• Title/Summary/Keyword: function approximations

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Peak Analysis of Gamma-ray and X-ray (감마선 및 엑스선의 피이크 분석)

  • Kim, Seung-Kon;Herr, Young-Hoi;Park, Kwang-June
    • Journal of Radiation Protection and Research
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    • v.9 no.1
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    • pp.33-42
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    • 1984
  • A great variety of nuclear gamma rays emitted from fission and activation products of spent nuclear fuel contains much information that can be elicited without affecting the integrity of the fuel elements. But the extraction of such information from the complex spectrum is difficult and requires computer codes. In the present work, a versatile code 'CAERI' was developed which locates peaks and calculates their areas for X-rays as well as gamma rays using elegant features of some widely used programs for gamma-ray peak fitting. 'CAERI' coded in FORTRAN used infinite series approximation more accurate than other workers various, simple, piecewise series approximations for evaluations of the Voigt function which represents the X-ray peak with non-negligible natural line width. 'CAERI' can handle even a complex multiplet consisting of peaks from X-rays and gamma rays in arbitrary mixture, which one often encounters in the isotopic analysis of heavy elements such as U and Pu. The results of the fitting performed on the test spectra of $^{177m}\;Lu\;{\gamma}-ray\;and\;^{235}U\;K_{\alpha}$X-ray show good agreement with those by previous workers.

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Finite Difference Model of Unsaturated Soil Water Flow Using Chebyshev Polynomials of Soil Hydraulic Functions and Chromatographic Displacement of Rainfall (Chebyshev 다항식에 의한 토양수분특성 및 불포화 수리전도도 추정과 부분 치환 원리에 의한 강우 분포를 이용한 토양수분 불포화 이동 유한차분 수리모형)

  • Ro, Hee-Myong;Yoo, Sun-Ho;Han, Kyung-Hwa;Lee, Seung-Heon;Lee, Goon-Taek;Yun, Seok-In;Noh, Young-Dong
    • Korean Journal of Soil Science and Fertilizer
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    • v.36 no.4
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    • pp.181-192
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    • 2003
  • We developed a mathematical simulation model to portray the vertical distribution of soil water from the measured weather data and the known soil hydraulic properties, and then compared simulation results with the periodically measured soil water profiles obtained on Jungdong sandy loam to verify the model, In this model, we solved potential-based Richards' equation by the implicit finite difference method superimposed on the predictor-corrector scheme. We presumed that: soil hydraulic properties are homogeneous; soil water flows isothermally; hysteresis is not considered; no vapor flows; no heat transfers into the soil profiles; and water added to soil surface is distributed along the soil profile following partial displacement principle. The input data were broadly classified into two groups: (1) daily weather data such as rainfall, maximum and minimum air temperatures, relative humidity and solar radiation and (2) soil hydraulic data to approximate unsaturated hydraulic conductivity and water retention. Each hydraulic polynomial function approximated using the Chebyshev polynomial and least square difference technique in tandem showed a fairly good fit of the given set of data. Vertical distribution of soil water as approximations to the Richards' equation subject to changing surface and phreatic boundaries was solved numerically during 53 days with a comparatively large time increment, and this pattern agreed well with field neutron scattering data, except for the surface 0.1 m slab.

Investigation of the interaction between spin density wave and superconductivity in two band high temperature iron based superconductor Ba1-xNaxFe2As2

  • Teklie Lissanu Tegegne
    • Progress in Superconductivity and Cryogenics
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    • v.26 no.2
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    • pp.9-18
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    • 2024
  • The current study deals with the possible interplay between superconductivity and spin density wave in two band model high temperature iron based superconductor (FeBSC) Ba1-xNaxFe2As2. The electron and hole bands in the presence of the inter-band interaction between the two bands is becoming a vital issue to deal with the high temperature physics of the iron-based superconductors. In this research work, a model Hamiltonian appropriate for the system under consideration has been developed and the temperature dependent Green's function technique has been employed to get the solution for the equations of motion constructed for the two band model high temperature FeBSC Ba1-xNaxFe2As2. By making use of the decoupling procedure, the equations of motion for the dependence of superconducting transition temperature (TC) on spin density wave(SDW) order parameter (ΔSDW) in the electron intra-band (Δsc(e)) , hole intra-band (Δsc(h)) and inter-band (Δsc(eh)) for Ba1-xNaxFe2As2 have been obtained. We have also obtained the expression for the dependence of spin density wave transition temperature(TSDW) on ΔSDW for Ba1-xNaxFe2As2. Using some plausible approximations and appropriate experimental values for the parameters in the obtained equations of motion, phase diagrams of TC versus Δsc(e), Δsc(h) and Δsc(eh) are plotted. Furthermore, a phase diagram of TSDW versus ΔSDW is plotted for the material under consideration. Finally, using the above mentioned phase diagrams, the interplay between superconductivity and spin density wave in the two band model high temperature FeBSC Ba1-xNaxFe2As2 has been demonstrated to be a very distinct possibility. The agreement of the current finding with the experimental observations is quite commendable.