• Title/Summary/Keyword: Matrix transformations

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Phase Transformations and Oxidation Properties of Fe$_{0.98}$Mn$_{0.02}$Si$_2$ Processed by Mechanical Alloying (기계적 합금화법에 의해 제조된 Fe$_{0.98}$Mn$_{0.02}$Si$_2$의 상변태와 산화특성)

  • 심웅식;이동복;어순철
    • Journal of the Korean institute of surface engineering
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    • v.36 no.2
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    • pp.200-205
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    • 2003
  • Thermoelectric p-type $Fe_{0.98}$ $Mn_{ 0.02}$$Si_2$ bulk specimens have been produced by mechanical alloying and consolidation by vacuum hot pressing. The subsequent isothermal annealing was not able to fully transform the mestastable as -milled powders into the $\beta$ $-FeSi_2$ phase, so that the obtained matrix consisted of not only thermoelectric semiconducting $\beta$-FeSi$_2$ but also some residual, untransformed metallic $\alpha$ $- Fe_2$$Si_{ 5}$ and $\varepsilon$-FeSi mixtures. Interestingly, $\beta$ - $FeSi_2$ was more easily obtained in the low density specimen when compared to the high density specimen. The oxidation at 700 and $800^{\circ}C$ in air led to the phase transformation of the above described iron - silicides and the formation of a thin silica surface layer.

Phase Transformation in Al-4at.%Zr Alloy during Mechanical Alloying and Heat-treatment Processes (Al-4at.%Zr합금의 기계적합금화 공정과 열처리과정에서 발생하는 상변화거동)

  • Park, Jae-Pil;Kim, Il-Ho;Kwun, S.I.
    • Journal of Powder Materials
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    • v.12 no.1
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    • pp.36-42
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    • 2005
  • Four different mechanical alloying(MA) processes were employed to fabricate very fine intermetallic compound $Al_3Zr$ particles dispersed Al composite materials(MMC) with Al-4at.%Zr composition. Phase transformations including phase stability during MA and heat treatment processes were investigated. Part of Zr atoms were dissolved into Al matrix and part of them reacted with hydrogen produced by decomposition of PCA(methanol) to form hydride $ZrH_2$ during first MA process. These $ZrH_2$ hydrides disappeared when alloy powders were heat treated at $500^{\circC}$. Stable $Al_3Zr$ dispersoids with $DO_23$ structure were formed by heat treating the mechanically alloyed powders at $400^{\circC}$. On the other hand, metastable $Al_3Zr$dispersoids with $L1_2$ structure were formed during first MA of powers with Al-25at.%Zr composition. These metastable $Al_3Zr$ dispersoids transformed to stable $Al_3Zr$ with $DO_23$ structure when heat treated above $450^{\circC}$.

Evaluation of vertical dynamic characteristics of cantilevered tall structures

  • Li, Q.S.;Xu, J.Y.;Li, G.Q.
    • Structural Engineering and Mechanics
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    • v.11 no.4
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    • pp.357-372
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    • 2001
  • In this paper, cantilevered tall structures are treated as cantilever bars with varying cross-section for the analysis of their free longitudinal (or axial) vibrations. Using appropriate transformations, exact analytical solutions to determine the longitudinal natural frequencies and mode shapes for a one step non-uniform bar are derived by selecting suitable expressions, such as exponential functions, for the distributions of mass and axial stiffness. The frequency equation of a multi-step bar is established using the approach that combines the transfer matrix procedure or the recurrence formula and the closed-form solutions of one step bars, leading to a single frequency equation for any number of steps. The Ritz method is also applied to determine the natural frequencies and mode shapes in the vertical direction for cantilevered tall structures with variably distributed stiffness and mass. The formulae proposed in this paper are simple and convenient for engineering applications. Numerical example shows that the fundamental longitudinal natural frequency and mode shape of a 27-storey building determined by the proposed methods are in good agreement with the corresponding measured data. It is also shown that the selected expressions are suitable for describing the distributions of axial stiffness and mass of typical tall buildings.

State-Space Analysis on The Stability of Limit Cycle Predicted by Harmonic Balance

  • Lee, Byung-Jin;Yun, Suk-Chang;Kim, Chang-Joo;Park, Jung-Keun;Sung, Sang-Kyung
    • Journal of Electrical Engineering and Technology
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    • v.6 no.5
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    • pp.697-705
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    • 2011
  • In this paper, a closed-loop system constructed with a linear plant and nonlinearity in the feedback connection is considered to argue against its planar orbital stability. Through a state space approach, a main result that presents a sufficient stability criterion of the limit cycle predicted by solving the harmonic balance equation is given. Preliminarily, the harmonic balance of the nonlinear feedback loop is assumed to have a solution that determines the characteristics of the limit cycle. Using a state-space approach, the nonlinear loop equation is reformulated into a linear perturbed model through the introduction of a residual operator. By considering a series of transformations, such as a modified eigenstructure decomposition, periodic averaging, change of variables, and coordinate transformation, the stability of the limit cycle can be simply tested via a scalar function and matrix. Finally, the stability criterion is addressed by constructing a composite Lyapunov function of the transformed system.

A Study on the Thermal Behavior and Phase Transformation of Iron-bearing Minerals in Clay of Cheju Island by M ssbauer Effect (M ssbauer 효과에 의한 제주도 찰흙의 함철 광물의 열적 거동과 상변환에 관한 연구)

  • 강동우;김두철;류재연;고정대;홍성락;송관철
    • Journal of the Mineralogical Society of Korea
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    • v.10 no.2
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    • pp.148-161
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    • 1997
  • Based on the X-ray powder diffraction (XRD) and M ssbauer spectroscopy, the thermal behavior and phase transformations of two clays are investigated for raw and fired conditions, which are collected from Kwangryeongli and Ildo district in Cheju Island. M ssbauer spectra at room temperature and 20for two clays show that paramagnetic Fe3- is the structural iron of the layer silicate and ferrihydrite, and superparamagnetic goethite has about 50% of total iron contents. The XRD peaks of hematite for the fired clays appear from 80$0^{\circ}C$ in Kwangryeongli clay and from $600^{\circ}C$ in Ildo district clay, respectively. The structural Fe2+ was completely oxidized into Fe3- at 40$0^{\circ}C$ for Kwangryeongli clay and 50$0^{\circ}C$~$600^{\circ}C$ for Ildo district clay, respectively. The structural Fe2+ was completely oxidized into Fe3- at 40$0^{\circ}C$. For the temperature ranging from 40$0^{\circ}C$ to $700^{\circ}C$~80$0^{\circ}C$, two fired clays exhibit the dehydroxylation of the clay mineral. A disintegration of the clay mineral structure is observed from $700^{\circ}C$~80$0^{\circ}C$ to 110$0^{\circ}C$, followed by the onset and spread of vitrification process. It is also shown that well-crystallized hematite phase is formed at the temperature higher than 110$0^{\circ}C$ and the relative absorption area decreases, which might be related to the recrystallization of alluminosilicate matrix.

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Probabilistic Constrained Approach for Distributed Robust Beamforming Design in Cognitive Two-way Relay Networks

  • Chen, Xueyan;Guo, Li;Dong, Chao;Lin, Jiaru;Li, Xingwang;Cavalcante, Charles Casimiro
    • KSII Transactions on Internet and Information Systems (TIIS)
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    • v.12 no.1
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    • pp.21-40
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    • 2018
  • In this paper, we propose the distributed robust beamforming design scheme in cognitive two-way amplify-and-forward (AF) relay networks with imperfect channel state information (CSI). Assuming the CSI errors follow a complex Gaussian distribution, the objective of this paper is to design the robust beamformer which minimizes the total transmit power of the collaborative relays. This design will guarantee the outage probability of signal-to-interference-plus-noise ratio (SINR) beyond a target level at each secondary user (SU), and satisfies the outage probability of interference generated on the primary user (PU) above the predetermined maximum tolerable interference power. Due to the multiple CSI uncertainties in the two-way transmission, the probabilistic constrained optimization problem is intractable and difficult to obtain a closed-form solution. To deal with this, we reformulate the problem to the standard form through a series of matrix transformations. We then accomplish the problem by using the probabilistic approach based on two sorts of Bernstein-type inequalities and the worst-case approach based on S-Procedure. The simulation results indicate that the robust beamforming designs based on the probabilistic method and the worst-case method are both robust to the CSI errors. Meanwhile, the probabilistic method can provide higher feasibility rate and consumes less power.

Phase Transformation of 2 Components(CaO-, $Y_2O_3$-, MgO-$ZrO_2$) and 3 Components(MgO-$ZrO_2-Al_2O_3)$ Zirconia by X-ray Diffraction and Raman Spectroscopy (X-선회절과 Raman 분광분석을 이용한 2성분계(CaO-, $Y_2O_3$-, MgO-$ZrO_2$) 및 3성분계(MgO-$ZrO_2-Al_2O_3)$ Zirconia의 상전이연구)

  • 은희태;황진명
    • Journal of the Korean Ceramic Society
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    • v.34 no.2
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    • pp.145-156
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    • 1997
  • ZrO2 phase transformations depending on the type and amount of dopants and the sintering temperatures were studied for the 2 components (CaO-, Y2O3-, MgO-ZrO2) and the 3 components(MgO-ZrO2-Al2O3)ZrO2 powder by X-ray diffraction and Raman spectroscopy. In the CaO- and Y2O3-ZrO2 systems, as the CaO and Y2O3 contents increased to 6~15mol% and 3~15mol% respectively, we were not able to identify between tetragonal and cubic in the X-ray diffraction patterns. On the other hand, all Raman modes shifted to lower wavenumbers, decreasing in intensity and the number of bands, markedly. These phenomena were caused by tetragonallongrightarrowcubic phase transformation and interpreted by the breakdown of the wave vector selection rule(k=0) and the structural disorder associated with the formation of oxygen sublattice which was caused by the substitution between Zr4+ ion and Ca2+ or Y3+ ion in ZrO2 matrix. The monoclinic to cubic phase transformation occurred in 10mol% MgO-ZrO2 system. As the Al2O3 content increased from 0 to 20mol% in the MgO-ZrO2-Al2O3 systems, cubic phase transformed to monoclinic phase, this is because the MgO didn't play a role in a stabilizer because of the formation of the spinel(MgAl2O4) by the reaction between MgO and Al2O3, Also, the ZrO2 phase transformation was explained by the change of it's lattice parameters depending on the type and amount of dopants. Namely, as the amount of dopant increased to 10~13mol%, the axial ra-tio c/a came close to unity with increasing the lattice parameter a and decreasing the lattice parameter c. At that time, the tetragonallongrightarrowcubic phase transformation occurred.

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