• Title/Summary/Keyword: and Cauchy Function

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Nuclide composition non-uniformity in used nuclear fuel for considerations in pyroprocessing safeguards

  • Woo, Seung Min;Chirayath, Sunil S.;Fratoni, Massimiliano
    • Nuclear Engineering and Technology
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    • v.50 no.7
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    • pp.1120-1130
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    • 2018
  • An analysis of a pyroprocessing safeguards methodology employing the Pu-to-$^{244}Cm$ ratio is presented. The analysis includes characterization of representative used nuclear fuel assemblies with respect to computed nuclide composition. The nuclide composition data computationally generated is appropriately reformatted to correspond with the material conditions after each step in the head-end stage of pyroprocessing. Uncertainty in the Pu-to-$^{244}Cm$ ratio is evaluated using the Geary-Hinkley transformation method. This is because the Pu-to-$^{244}Cm$ ratio is a Cauchy distribution since it is the ratio of two normally distributed random variables. The calculated uncertainty of the Pu-to-$^{244}Cm$ ratio is propagated through the mass flow stream in the pyroprocessing steps. Finally, the probability of Type-I error for the plutonium Material Unaccounted For (MUF) is evaluated by the hypothesis testing method as a function of the sizes of powder particles and granules, which are dominant parameters to determine the sample size. The results show the probability of Type-I error is occasionally greater than 5%. However, increasing granule sample sizes could surmount the weakness of material accounting because of the non-uniformity of nuclide composition.

Electric Conduction Mechanisms Study within Zr Doped Mn3O4 Hausmannite Thin Films through an Oxidation Process in Air

  • Said, L. Ben;Boughalmi, R.;Inoubli, A.;Amlouk, M.
    • Applied Microscopy
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    • v.47 no.3
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    • pp.131-147
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    • 2017
  • In this work further optical and electrical investigations of pure and Zr doped $Mn_3O_4$ (from 0 up to 20 at.%) thin films as a function of frequency. First, the refractive index, the extinction coefficient and the dielectric constants in terms of Zr content are reached from transmittance and reflectance data. The dispersion of the refractive index is discussed by means of Cauchy model and Wemple and DiDomenico single oscillator models. By exploiting these results, it was possible to estimate the plasma pulse ${\omega}_p$, the relaxation time ${\tau}$ and the dielectric constant ${\varepsilon}_{\infty}$. Second, we have performed original ac and dc conductivity studies inspired from Jonscher model and Arrhenius law. These studies helped establishing significant correlation between temperature, activation energy and Zr content. From the spectroscopy impedance analysis, we investigated the frequency relaxation phenomenon and hopping mechanisms of such thin films. Moreover, a special emphasis has been putted on the effect of the oxidation in air of hausmannite thin films to form $Mn_2O_3$ ones at $350^{\circ}C$. This intrigue phenomenon which occurred at such temperature is discussed along with this electrical study. Finally, all results have been discussed in terms of the thermal activation energies which were determined with two methods for both undoped and Zr doped $Mn_3O_4$ thin films in two temperature ranges.

Fluoride single crystals for UV/VUV nonlinear optical applications

  • Shimamura Kiyoshi;Villora Encarnacion G.;Muramatsu Kenichi;Kitamura Kenji;Ichinose Noboru
    • Journal of the Korean Crystal Growth and Crystal Technology
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    • v.16 no.4
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    • pp.133-140
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    • 2006
  • The growth characteristics and properties of large size $SrAlF_5$ single crystals are described and compared with those of $BaMgF_4$. Transmission spectra in the vacuum ultraviolet wavelength region indicate a high transparency of $SrAlF_5$ (about 90% without considering surface reflection loses) down to 150 nm, on contrast to the optical loses observed for $BaMgF_4$. The ferroelectric character of $SrAlF_5$ is evidenced by the reversal of the spontaneous polarization in a hysteresis loop. The higher potential of $SrAlF_5$ in comparison with $BaMgF_4$ for the realization of all-solid-state lasers in the ultraviolet wavelength region by the quasi-phase matching (QPM) technique is pointed out. $SrAlF_5$, besides a higher grade of transparency, shows a nonlinear effective coefficient similar to that of quartz and uniaxial nature, on contrast to the one order smaller nonlinear coefficient and biaxial character of $BaMgF_4$. The refractive index of $SrAlF_5$ from the ultraviolet to the near-infrared wavelength region is measured by the minimum deviation method. The Sellmeier and Cauchy coefficients are obtained from the fits to the curves of the ordinary and extraordinary refractive indices, and the grating period for the first order QPM is estimated as a function of the wavelength. The poling periodicity for 193 nm SHG from 386 nm is $4{\mu}m$.

The Nonlinear Motions of Cylinders(I) (주상체의 비선형 운동(I) -강제동요문제, 조파저항문제-)

  • H.Y. Lee;J.H. Hwang
    • Journal of the Society of Naval Architects of Korea
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    • v.29 no.4
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    • pp.114-131
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    • 1992
  • In the present work, a two-dimensional boundary-value problem for a large amplitude motion is treated as an initial-value problem by satisfying the exact body-boundary and nonlinear free-surface boundary conditions. The present nonlinear numerical scheme is similar to that described by Vinje and Brevig(1981) who utilized the Cauchy's theorem and assumed the periodicity in the horizontal coordinate. In the present thesis, however, the periodicity in the horizontal coordinate is not assumed. Thus the present method can treat more realistic problems, which allow radiating waves to infinities. In the present method of solution, the original infinite fluid domain, is divided into two subdomains ; ie the inner and outer subdomains which are a local nonlinear subdomain and the truncated infinite linear subdomain, respectively. By imposing an appropriate matching condition, the computation is carried out only in the inner domain which includes the body. Here we adopt the nonlinear scheme of Vinje & Brevig only in the inner domain and respresent the solution in the truncated infinite subdomains by distributing the time-dependent Green function on the matching boundaries. The matching condition is that the velocity potential and stream function are required to be continuous across the matching boundary. In the computations we used, if necessary, a regriding algorithm on the free surface which could give converged stable solutions successfully even for the breaking waves. In harmonic oscillation problem, each harmonic component and time-mean force are obtained by the Fourier transform of the computed forces in the time domain. The numerical calculations are made for the following problems. $\cdot$ Forced harmonic large-amplitude oscillation(${\omega}{\neq}0,\;U=0$) $\cdot$ Translation with a uniform speed(${\omega}=0,\;U{\neq}0$) The computed results are compared with available experimental data and other analytical results.

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Initialization by using truncated distributions in artificial neural network (절단된 분포를 이용한 인공신경망에서의 초기값 설정방법)

  • Kim, MinJong;Cho, Sungchul;Jeong, Hyerin;Lee, YungSeop;Lim, Changwon
    • The Korean Journal of Applied Statistics
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    • v.32 no.5
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    • pp.693-702
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    • 2019
  • Deep learning has gained popularity for the classification and prediction task. Neural network layers become deeper as more data becomes available. Saturation is the phenomenon that the gradient of an activation function gets closer to 0 and can happen when the value of weight is too big. Increased importance has been placed on the issue of saturation which limits the ability of weight to learn. To resolve this problem, Glorot and Bengio (Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics, 249-256, 2010) claimed that efficient neural network training is possible when data flows variously between layers. They argued that variance over the output of each layer and variance over input of each layer are equal. They proposed a method of initialization that the variance of the output of each layer and the variance of the input should be the same. In this paper, we propose a new method of establishing initialization by adopting truncated normal distribution and truncated cauchy distribution. We decide where to truncate the distribution while adapting the initialization method by Glorot and Bengio (2010). Variances are made over output and input equal that are then accomplished by setting variances equal to the variance of truncated distribution. It manipulates the distribution so that the initial values of weights would not grow so large and with values that simultaneously get close to zero. To compare the performance of our proposed method with existing methods, we conducted experiments on MNIST and CIFAR-10 data using DNN and CNN. Our proposed method outperformed existing methods in terms of accuracy.