• Journal of the Korean Ceramic Society
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• v.49 no.1
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• pp.29-36
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• 2012

In many applications of functional oxides originally homogeneous materials are exposed to gradients in the chemical potential of oxygen. Prominent examples are solid oxide fuel cells (SOFCs) or oxygen permeation membranes (OPMs). Other thermodynamic potential gradients are gradients of electrical potential, temperature or uni-axial pressure. The applied gradients act as generalized thermodynamic forces and induce directed fluxes of the mobile components. These fluxes may lead to three basic degradation phenomena of the materials, which are kinetic demixing, kinetic decomposition, and morphological instabilities.

• Steel and Composite Structures
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• v.26 no.6
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• pp.663-672
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• 2018

This paper contains a consistent couple-stress theory to capture size effects in Euler-Bernoulli nano-beams made of three-directional functionally graded materials (TDFGMs). These models can degenerate into the classical models if the material length scale parameter is taken to be zero. In this theory, the couple-stress tensor is skew-symmetric and energy conjugate to the skew-symmetric part of the rotation gradients as the curvature tensor. The material properties except Poisson's ratio are assumed to be graded in all three axial, thickness and width directions, which it can vary according to an arbitrary function. The governing equations are obtained using the concept of minimum potential energy. Generalized differential quadrature method (GDQM) is used to solve the governing equations for various boundary conditions to obtain the natural frequencies of TDFG nano-beam. At the end, some numerical results are performed to investigate some effective parameter on buckling load. In this theory the couple-stress tensor is skew-symmetric and energy conjugate to the skew-symmetric part of the rotation gradients as the curvature tensor.

• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.467-474
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• 2006

We present and study the stability and convergence of a deflation-preconditioned conjugate gradient(PCG) scheme for the interior generalized eigenvalue problem $Ax = {\lambda}Bx$, where A and B are large sparse symmetric positive definite matrices. Numerical experiments are also presented to support our theoretical results.

• Journal of applied mathematics & informatics
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• v.9 no.1
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• pp.331-339
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• 2002

A preconditioned conjugate gradient(PCG) scheme with the aid of deflation for computing a few of the smallest eigenvalues arid their corresponding eigenvectors of the large generalized eigenproblems is considered. Topically there are two types of deflation techniques, the deflation with partial shifts and an arthogonal deflation. The efficient way of determining partial shifts is suggested and the deflation-PCG schemes with various partial shifts are investigated. Comparisons of theme schemes are made with orthogonal deflation-PCG, and their asymptotic behaviors with restart operation are also discussed.

• Structural Engineering and Mechanics
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• v.63 no.2
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• pp.161-169
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• 2017

In this paper, using consistent couple stress theory and Hamilton's principle, the free vibration analysis of Euler-Bernoulli nano-beams made of bi-directional functionally graded materials (BDFGMs) with small scale effects are investigated. To the best of the researchers' knowledge, in the literature, there is no study carried out into consistent couple-stress theory for free vibration analysis of BDFGM nanostructures with arbitrary functions. In addition, in order to obtain small scale effects, the consistent couple-stress theory is also applied. These models can degenerate into the classical models if the material length scale parameter is taken to be zero. In this theory, the couple-tensor is skew-symmetric by adopting the skew-symmetric part of the rotation gradients as the curvature tensor. The material properties except Poisson's ratio are assumed to be graded in both axial and thickness directions, which it can vary according to an arbitrary function. The governing equations are obtained using the concept of Hamilton principle. Generalized differential quadrature method (GDQM) is used to solve the governing equations for various boundary conditions to obtain the natural frequencies of BDFG nano-beam. At the end, some numerical results are presented to study the effects of material length scale parameter, and inhomogeneity constant on natural frequency.

• Journal of the korean Society of Automotive Engineers
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• v.7 no.1
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• pp.24-34
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• 1985

The study of unsteady gas exchange processes in the inlet and exhaust systems of the single-cylinder 4-stroke cycle spark ignition engine is presented in this paper. The generalized method of characteristics including friction, heat transfer, change of flow area and entropy gradients was used for solving the equations defining the gas exchange process. The path line calculation was also conducted to allow for calculation of the gas composition and entropy change along the path lines, and of the variable specific heat due to the change of temperature and composition. As the result of the simulation, the properties at each point in the inlet and exhaust pipe, pressure and temperature in the cylinder, and charging efficiency were obtained. Pumping loss and residual gas fraction were also computed. The effect of engine speed, exhaust and inlet pipe length on the pumping loss and charging efficiency were studied showing that the results were in agreement with what has been known from experiments.

• 한국전산유체공학회:학술대회논문집
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• 2000.05a
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• pp.51-59
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• 2000

The Interactions of shock wave with turbulent boundary layers in high-speed flows cause complex flowfields which result in increased adverse pressure gradients, skin friction and temperature. Accurate and reliable prediction of such phenomena is needed in designing high-speed propulsion systems. Such analyses of the complex flowfields require sophisticated numerical scheme that can resolve interactions between shock wave and boundary layers accurately. Therefore the purpose of the present. article is to introduce an accurate and efficient mixed explicit-implicit generalized Galerkin finite element method. To demonstrate the validity of the theory and numerical procedure, several benchmark cases are investigated.

• Bulletin of the Korean Mathematical Society
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• v.51 no.1
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• pp.287-301
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• 2014

In this paper, we prove a necessary optimality theorem for a nonsmooth optimization problem in the face of data uncertainty, which is called a robust optimization problem. Recently, the robust optimization problems have been intensively studied by many authors. Moreover, we give examples showing that the convexity of the uncertain sets and the concavity of the constraint functions are essential in the optimality theorem. We present an example illustrating that our main assumptions in the optimality theorem can be weakened.

• Animal cells and systems
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• v.2 no.2
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• pp.209-216
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• 1998

The invasion of Ambrosia artemisiifolia in the Ukrainian Carpathians Mts. and the Transcarpathian Plain in Central Europe was reconstructed on the basis of floristic records. The first spontaneous occurrence was dated from the beginning of the 1940s. Within the next 55 year period, the distributional spread speed of the species was of 67.6 $km^2/y$ (by the average data). The occupied area by A. artemisiifolia in the range of the studied areas is about $3716.5km^2$ now. The features of behavior of the invader and the habitat preference were determined. The frequency of occurrence by sociologic-ecological classification was carried out. The generalized model of correlations among the gravitation, the active temperature sum and the disturbance gradients and the frequency of occurrence of the species was presented. The scheme of the invasion stages of A. artemisiifolia is reflected in the population status changes of the species during the areal dynamics.

• Journal of the korean Society of Automotive Engineers
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• v.8 no.1
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• pp.62-74
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• 1986

The simulation of power cycle and unsteady gas exchange processes in the inlet and exhaust systems of the single-cylinder 2-stroke cycle compression ignition engine was studied in this paper. In power cycle process, the single-zone model proposed by Whitehouse and Way was used, and the convective and radiative heat transfer from cylinder contents to surroundings was considered. To solve the equations for gas exchange process, the generalized method of characteristics including area change, friction, heat transfer and entropy gradients was used. Also with the path line calculation, the entropy change along the path line and the variation of specific heat due to the change of temperature and the composition of cylinder gas were considered. As a result of the simulation, the change of pressure and temperature in the cylinder against the crank angle, the rate of net heat release, and the change of properties at each point in the inlet and exhaust pipe against the crank angle were obtained. The engine performances under various operating conditions were also calculated.