• Journal of the Korean Applied Science and Technology
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• v.27 no.4
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• pp.452-460
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• 2010

Any theory of liquid should account for interactions between molecules, since molecules in a liquid are close to each other. For this matter statistical-mechanical methodology has been used and various models have been proposed on the basis of this methodology. Among them Kirkwood-Buff solution theory has attracted a lot of interest, because it is regarded as being the most powerful. In this article Kirkwood-Buff solution theory is revisited and its key equations are derived. On the way to these equations, the concepts of pair correlation function, radial distribution function, Kirkwood-Buff integration are explained and implemented. Since complexity of statical mechanics involved in this theory, the equations are applied to one-component systems and the results are compared to those obtained by classical thermodynamics. This may be a simple way for Kirkwood-Buff solution theory to be examined for its validity.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.22 no.4
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• pp.740-746
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• 2013

Angular contact ball bearings are often adopted for a high-speed spindle owing to their durability against axial and radial loads. The dynamic characteristics of an angular contact ball bearing, however, are very complicated because they are dependent on the applied loads as well as on the system configuration. This study systematically analyzes the radial-load-dependent characteristics of spindles as well as angular contact ball bearings. Toward this end, a spindle dynamic model along with the bearing dynamics model is established. An iterative solution algorithm is implemented to resolve the statically indeterminate problem associated with spindle-bearing systems subjected to radial load. Two numerical examples are provided to investigate the spindle and bearing characteristics as a function of radial load with regard to the system configuration.

• Journal of applied mathematics & informatics
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• v.30 no.5_6
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• pp.951-969
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• 2012

In this paper, we propose a class of meshless collocation approaches for the solution of time dependent partial differential algebraic equations (PDAEs) in terms of a radial basis function interpolation numerical scheme. Kansa's method and the Hermite collocation method (HCM) for PDAEs are given. A sensitivity analysis of the solutions from different shape parameter c is obtained by numerical experiments. With use of the random collocation points, we have obtain the more accurate solution by the methods than those by the finite difference method for the PDAEs with index-2, i.e, we avoid the influence from an index jump of PDAEs in some degree. Several numerical experiments show that the methods are efficient.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.19 no.6
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• pp.560-568
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• 2009

Modal vibration characteristics of a thin annular disk containing narrow radial slots are studied numerically and experimentally. Existing analytical solution is examined based on these results revealing that it can not precisely predict eigenvalues of the disk with slots since it does not accurately consider change in the vibration modes and change in strain energy density distributions due to the slots. Parametric study on slot length found that distortions in the mode shape as well as changes in the corresponding natural frequencies are proportional to the slot length. Consequently, errors in the calculated eigenvalues are also proportional to the slot length and accurate data can not be obtained with existing analytical solution above a certain level of slot length. Same phenomena can be observed in both free-free disk and fixed-free disk.

• Interaction and multiscale mechanics
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• v.5 no.2
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• pp.131-144
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• 2012

We study a radial basis function collocation method (RBFCM) to discretize a coupled nonlinear Schr$\ddot{o}$dinger equation (CNLSE) that governs a two dimensional rotating Bose-Einstein condensate (BEC) with an angular momentum rotation term. We exploit a RBFCM-continuation method (RBFCM-CM) to trace the solution curve of the CNLSE. We compare the performance of the RBFCM-CM with the FEM-CM. We observe that the RBFCM-CM is very robust in a coarse grid for resolving the ground state solution with many vortices when the angular momentum rotation is close to the limit. Numerical results demonstrate the efficiency and accuracy of the RBFCM-CM for computing the superfluid density of the ground level of the BEC.

• Journal of the Korean Mathematical Society
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• v.33 no.2
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• pp.381-386
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• 1996

We consider the behavior of positive radial solutions (or, briefly, pp.r.s.) of the equation $$ (1.1) ^\Delta u + \lambda f(u) = 0 in\Omega, _u = 0 on \partial\Omega, $$ where $\Omega = {x \in R^n$\mid$A < $\mid$x$\mid$ < B}$ is an annulus in $R^n, n \geq 2, \lambda > 0 and f \geq 0$ is superlinear in u and satisfies f(0) = 0.

• Steel and Composite Structures
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• v.18 no.3
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• pp.659-672
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• 2015

This research deals with the analytical solution of a curved beam with different shapes made of functionally graded materials (FGM's). It was assumed that modulus of elasticity is graded along the thickness direction of curved beam based on a power function. The beam was loaded under pure bending. Using the linear theory of elasticity, the general relation for radial distribution of radial and circumferential stresses of arbitrary cross section was derived. The effect of nonhomogeneity was considered on the radial distribution of circumferential stress. This behavior can be investigated for positive and negative values of nonhomogeneity index. The novelty of this study is application of the obtained results for different combination of material properties and cross sections. Achieved results indicate that employing different nonhomogeneity index and selection of various types of cross sections (rectangular, triangular or circular) can control the distribution of radial and circumferential stresses as designer want and propose new solutions by these options. Increasing the nonhomogeneity index for positive or negative values of nonhomogeneity index and for various cross sections presents different behaviors along the thickness direction. In order to validate the present research, the results of this research can be compared with previous result for reachable cross sections and non homogeneity index.

• Tribology and Lubricants
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• v.31 no.5
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• pp.221-228
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• 2015

It is possible to prevent a piston from contacting the cylinder by changing the shape of the piston or by applying micro-textures, such as micro-grooves or micro-holes, over the piston surface. Usually, the minimum radial clearance reaches its minimum value at the beginning of the suction stroke because the pressure around the piston is low and almost axisymmetric such that the net pressure force on the piston is not sufficiently high to support the piston from touching the cylinder. In this study, we apply a series of saw-tooth-shaped grooves on the piston surface, and numerically investigate the effects of groove depth, groove angle, and the number of grooves with radial clearance variations using a finite difference method. We conduct a dynamic analysis of the piston for various changes in groove geometries to obtain the minimum radial clearance variation for the entire compression cycle. The minimum radial clearance increases while friction loss decreases when we apply the series of saw-tooth-shaped grooves on the piston. In addition, we analyze the impact of the change in the groove shape variable due to changes in radial clearance. Leakage variations are relevant to radial clearance, but have almost no effect on the groove parameters.

• Journal of the Korea Furniture Society
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• v.28 no.3
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• pp.248-258
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• 2017

A study was carried out to observe the 1% aqueous safranine solution flow speed in longitudinal and radial directions of softwood Thuja orientalis L., diffuse-porous wood Gmelina arborea Roxb., and ring-porous wood Phellodendron amurense Rupr., Longitudinal flow was considered from bottom to top while the radial flow was considered from bark to pith directions. In radial direction, ray cells and in longitudinal direction tracheids, vessel and wood fiber were considered for the measurement of liquid penetration speed at less than 12% moisture contents(MC). The variation of penetration speed for different species was observed and the reasons behind for this variation were explored. The highest radial penetration depth was found in ray parenchyma of T. orientalis but the lowest one was found in ray parenchyma of P. amurense. The average liquid penetration depth in longitudinal trachied of T. orientalis was found the highest among all the other cells. The penetration depth in fiber of G. arborea was found the lowest among the other longitudinal cells. It was found that cell dimension and also meniscus angle of safranine solution with cell walls were the prime factors for the variation of liquid flow speed in wood. Vessel was found to facilitate prime role in longitudinal penetration for hardwood species. The penetration depth in vessel of G. arborea was found highest among all vessels. Anatomical features like ray parenchyma cell length and diameter, end-wall pits number were found also responsible fluid flow differences. Initially liquid penetration speed was high and the nit gradually decreased in an uneven rate. Liquid flow was captured via video and the penetration depths in those cells were measured. It was found that even in presence of abundant rays in hardwood species, penetration depth of liquid in radial direction of softwood species was found high. Herein the ray length, lumen area, end wall pit diameter determined the radial permeability. On the other hand, vessel and fiber structure affected the longitudinal flow of liquids. Following a go-stop-go cycle, the penetration speed of a liquid decreased over time.

• Journal of the Korean Mathematical Society
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• v.37 no.5
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• pp.763-777
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• 2000

We investigate the existence of group invariant solutions of the Emden-Fowler equation, - u=$\mid$x$\mid$$\sigma$$\mid$u$\mid$p-1u in B, u=0 on B and u(gx)=u(x) in B for g G. Here B is the unit ball in n 2, 1$\sigma$ 0 and G is a closed subgrop of the orthogonal group. A soultion of the problem is called a G in variant solution. We prove that there exists a G invariant non-radial solution if and only if G is not transitive on the unit sphere.