• 제목/요약/키워드: Tensor Analysis

검색결과 271건 처리시간 0.023초

STATIC AND RELATED CRITICAL SPACES WITH HARMONIC CURVATURE AND THREE RICCI EIGENVALUES

  • Kim, Jongsu
    • 대한수학회지
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    • 제57권6호
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    • pp.1435-1449
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    • 2020
  • In this article we make a local classification of n-dimensional Riemannian manifolds (M, g) with harmonic curvature and less than four Ricci eigenvalues which admit a smooth non constant solution f to the following equation $$(1)\hspace{20}{\nabla}df=f(r-{\frac{R}{n-1}}g)+x{\cdot} r+y(R)g,$$ where ∇ is the Levi-Civita connection of g, r is the Ricci tensor of g, x is a constant and y(R) a function of the scalar curvature R. Indeed, we showed that, in a neighborhood V of each point in some open dense subset of M, either (i) or (ii) below holds; (i) (V, g, f + x) is a static space and isometric to a domain in the Riemannian product of an Einstein manifold N and a static space (W, gW, f + x), where gW is a warped product metric of an interval and an Einstein manifold. (ii) (V, g) is isometric to a domain in the warped product of an interval and an Einstein manifold. For the proof we use eigenvalue analysis based on the Codazzi tensor properties of the Ricci tensor.

이차적인 변형률효과를 나타내는 새로운 변수의 제안 (Proposal of a New Parameter for Extra Straining Effects)

  • 명현국
    • 대한기계학회논문집
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    • 제18권1호
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    • pp.184-192
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    • 1994
  • The parameters such as Richardson numbers or stability parameters are widely used to account for the extra straining effects due to three-dimensionality, curvature, rotation, swirl and others arising in paractical complex flows. Existing expressions for the extra strain in turbulence models such as $k-{\epsilon}$ models, however, do not satisfy the tensor invariant condition representing the coordinate indifference. In the present paper, considering the characteristics of both the mean strain rate and the mean vorticity, a new parameter to deal with the extra straining effects is proposed. The new parameter has a simple form and satisfies the tensor invariant condition. A semi-quantitative analysis between the present and previous parameters for several typical complex flows suggests that the newly proposed parameter is more general and adequate in representing the extra straining effects than the previous ad-hoc parameters.

익단 누설 와류내의 레이놀즈 응력 분포 (Distribution of the Reynolds Stress Tensor inside Tip Leakage Vortex)

  • 이공희;박종일;백제현
    • 유체기계공업학회:학술대회논문집
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    • 유체기계공업학회 2003년도 유체기계 연구개발 발표회 논문집
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    • pp.496-501
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    • 2003
  • Reynolds averaged Wavier-Stokes simulations based on the Reynolds stress model was performed to investigated the effect of inlet flow angle on the distributions of the Reynolds stress tensor inside tip leakage vortex of a linear compressor cascade. Two different inlet flow angles ${\beta}=29.3^{\circ}$(design condition) and $36.5^{\circ}$(off-design condition) were considered. Stress tensor analysis, which transforms the Reynolds stress into the principal direction, was applied to show an anisotropy of the normal stresses. Whereas the anisotropy was highest in the region where the tip leakage vortex collides the suction side of the blade and tip leakage flow enters between blade tip of the pressure side and the endwall, it had the lowest value at the center of tip leakage vortex. It was also found that the magnitude of maximum shear stress at design condition was greater than that of off-design condition.

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Estimation of the Ratio of Nonlinear Optical Tensor Components by Measuring Second Harmonic Generation and Parametric Down Conversion Outputs in a Single Periodically Poled LiNbO3 Crystal

  • Kumar, CH. S.S. Pavan;Kim, Jiung;Kim, Byoung Joo;Cha, Myoungsik
    • Current Optics and Photonics
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    • 제2권6호
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    • pp.606-611
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    • 2018
  • Measurement of the nonlinear optical coefficients is not an easy task since it requires complicated experimental setup and analysis. We suggest an easy way to estimate the relative nonlinear optical tensor components by direct measurement of the output powers of the second harmonic generation and spontaneous parametric down conversion experiments. The experiments were done in quasi-phase-matched type-0 as well as type-1 interactions at similar pump wavelengths in a 5% MgO-doped periodically poled $LiNbO_3$ crystal to obtain the ratio of the nonlinear optical tensor components $d_{33}/d_{31}$ in each experiment. The obtained ratios were then compared with the previously ascertained values [J. Opt. Soc. Am. B, 14, 2268-2294 (1997)].

일산화탄소중독 이후 발생한 지연무산소뇌병증: 확산텐서영상 및 신경인지기능검사를 이용한 치료 효과의 평가 (Delayed Anoxic Encephalopathy after Carbon Monoxide Poisoning: Evaluation of Therapeutic Effect by Serial Diffusion-Tensor Magnetic Resonance Imaging and Neurocognitive Test)

  • 유호성;김영욱;정부경;김용원
    • 대한신경과학회지
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    • 제36권4호
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    • pp.358-362
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    • 2018
  • Delayed anoxic encephalopathy after carbon monoxide (CO) poisoning is characterized by neurological deterioration that occurs after recovery from acute CO intoxication. There has been no established therapy. We report a patient recovered from acute CO intoxication developed various neurological symptoms. After the administration of high dose prednisolone and anticholinesterase inhibitor, the therapeutic effect was remarkable and confirmed by quantitative analysis of diffusion-tensor imaging (DTI). DTI could be used to evaluate the therapeutic effect for delayed anoxic encephalopathy after CO poisoning.

Concerning the tensor-based flexural formulation: Theory

  • Al-Rousan, Rajai Z.;Alhassan, Mohammed A.;Hejazi, Moheldeen A.
    • Structural Engineering and Mechanics
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    • 제70권4호
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    • pp.445-455
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    • 2019
  • Since the days of yore, plate's flexural analysis and formulation were dependent on the assumed coordinate system. In uncovering the coordinates-independent flexural interpretation, in this study, the plate bending analysis has been interpreted in terms of the tensor's components of curvatures and bending moments, in accordance with the continuum mechanics. The paper herein presents the theoretical formulations and conceptual perspectives of the Hydrostatic Method of Analysis (HM) that combines the continuum mechanics with the elasticity theory; the graphical statics and analysis; the theory of thin isotropic and orthotropic plates.

A Computationally Efficient Finite Element Analysis Algorithm Considering 2-D Magnetic Properties of Electrical Steel Sheet

  • Yao, Yingying;Li, Wei;Yoon, Hee-Sung;Fujiwara, Koji;Koh, Chang-Seop
    • Journal of Electrical Engineering and Technology
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    • 제3권3호
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    • pp.385-390
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    • 2008
  • For taking account of the two-dimensional magnetic properties of a grain-oriented electrical steel sheet, the effective anisotropic tensor reluctivity is examined, and a computationally efficient algorithm is suggested by using the response surface method to model the two-dimensional magnetic properties. It is shown that the reconstructed two-dimensional magnetic properties are fairly effective to stabilize the convergence characteristics of the Newton-Raphson iteration in the nonlinear magnetic field analysis.