• Title/Summary/Keyword: J-A$_2$ theory

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Variation of A2 with Crack Propagation in a Ductile Metal; Experimental Evaluation (연성재료의 균열진전에 따른 A2의 변화; 실험적 측정)

  • Kim, Heon-Joong;Kim, Dong-Hak;Yang, Kyeong-Jin;Kang, Ki-Ju
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.27 no.1
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    • pp.119-125
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    • 2003
  • A way to measure the second parameter $A_2$of CT specimens is described. The displacement $\delta$$_{5}$ which is measured continuously from visual images of the lateral surface during crack growth is used to calculate the A, as a function of crack growth. The crack length is measured by DCPD(Direct Current Potential Drop) method and the J-resistance curve is determined according to ASTM standard E1737-96. To prove the validity of this method, three dimensional finite element analyses were performed, and variations of the displacements $\delta$$_{5}$ and $A_2$along the thickness were explored. As the result, it has been shown that the $\delta$$_{5}$ measured from the visual images of the lateral surface and the corresponding $A_2$can be regarded as the average through the thickness for 1T and 1/2T specimens of SA106Gr.C steel.steel.

Jacket Matrix in Hyperbola (쌍곡선에서의 재킷 행렬)

  • Yang, Jae-Seung;Park, Ju-Yong;Lee, Moon-Ho
    • The Journal of the Institute of Internet, Broadcasting and Communication
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    • v.15 no.3
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    • pp.15-24
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    • 2015
  • Jacket matrices which are defined to be $m{\times}m$ matrices $J^{\dagger}=[J_{ik}^{-1}]^T$ over a Galois field F with the property $JJ^{\dagger}=mI_m$, $J^{\dagger}$ is the transpose matrix of element-wise inverse of J, i.e., $J^{\dagger}=[J_{ik}^{-1}]^T$, were introduced by Lee in 1984 and are used for Digital Signal Processing and Coding theory. This paper presents some square matrices $A_2$ which can be eigenvalue decomposed by Jacket matrices. Specially, $A_2$ and its extension $A_3$ can be used for modifying the properties of hyperbola and hyperboloid, respectively. Specially, when the hyperbola has n times transformation, the final matrices $A_2^n$ can be easily calculated by employing the EVD[7] of matrices $A_2$. The ideas that we will develop here have applications in computer graphics and used in many important numerical algorithms.

STABILITY THEOREM FOR THE FEYNMAN INTEGRAL APPLIED TO MULTIPLE INTEGTALS

  • Kim, Bong-Jin
    • The Pure and Applied Mathematics
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    • v.8 no.1
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    • pp.71-78
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    • 2001
  • In 1984, Johnson[A bounded convergence theorem for the Feynman in-tegral, J, Math. Phys, 25(1984), 1323-1326] proved a bounded convergence theorem for hte Feynman integral. This is the first stability theorem of the Feynman integral as an $L(L_2 (\mathbb{R}^N), L_2(\mathbb{R}^{N}))$ theory. Johnson and Lapidus [Generalized Dyson series, generalized Feynman digrams, the Feynman integral and Feynmans operational calculus. Mem, Amer, Math, Soc. 62(1986), no 351] studied stability theorems for the Feynman integral as an $L(L_2 (\mathbb{R}^N), L_2(\mathbb{R}^{N}))$ theory for the functional with arbitrary Borel measure. These papers treat functionals which involve only a single integral. In this paper, we obtain the stability theorems for the Feynman integral as an $L(L_1 (\mathbb{R}^N), L_{\infty}(\mathbb{R}^{N}))$theory for the functionals which involve double integral with some Borel measures.

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Algorithm for identifying cross-linked protein subsequences (크로스 링크된 단백질 서브시퀀스를 찾는 알고리즘)

  • Kim, Sung-Kwon
    • Journal of KIISE:Computer Systems and Theory
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    • v.29 no.9
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    • pp.514-519
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    • 2002
  • We are considering the following problem that can be used in the prediction of the structure of proteins. Given two length n arrays A, B with positive numbers and a positive number M, find all pairs of subarrays A[i]+…A[j],$1{\leq}i{\leq}j{\leq}n$ such that A[i]+…A[j]+B[k]+…B[l]=M. This paper presents an algorithm with $Ο(n^2log n+K)$ time using Ο(n) memory, where K is the number of pairs output. The previously best known one is with $Ο(n^2log +Klog n)$ time and Ο(n) memory.

RELATIVE ROTA-BAXTER SYSTEMS ON LEIBNIZ ALGEBRAS

  • Apurba Das;Shuangjian Guo
    • Journal of the Korean Mathematical Society
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    • v.60 no.2
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    • pp.303-325
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    • 2023
  • In this paper, we introduce relative Rota-Baxter systems on Leibniz algebras and give some characterizations and new constructions. Then we construct a graded Lie algebra whose Maurer-Cartan elements are relative Rota-Baxter systems. This allows us to define a cohomology theory associated with a relative Rota-Baxter system. Finally, we study formal deformations and extendibility of finite order deformations of a relative Rota-Baxter system in terms of the cohomology theory.

THE 3D BOUSSINESQ EQUATIONS WITH REGULARITY IN THE HORIZONTAL COMPONENT OF THE VELOCITY

  • Liu, Qiao
    • Bulletin of the Korean Mathematical Society
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    • v.57 no.3
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    • pp.649-660
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    • 2020
  • This paper proves a new regularity criterion for solutions to the Cauchy problem of the 3D Boussinesq equations via one directional derivative of the horizontal component of the velocity field (i.e., (∂iu1; ∂ju2; 0) where i, j ∈ {1, 2, 3}) in the framework of the anisotropic Lebesgue spaces. More precisely, for 0 < T < ∞, if $$\large{\normalsize\displaystyle\smashmargin{2}{\int\nolimits_o}^T}({\HUGE\left\|{\small{\parallel}{\partial}_iu_1(t){\parallel}_{L^{\alpha}_{x_i}}}\right\|}{\small^{\gamma}_{L^{\beta}_{x_{\hat{i}}x_{\bar{i}}}}+}{\HUGE\left\|{\small{\parallel}{\partial}_iu_2(t){\parallel}_{L^{\alpha}_{x_j}}}\right\|}{\small^{\gamma}_{L^{\beta}_{x_{\hat{i}}x_{\bar{i}}}}})dt<{{\infty}},$$ where ${\frac{2}{{\gamma}}}+{\frac{1}{{\alpha}}}+{\frac{2}{{\beta}}}=m{\in}[1,{\frac{3}{2}})$ and ${\frac{3}{m}}{\leq}{\alpha}{\leq}{\beta}<{\frac{1}{m-1}}$, then the corresponding solution (u, θ) to the 3D Boussinesq equations is regular on [0, T]. Here, (i, ${\hat{i}}$, ${\tilde{i}}$) and (j, ${\hat{j}}$, ${\tilde{j}}$) belong to the permutation group on the set 𝕊3 := {1, 2, 3}. This result reveals that the horizontal component of the velocity field plays a dominant role in regularity theory of the Boussinesq equations.

MODEL BASED DIAGNOSTICS FOR A GEARBOX USING INFORMATION THEORY

  • Choi, J.;Bryant, M.D.
    • Proceedings of the Korean Society of Tribologists and Lubrication Engineers Conference
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    • 2002.10b
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    • pp.459-460
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    • 2002
  • This article discusses a diagnostics method based on models, and information theory. From an extensive system dynamics bond graph model of a gearbox [1], simulated were various cases germane to this diagnostics approach, including the response of an ideal gearbox, which functions perfectly to designer's specifications, and degraded gearboxes with tooth root cracking. By comparing these cases and constructing a signal flow analogy between the gearbox and a communication channel, Shannon' s information theory [2], including theorems, was applied to the gearbox to assess system health, in terms of ability to function.

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EVELOPMENT OF AXISYMMETRIC MULTI-SPECIES GH EQUATION FOR HYPERSONIC RAREFIED FLOW ANALYSES (극초음속 희박유동 해석을 위한 축대칭 다화학종 GH 방정식의 개발)

  • Ahn, J.W.;Kim, C.
    • 한국전산유체공학회:학술대회논문집
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    • 2008.03a
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    • pp.84-91
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    • 2008
  • Generalized hydrodynamic (GH) theory for multi-species gas and the computational models are developed for the numerical simulation of hypersonic rarefied gas flow on the basis of Eu's GH theory. The rotational non-equilibrium effect of diatomic molecules is taken into account by introducing excess normal stress associated with the bulk viscosity. The numerical model for the diatomic GH theory is developed and tested. Moreover, with the experience of developing the dia-tomic GH computational model, the GH theory is extended to a multi-species gas including 5 species; O$_2$, N$_2$, NO, O, N. The multi-species GH model includes diffusion relation due to the molecular collision and thermal phenomena. Two kinds of GH models are developed for an axisymmetric flow solver. By compar-ing the computed results of diatomic and multi-species GH theories with those of the Navier-Stokes equations and the DSMC results, the accuracy and physical consistency of the GH computational models are examined.

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EVELOPMENT OF AXISYMMETRIC MULTI-SPECIES GH EQUATION FOR HYPERSONIC RAREFIED FLOW ANALYSES (극초음속 희박유동 해석을 위한 축대칭 다화학종 GH 방정식의 개발)

  • Ahn, J.W.;Kim, C.
    • 한국전산유체공학회:학술대회논문집
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    • 2008.10a
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    • pp.84-91
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    • 2008
  • Generalized hydrodynamic (GH) theory for multi-species gas and the computational models are developed for the numerical simulation of hypersonic rarefied gas flow on the basis of Eu's GH theory. The rotational non-equilibrium effect of diatomic molecules is taken into account by introducing excess normal stress associated with the bulk viscosity. The numerical model for the diatomic GH theory is developed and tested. Moreover, with the experience of developing the dia-tomic GH computational model, the GH theory is extended to a multi-species gas including 5 species; $O_2,\;N_2$, NO, O, N. The multi-species GH model includes diffusion relation due to the molecular collision and thermal phenomena. Two kinds of GH models are developed for an axisymmetric flow solver. By compar-ing the computed results of diatomic and multi-species GH theories with those of the Navier-Stokes equations and the DSMC results, the accuracy and physical consistency of the GH computational models are examined.

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The use of network theory to model disparate ship design information

  • Rigterink, Douglas;Piks, Rebecca;Singer, David J.
    • International Journal of Naval Architecture and Ocean Engineering
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    • v.6 no.2
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    • pp.484-495
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    • 2014
  • This paper introduces the use of network theory to model and analyze disparate ship design information. This work will focus on a ship's distributed systems and their intra- and intersystem structures and interactions. The three system to be analyzed are: a passageway system, an electrical system, and a fire fighting system. These systems will be analyzed individually using common network metrics to glean information regarding their structures and attributes. The systems will also be subjected to community detection algorithms both separately and as a multiplex network to compare their similarities, differences, and interactions. Network theory will be shown to be useful in the early design stage due to its simplicity and ability to model any shipboard system.