• Title/Summary/Keyword: Green function

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THE GREEN FUNCTION AND THE SZEGŐ KERNEL FUNCTION

  • Chung, Young-Bok
    • Honam Mathematical Journal
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    • v.36 no.3
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    • pp.659-668
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    • 2014
  • In this paper, we express the Green function in terms of the classical kernel functions in potential theory. In particular, we obtain a formula relating the Green function and the Szegő kernel function which consists of only the Szegő kernel function in a $C^{\infty}$ smoothly bounded finitely connected domain in the complex plane.

Non-Equilibrium Green Function Method in Spin Transfer Torque

  • You, Chun-Yeol
    • Journal of Magnetics
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    • v.12 no.2
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    • pp.72-76
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    • 2007
  • We investigate the spin transfer torque in metallic multilayer system by employing Keldysh non-equilibrium Green function method. We study the dependences of the spin transfer torque on the detailed energy configuration of ferromagnetic, spacer, and lead layers. With Keldysh non-equilibrium Green function method applied to a single band model, we explore spin transfer torque effect in various layer structures and for various material parameters.

Analysis of added resistance of a ship advancing in waves (파랑중에서 전진하는 선박의 부가저항 해석)

  • 이호영;곽영기
    • Journal of Ocean Engineering and Technology
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    • v.11 no.2
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    • pp.91-99
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    • 1997
  • This paper presents theoretical formulations and numerical computations for predicting first-and second-order hydrodynamic force on a ship advvancing in waves. The theoretical formulation leads to linearized radiation and diffration problems solving the three-dimensional Green function integral equations over the mean wetted body surface. Green function representing a translating and pulsating source potantial for infinite water depth is used. In order to solve integral equations for three dimentional flows using Green function efficiently, the Hoff's method is adopted for numerical calculation of the Green function. Based on the first-order solution, the mean seconder-order forces and moments are obtained by directly integrating second-order pressure over the mean wetted body surface. The calculated items are carried out for analyzing the seakeeping characteristics of Series 60. The calculated items are hydrodynamic coefficients, wave exciting forces, frequency response functions and addd resistance in waves.

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A Representation of Green Function Using Discrete Wavelet Concept for Fast Field Analysis (고속 전자파 해석을 위한 그린 함수의 이산 웨이블릿 표현법)

  • Kim Hyung-Hoon;Park Jong-Il;Kim Hyeong-Dong
    • The Journal of Korean Institute of Electromagnetic Engineering and Science
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    • v.17 no.9 s.112
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    • pp.895-899
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    • 2006
  • A compact representation of Green function is proposed by applying the discrete wavelet concept in the k-domain, which can be used for the acceleration of scattered field calculations in integral equation methods. Since the representation of Green function is very compact in the joint spatio-spectral domain, it can be effectively utilized in the fast computation of radiation integral of electromagnetic problems. A mathematical expression of Green function based on the discrete wavelet concept is derived and its characteristics are discussed.

A more efficient numerical evaluation of the green function in finite water depth

  • Xie, Zhitian;Liu, Yujie;Falzarano, Jeffrey
    • Ocean Systems Engineering
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    • v.7 no.4
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    • pp.399-412
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    • 2017
  • The Gauss-Legendre integral method is applied to numerically evaluate the Green function and its derivatives in finite water depth. In this method, the singular point of the function in the traditional integral equation can be avoided. Moreover, based on the improved Gauss-Laguerre integral method proposed in the previous research, a new methodology is developed through the Gauss-Legendre integral. Using this new methodology, the Green function with the field and source points near the water surface can be obtained, which is less mentioned in the previous research. The accuracy and efficiency of this new method is investigated. The numerical results using a Gauss-Legendre integral method show good agreements with other numerical results of direct calculations and series form in the far field. Furthermore, the cases with the field and source points near the water surface are also considered. Considering the computational efficiency, the method using the Gauss-Legendre integral proposed in this paper could obtain the accurate numerical results of the Green function and its derivatives in finite water depth and can be adopted in the near field.

FRACTIONAL GREEN FUNCTION FOR LINEAR TIME-FRACTIONAL INHOMOGENEOUS PARTIAL DIFFERENTIAL EQUATIONS IN FLUID MECHANICS

  • Momani, Shaher;Odibat, Zaid M.
    • Journal of applied mathematics & informatics
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    • v.24 no.1_2
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    • pp.167-178
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    • 2007
  • This paper deals with the solutions of linear inhomogeneous time-fractional partial differential equations in applied mathematics and fluid mechanics. The fractional derivatives are described in the Caputo sense. The fractional Green function method is used to obtain solutions for time-fractional wave equation, linearized time-fractional Burgers equation, and linear time-fractional KdV equation. The new approach introduces a promising tool for solving fractional partial differential equations.

An Application of k-domain Discrete Wavelet Transform for the Efficient Representation of Green Function (파수영역 이산 웨이블릿 변환을 이용한 효율적인 그린함수 표현에 관한 연구)

  • 주세훈;김형동
    • The Journal of Korean Institute of Electromagnetic Engineering and Science
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    • v.12 no.7
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    • pp.1110-1114
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    • 2001
  • The discrete wavelet concept in the k-domain is applied to efficiently represent Green function of integral equations. Application of discrete wavelet concept to Green function in the k-domain can be implemented equivalently by using spatial domain variable-sized windows. The proposed method consists of constant Q-filtering, changing the center of coordinates, and transforming spatially filtered Green functions into those in the k-domain. A mathematical expression of Green function based on the discrete wavelet concept is derived and its characteristics are discussed.

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THE SPACE-TIME FRACTIONAL DIFFUSION EQUATION WITH CAPUTO DERIVATIVES

  • HUANG F.;LIU F.
    • Journal of applied mathematics & informatics
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    • v.19 no.1_2
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    • pp.179-190
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    • 2005
  • We deal with the Cauchy problem for the space-time fractional diffusion equation, which is obtained from standard diffusion equation by replacing the second-order space derivative with a Caputo (or Riemann-Liouville) derivative of order ${\beta}{\in}$ (0, 2] and the first-order time derivative with Caputo derivative of order ${\beta}{\in}$ (0, 1]. The fundamental solution (Green function) for the Cauchy problem is investigated with respect to its scaling and similarity properties, starting from its Fourier-Laplace representation. We derive explicit expression of the Green function. The Green function also can be interpreted as a spatial probability density function evolving in time. We further explain the similarity property by discussing the scale-invariance of the space-time fractional diffusion equation.

Fast Scattered-Field Calculation using Windowed Green Functions (윈도우 그린함수를 이용한 고속 산란필드 계산)

  • 주세훈;김형훈;김형동
    • The Journal of Korean Institute of Electromagnetic Engineering and Science
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    • v.12 no.7
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    • pp.1122-1130
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    • 2001
  • In this paper, by applying the spectral domain wavelet concept to Green function, a fast spectral domain calculation of scattered fields is proposed to get the solution for the radiation integral. The spectral domain wavelet transform to represent Green function is implemented equivalently in space via the constant-Q windowing technique. The radiation integral can be calculated efficiently in the spectral domain using the windowed Green function expanded by its eigen functions around the observation region. Finally, the same formulation as that of the conventional fast multipole method (FMM) is obtained through the windowed Green function and the spectral domain calculation of the radiation integral.

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The effect of small forward speed on prediction of wave loads in restricted water depth

  • Guha, Amitava;Falzarano, Jeffrey
    • Ocean Systems Engineering
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    • v.6 no.4
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    • pp.305-324
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    • 2016
  • Wave load prediction at zero forward speed using finite depth Green function is a well-established method regularly used in the offshore and marine industry. The forward speed approximation in deep water condition, although with limitations, is also found to be quite useful for engineering applications. However, analysis of vessels with forward speed in finite water depth still requires efficient computing methods. In this paper, a method for analysis of wave induced forces and corresponding motion on freely floating three-dimensional bodies with low to moderate forward speed is presented. A finite depth Green function is developed and incorporated in a 3D frequency domain potential flow based tool to allow consideration of finite (or shallow) water depth conditions. First order forces and moments and mean second order forces and moments in six degree of freedom are obtained. The effect of hull flare angle in predicting added resistance is incorporated. This implementation provides the unique capability of predicting added resistance in finite water depth with flare angle effect using a Green function approach. The results are validated using a half immersed sphere and S-175 ship. Finally, the effect of finite depth on a tanker with forward speed is presented.