• Title/Summary/Keyword: Scattering problem

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The critical slab problem with the Anlı-Güngor scattering function

  • R.G. Tureci
    • Nuclear Engineering and Technology
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    • v.55 no.8
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    • pp.2864-2872
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    • 2023
  • The criticality problem in this study is studied with the recently investigated the Anlı-Güngör scattering function. The scattering function depends on the Legendre polynomials as the Mika scattering function, but it includes only one scattering parameter, t, and its orders. Both Mika and Anlı-Güngör scattering are the same for only linear anisotropic scattering. The difference appears for the quadratic scattering and further. The analytical calculations are performed with the HN method, and the numerical results are calculated with Wolfram Mathematica. Interpolation technique in Mathematica is also used to approximate the isotropic scattering results when t parameter goes to zero. Thus, the calculated results could be compared with the literature data for isotropic scattering.

ON THE INVERSE PROBLEM FOR STURM-LIOUVILLE OPERATOR WITH A NONLINEAR SPECTRAL PARAMETER IN THE BOUNDARY CONDITION

  • Mamedov, Khanlar R.
    • Journal of the Korean Mathematical Society
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    • v.46 no.6
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    • pp.1243-1254
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    • 2009
  • The inverse scattering problem is investigated for some second order differential equation with a nonlinear spectral parameter in the boundary condition on the half line [0, $\infty$). In the present paper the coefficient of spectral parameter is not a pure imaginary number and the boundary value problem is not selfadjoint. We define the scattering data of the problem, derive the main integral equation and show that the potential is uniquely recovered.

Half-space albedo problem for İnönü, linear and quadratic anisotropic scattering

  • Tureci, R.G.
    • Nuclear Engineering and Technology
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    • v.52 no.4
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    • pp.700-707
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    • 2020
  • This study is concerned with the investigation of the half-space albedo problem for "İnönü-linear-quadratic anisotropic scattering" by the usage of Modified FN method. The method is based on Case's method. Therefore, Case's eigenfunctions and its orthogonality properties are derived for anisotropic scattering of interest. Albedo values are calculated for various linear, quadratic and İnönü anisotropic scattering coefficients and tabulated in Tables.

A SCATTERING PROBLEM IN A NONHOMOGENEOUS MEDIUM

  • Anar, I.Ethem
    • Bulletin of the Korean Mathematical Society
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    • v.34 no.3
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    • pp.335-350
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    • 1997
  • In this article, a scattering problem in a nonhomogeneous medium is formulated as an integral equation which contains boundary and volume integrals. The integral equation is solved for sufficiently small $$\mid$$\mid$1-p$\mid$$\mid$,$\mid$$\mid${k_i}^2-k^2$\mid$$\mid$\;and\;$\mid$$\mid${\nabla}p$\mid$$\mid$$ where $k,\;k_i$ and p the wave numbers and the density respectively.

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Prediction of Radiative Heat Transfer in a Three-Dimensional Gas Turbine Combustor with the Finite-Volume Method (유한체적법에 의한 복잡한 형상을 갖는 3차원 가스터빈 연속기내의 복사열 전달 해석)

  • Kim, Man-Yeong;Baek, Seung-Uk
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.20 no.8
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    • pp.2681-2692
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    • 1996
  • The finite-volume method for radiation in a three-dimensional non-orthogonal gas turbine combustion chamber with absorbing, emitting and anisotropically scattering medium is presented. The governing radiative transfer equation and its discretization equation using the step scheme are examined, while geometric relations which transform the Cartesian coordinate to a general body-fitted coordinate are provided to close the finite-volume formulation. The scattering phase function is modeled by a Legendre polynomial series. After a benchmark solution for three-dimensional rectangular combustor is obtained to validate the present formulation, a problem in three-dimensional non-orthogonal gas turbine combustor is investigated by changing such parameters as scattering albedo, scattering phase function and optical thickness. Heat flux in case of isotropic scattering is the same as that of non-scattering with specified heat generation in the medium. Forward scattering is found to produce higher radiative heat flux at hot and cold wall than backward scattering and optical thickness is also shown to play an important role in the problem. Results show that finite-volume method for radiation works well in orthogonal and non-orthogonal systems.

New Resonance Scattering Theory of Electromagnetic Waves for a Homogeneous Dielectric Cylinder (원통형 유전체에 대한 전자기파의 새로운 공진산란 이론)

  • 정용화;안창희;최명선
    • Proceedings of the Korea Electromagnetic Engineering Society Conference
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    • 2001.11a
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    • pp.332-336
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    • 2001
  • The new RST is recently developed by the product expansion of the scattering functions in the field of acoustics. The new formulation suggests that the scattering coefficients consist of resonance, non-resonance, and their interactional components. In the scattering problems of acoustic waves, the moduli and phase of the resonance coefficient are obtained the appropriate results through the new RST. In our recent works the new RST was successfully applied to the scattering problem of electromagnetic waves for coated conducting cylinder and sphere. In this paper, the new RST is applied to the 2-dimensional scattering problem of electromagnetic waves for a homogeneous dielectric cylinder, and the numerical results are compared with the previous RST.

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New Resonance Scattering Theory of Electromagnetic Waves for a Homogeneous Dielectric Cylinder (원통형 유전체에 대한 전자기파의 새로운 공진산란 이론)

  • 정용화;안창회;최명선
    • The Journal of Korean Institute of Electromagnetic Engineering and Science
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    • v.13 no.1
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    • pp.87-93
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    • 2002
  • The previous RST postulates that the scattering field, within each modal partial wave, comprise of the resonance and the background components. The new RST is recently developed by the product expansion of the scattering functions in the field of acoustics. The new formulation suggests that the scattering coefficients consist of resonance, non-resonance, and their interactional portions. In the scattering problems of acoustic waves, the moduli and phase of the resonance coefficient are obtained correctly by the new RST. In our recent works the new RST was successfully applied to the scattering problem of electromagnetic waves for coated conducting cylinder and sphere. In this paper, the new RST is extended to the 2-dimensional scattering problem of electromagnetic waves for a homogeneous dielectric cylinder, and the numerical results are compared with the previous RST.

ELASTIC WAVE RESONANCE SCATTERING FROM AN ELASTIC CYLINDER (탄성체로 인한 탄성파의 공명산란)

  • 이희남
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2003.05a
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    • pp.833-838
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    • 2003
  • The problem of elastic wave resonance scattering from elastic targets is studied in this paper. A new resonance formalism to extract the elastic resonance information of the target from scattered elastic waves is introduced. The proposed resonance formalism is an extension of the works developed for acoustic wave scattering problems by the author. The classical resonance scattering theory computes reasonable magnitude information of the resonances in each partial wave, but the phase behaves in somewhat irregular way, therefore, is not clearly explainable. The proposed method is developed to obtain physically meaningful magnitude and phase of the resonances. As an example problem, elastic wave scattering from an infinitely-long elastic cylinder was analyzed by the proposed method and compared to the results by RST. In case of no mode conversion, both methods generate identical magnitude. However, the new method computes exact $\pi$ radian phase shills through resonances and anti-resonances while RST produces physically unexplainable phases. In case of mode conversion, in addition to the phase even magnitudes are different. The phase shifts through resonances and antiresonances obtained by the proposed method are not exactly $\pi$ radians due to energy leak by mode conversion. But, the phases by the proposed method show reasonable and intuitively correct behavior compared to those by RST.

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Source Identification in 2-Dimensional Scattering Field Based on Inverse Problem (역문제를 이용한 2차원 산란장에서의 소스 추정)

  • Kim, Tae Yong;Lee, Hoon-Jae
    • Journal of the Korea Institute of Information and Communication Engineering
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    • v.18 no.6
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    • pp.1262-1268
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    • 2014
  • Inverse problem is very interest in the sciences and engineering, in particular for modeling and monitoring applications. By applying inverse problem, it can be widely used to exploration of mineral resources, identification of underground cables and buried pipelines, and diagnostic imaging in medical area. In this paper, we firstly consider 2-dimensional EM scattering problem and present the FDTD method to estimate unknown source. In this case, non-linear CGM technique is used to investigate unknown sources corresponding to measured data obtained from forward problem in near field. The proposed technique for solving the inverse source problem presents a reasonable agreement and can be applied to investigate an internal source signal of embedded security module.

Solution of the Inverse Electromagnetic Scattering Problem for Cylindrical Objects by Using the Resonance Scattering Ttheory (공진산란이론을 이용한 원통형 산란체에 대한 전자기파문제의 역산란 이론)

  • Jung, Yong-Hwa;Jeon, Sang-Bong;Ahn, Chang-Hoi
    • The Transactions of the Korean Institute of Electrical Engineers C
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    • v.55 no.3
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    • pp.142-148
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    • 2006
  • The resonances that contain the information on the properties of the scattering target can be used for target reconstruction approaches. The inverse scattering theory for the resonances has been applied to the problems of the scattering for a spherical, cylindrical dielectric objects and dielectrically coated conductors, shown reasonable results. Though by using this method the thickness and the dielectric constants of the target can be obtained from a determination of the spacing and of the widths of the scattering resonances, the radius of the target should be given. In this paper, we suggest the improved inverse theory combined with the resonance scattering theory to obtain the radius in addition to the dielectric constant of the target. The applications of this method for scattering problems of electromagnetic waves from cylindrical targets were accomplished, and it shows its validity.