. © 1997 by John Wiley & Sons, Inc.