• Journal of the Korean institute of surface engineering
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• v.41 no.1
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• pp.23-27
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• 2008

The effect of solution agitation on the copper electroless deposition process of ULSI (ultra large scale integration) interconnections was investigated by using physical, electrochemical and electrical techniques. It was found that proper solution agitation was effective to obtain superconformal copper configuration within the trenches of $130{\sim}80nm$ width. The transition of open potential during electroless deposition process showed that solution agitation induced compact structure of copper deposits by suppressing mass transfer of cuprous ions toward substrate. Also, the specific resistivity of copper layers was lowered by increasing agitation speed, which made the deposited copper particles smaller. Considering both copper deposit configuration and electric property, around 500 rpm of solution agitation was the most suitable for the homogeneous electroless copper filling within the ultra-fine patterns.

• Korean Journal of Mathematics
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• v.23 no.3
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• pp.479-489
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• 2015

We study the GMGHS spacetime to analyze anisotropic cosmology model which represents homogeneous but anisotropically expanding(contracting)cosmology. In this paper we investigate the solution of GMGHS spacetime in form of doubly warped products possessing warping functions and find the Ricci curvature associated with three phases in the evolution of the universe.

• Communications of the Korean Mathematical Society
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• v.15 no.4
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• pp.605-616
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• 2000

We prove the non-homogeneous boundary value problem for population evolution equations is well-posed in Sobolev space H(sup)3/2,3/2($\Omega$). It provides a strictly mathematical basis for further research of population control problems.

• Journal of the Korean Ceramic Society
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• v.25 no.2
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• pp.168-172
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• 1988

In order to prevent the PbO vaporization during calcination and to produce the powder of good sinterability, a coprecipitation method for preparing homogeneous Lead-Zirconate-Titanate (PZT) powder from aqueous salt solution is described. In this method, the PZT-ceramics show low calcining and sintering temperature, and they have good sintering and electronic properties.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.4 no.2
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• pp.91-107
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• 1992

A numerical formulation is developed to solve the linear three-dimensional hydrodynamic equations which describes wind induced flows in a homogeneous shelf sea. The hydmdynamic equations are at the outset separated into two systems. namely, an equation containing the gradient of sea surface elevation and the mean flow (external mode) and an equation describing the deviation from the mean flow (internal mode). The Galerkin method is then applied to the internal mode equation. The eigenvalues are determined from the eigenvalue problem involving the vertical eddy viscosity subject to a homogeneous boundary condition at the surface and a sheared boundary condition at the sea bed. The model is tested in a one-dimensional channel with uniform depth under a steady, uniform wind. The analytical velocity profile by Cooper and Pearce (1977) using a constant vertical eddy viscosity in channels of infinite and finite length is chosen as a benchmark solution. The model is also tested in a homogeneous, rectangular basin with constant depth under a steady, uniform wind field (the Heaps' Basin of the North Sea scale).

• Computers and Concrete
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• v.27 no.3
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• pp.199-210
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• 2021

The aim of this paper was to examine the continuous and discontinuous contact problems between the functionally graded (FG) layer pressed with a uniformly distributed load and homogeneous half plane using an analytical method and FEM. The FG layer is made of non-homogeneous material with an isotropic stress-strain law with exponentially varying properties. It is assumed that the contact at the FG layer-half plane interface is frictionless, and only the normal tractions can be transmitted along the contacted regions. The body force of the FG layer is considered in the study. The FG layer was positioned on the homogeneous half plane without any bonds. Thus, if the external load was smaller than a certain critical value, the contact between the FG layer and half plane would be continuous. However, when the external load exceeded the critical value, there was a separation between the FG layer and half plane on the finite region, as discontinuous contact. Therefore, there have been some steps taken in this study. Firstly, an analytical solution for continuous and discontinuous contact cases of the problem has been realized using the theory of elasticity and Fourier integral transform techniques. Then, the problem modeled and two-dimensional analysis was carried out by using ANSYS package program based on FEM. Numerical results for initial separation distance and contact stress distributions between the FG layer and homogeneous half plane for continuous contact case; the start and end points of separation and contact stress distributions between the FG layer and homogeneous half plane for discontinuous contact case were provided for various dimensionless quantities including material inhomogeneity, distributed load width, the shear module ratio and load factor for both methods. The results obtained using FEM were compared with the results found using analytical formulation. It was found that the results obtained from analytical formulation were in perfect agreement with the FEM study.

• Applied Chemistry for Engineering
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• v.16 no.6
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• pp.785-789
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• 2005

$TiO_2$ powders with rutile and brookite phases were synthesized through homogeneous precipitation of the aqueous $TiOCl_2$ solution, prepared from $TiCl_4$ and HCl solution, and their properties were characterized. Based on the analytical results appropriate molar ratios of ${Cl^-}_{total}:Ti^{+4}$ in precipitating solution for synthesis of pure rutile phase and a mixture of rutile and brookite phases were proposed. The volumetric proportion of brookite increased with increasing HCl concentration under a typical condition obtaining mixed phase of rutile and brookite. The brookite phase in the mixture was transformed to anatase phase by heat treatment at about $800^{\circ}C{\sim}850^{\circ}C$, and finally converted to rutile phase at $1000^{\circ}C$.

• Earthquakes and Structures
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• v.5 no.2
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• pp.161-205
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• 2013

We study seismically induced, anti-plane strain wave motion in a non-homogeneous geological region containing tunnels. Two different scenarios are considered: (a) The first models two tunnels in a finite geological region embedded within a laterally inhomogeneous, layered geological profile containing a seismic source. For this case, labelled as the first boundary-value problem (BVP 1), an efficient hybrid technique comprising the finite difference method (FDM) and the boundary element method (BEM) is developed and applied. Since the later method is based on the frequency-dependent fundamental solution of elastodynamics, the hybrid technique is defined in the frequency domain. Then, an inverse fast Fourier transformation (FFT) is used to recover time histories; (b) The second models a finite region with two tunnels, is embedded in a homogeneous half-plane, and is subjected to incident, time-harmonic SH-waves. This case, labelled as the second boundary-value problem (BVP 2), considers complex soil properties such as anisotropy, continuous inhomogeneity and poroelasticity. The computational approach is now the BEM alone, since solution of the surrounding half plane by the FDM is unnecessary. In sum, the hybrid FDM-BEM technique is able to quantify dependence of the signals that develop at the free surface to the following key parameters: seismic source properties and heterogeneous structure of the wave path (the FDM component) and near-surface geological deposits containing discontinuities in the form of tunnels (the BEM component). Finally, the hybrid technique is used for evaluating the seismic wave field that develops within a key geological cross-section of the Metro construction project in Thessaloniki, Greece, which includes the important Roman-era historical monument of Rotunda dating from the 3rd century A.D.

• Journal of Electrochemical Science and Technology
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• v.4 no.2
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• pp.71-80
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• 2013

The study of methyl viologen ($MV^{2+}$) mediated oxygen reduction in electrolytic ethanol media possesses potential application in the electrochemical synthesis of hydrogen peroxide mainly due to the advantages of the much increased solubility of molecular oxygen ($O_2$) and high degree of reversibility of $MV^{2+/{\bullet}+}$ redox couple. The diffusion coefficients of both $MV^{2+}$ and $O_2$ were investigated via electrochemical techniques. For the first time, $MV^{2+}$ mediated $O_2$ reduction in electrolytic ethanol solution has been proved to be feasible on both boron-doped diamond and micro-carbon disc electrodes. The electrocatalytic response is demonstrated to be due to the radical cation, $MV^{{\bullet}+}$. The homogeneous electron transfer step is suggested to be the rate determining step with a rate constant of $(1{\pm}0.1){\times}10^5M^{-1}s^{-1}$. With the aid of a simulation program describing the EC' mechanism, by increasing the concentration ratio of $MV^{2+}$ to $O_2$ electrochemical catalysis can be switched from a partial to a 'total catalysis' regime.

• Smart Structures and Systems
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• v.13 no.1
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• pp.1-24
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• 2014

The present study deals with two dimensional electro-elastic analysis of a functionally graded piezoelectric (FGP) cylinder under internal pressure. Energy method and first order shear deformation theory (FSDT) are employed for this purpose. All mechanical and electrical properties except Poisson ratio are considered as a power function along the radial direction. The cylinder is subjected to uniform internal pressure. By supposing two dimensional displacement and electric potential fields along the radial and axial direction, the governing differential equations can be derived in terms of unknown electrical and mechanical functions. Homogeneous solution can be obtained by imposing the appropriate mechanical and electrical boundary conditions. This proposed solution has capability to solve the cylinder structure with arbitrary boundary conditions. The previous solutions have been proposed for the problem with simple boundary conditions (simply supported cylinder) by using the routine functions such as trigonometric functions. The axial distribution of the axial displacement, radial displacement and electric potential of the cylinder can be presented as the important results of this paper for various non homogeneous indexes. This paper evaluates the effect of a local support on the distribution of mechanical and electrical components. This investigation indicates that a support has important influence on the distribution of mechanical and electrical components rather than a cylinder with ignoring the effect of the supports. Obtained results using present method at regions that are adequate far from two ends of the cylinder can be compared with previous results (plane elasticity and one dimensional first order shear deformation theories).