• Journal of the Korean Mathematical Society
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• v.46 no.6
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• pp.1151-1164
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• 2009

Let E be a reflexive Banach space with a weakly sequentially continuous duality mapping, C be a nonempty closed convex subset of E, f : C $\rightarrow$C a contractive mapping (or a weakly contractive mapping), and T : C $\rightarrow$ C a nonexpansive mapping with the fixed point set F(T) ${\neq}{\emptyset}$. Let {$x_n$} be generated by a new composite iterative scheme: $y_n={\lambda}_nf(x_n)+(1-{\lambda}_n)Tx_n$, $x_{n+1}=(1-{\beta}_n)y_n+{\beta}_nTy_n$, ($n{\geq}0$). It is proved that {$x_n$} converges strongly to a point in F(T), which is a solution of certain variational inequality provided the sequence {$\lambda_n$} $\subset$ (0, 1) satisfies $lim_{n{\rightarrow}{\infty}}{\lambda}_n$ = 0 and $\sum_{n=0}^{\infty}{\lambda}_n={\infty}$, {$\beta_n$} $\subset$ [0, a) for some 0 < a < 1 and the sequence {$x_n$} is asymptotically regular.

• Korean Journal of Mathematics
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• v.16 no.2
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• pp.215-231
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• 2008

Let E be a uniformly convex Banach space with a uniformly $G{\hat{a}}teaux$ differentiable norm, C a nonempty closed convex subset of E, and $T:C{\rightarrow}{\mathcal{K}}(E)$ a multivalued nonself-mapping such that $P_T$ is nonexpansive, where $P_T(x)=\{u_x{\in}Tx:{\parallel}x-u_x{\parallel}=d(x,Tx)\}$. For $f:C{\rightarrow}C$ a contraction and $t{\in}(0,1)$, let $x_t$ be a fixed point of a contraction $S_t:C{\rightarrow}{\mathcal{K}}(E)$, defined by $S_tx:=tP_T(x)+(1-t)f(x)$, $x{\in}C$. It is proved that if C is a nonexpansive retract of E and $\{x_t\}$ is bounded, then the strong ${\lim}_{t{\rightarrow}1}x_t$ exists and belongs to the fixed point set of T. Moreover, we study the strong convergence of $\{x_t\}$ with the weak inwardness condition on T in a reflexive Banach space with a uniformly $G{\hat{a}}teaux$ differentiable norm. Our results provide a partial answer to Jung's question.

• Fibers and Polymers
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• v.2 no.4
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• pp.203-211
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• 2001

Residual stresses were predicted by a flow analysis in the mold cavity and residual stress distribution in the injection molded product was measured. Flow field was analyzed by the hybrid FEM/FDM method, using the Hele Shaw approximation. The Modified Cross model was used to determine the dependence of the viscosity on the temperature and the shear rate. The specific volume of the polymer melt which varies with the pressure and temperature fields was calculated by the Tait\`s state equation. Flow analysis results such as pressure, temperature, and the location of the liquid-solid interface were used as the input of the stress analysis. In order to calculate more accurate gap-wise temperature field, a coordinate transformation technique was used. The residual stress distribution in the gap-wise temperature field, a coordinate transformation technique was used. The residual stress distribution in the gap-wise direction was predicted in two cases, the free quenching, under the assumption that the shrinkage of the injection molded product occurs within the mold cavity and that the solid polymer is elastic. Effects of the initial flow rate, packing pressure, and mold temperature on the residual stress distribution was discussed. Experimental results were also obtained by the layer removal method for molded polypropylene.

• Tribology and Lubricants
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• v.10 no.1
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• pp.14-26
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• 1994

The minimum oil film thickness(MOFT) in the connecting-rod bearing of a 1.5 liter, L-4, gasoline engine is measured up to 5500 rpm and calculated to study the dynamically loaded engine bearing. Short bearing approximation and Mobility method are used for theoretical analysis of oil film characteristics. And cylinder pressure, crank-pin surface temperature and bearing temperature are measured as the input data of theoretical analysis. The MOFT are measured by the total capacitance method(TCM). To improve the reliability of the test results, a reasonable determination method of bearing clearance is introduced and used, and the effects of cavitation and aeration on the test results are neglected. The crankshaft is grounded by means of a slip ring. A scissor type linkage system was developed to measure the MOFT and bearing temperature. The effects of engine speed, load and oil viscosity on the measured and calculated minimum oil film thicknesses are investigated at 1500 to 5500 rpm. From the comparison between the measured and calculated MOFT, it is found that a qualitative similarity exists between them, but in all cases, the measured MOFT are smaller than those calculated.

• International Journal of Aerospace System Engineering
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• v.2 no.2
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• pp.67-72
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• 2015

The main concern of this study is to integrate the EARSM into an industrial RANS solver in conjunction with the $k-{\omega}$ model, as proposed by Hellsten (EARSMKO2005). In order to improve the robustness, particular limiters are introduced to turbulent conservative variables, and a suitable full-approximation storage (FAS) multi-grid (MG) strategy is designed to incorporate turbulence model equations. The present limiters and MG strategy improve both robustness and efficiency significantly but without degenerating accuracy. Two discretization approachs for velocity gradient on cell interfaces are implemented and compared with each other. Numerical results of a three-dimensional supersonic square duct flow show that the proper discretization of velocity gradient improves the accuracy essentially. To assess the capability of the resulting EARSM $k-{\omega}$ model to predict complex engineering flow, the case of Common Research Model (CRM, Wing-Body) is performed. All the numerical results demonstrate that the resulting model performs well and is comparable to the standard two-equation models such as SST $k-{\omega}$ model in terms of computational effort, thus it is suitable for industrial applications.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.14 no.2
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• pp.355-365
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• 1994

An analytical model of return flow is presented outside the surf zone. The governing equation is derived from the Navier-Stokes equation and the continuity. Each term of the governing equation is evaluated by the ordering analysis. Then the infinitesimal terms, i.e. the turbulent normal stress, the squared vertical velocity of water particle and the streaming velocity, are neglected. The driving forces of return flow are calculated using the linear wave theory for the shallow water approximation. Especially, the space derivative of local wave heights is described considering a shoaling coefficient. The vertical distribution of eddy viscosity is discussed to the customary types which are the constant, the linear function and the exponential function. Each coefficient of the eddy viscosities which sensitively affect the precision of solutions is uniquely decided from the additional boundary condition which the velocity becomes zero at the wave trough level. Also the boundary conditions at the bottom and the continuity relation are used in the integration of the governing equation. The theoretical solutions of present model are compared with the various experimental results. The solutions show a good agreement with the experimental results in the case of constant or exponential function type eddy viscosity.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.8 no.2
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• pp.123-136
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• 1996

A three-dimensional Galerkin-FEM model which can handle the temporal and spatial variation of density is presented. The hydrostatic approximation is used and density effects are included by means of conservation equation of heat and the equation of state. The finite difference grids are used in the horizontal plane and a set of linear-shape functions is used for the vertical expansion. The similarity transform is introduced to solve resultant matrix equations. The proposed model was first applied to the density-driven circulation in an idealized basin in the presence of the heat exchange between the air and the sea. The advection terms in the momentum equation were ignored, while the convection terms were retained in the heat equation. Coefficients of the vertical eddy viscosity and diffusivity were fixed to be constant. Calculation in a non-rotating idealized basin shows that the difference in heat capacity with depth gives rise to the horizontal gradient of temperature. Consequently, there is a steady new in the upper layer in the direction of increasing depth with compensatory counter flow .in the lower layer. With Coriolis force, geostrophic flow was predominant due to the balance between the pressure gradient and the Coriolis force. As a test in region of irregular topography, the model is applied to the Yellow Sea. Although the resultant flow was very complex, the character of the flow Showed to be geostrophic on the whole.

• Proceedings of the Korean Society of Rheology Conference
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• 2006.06a
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• pp.81-84
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• 2006

Slot coating process, in continuous and patch modes, has been applied for the many precise coating products, e.g., flat panel displays and second batteries. However, manufacturing uniform coating products is not a trivial task at high-speed operations because various flow instabilities or defects such as leaking, bubbles, ribbing, and rivulets are frequently observed in this process. It is no wonder, therefore, that many efforts to understand the various aspects of dynamics and coating windows of this process have been made both in academia and industry. In this study, as the first topic, flow dynamics within the coating bead in slot coating process has been investigated using the one-dimensional viscocapillary model by lubrication approximation and two-dimensional model by Flow-3D software. Especially, operability windows in both 1D and 2D cases with various slot die lip designs have been successfully portrayed. Also, effects of process conditions like viscosity and coating gap size on slot coating window have been analyzed. Also, some experiments to find minimum coating thickness and coating windows have been conducted using slot die coater implemented with flow visualization device, corroborating the numerical results. As the second topic, flow dynamics of both Newtonian and Non-Newtonian fluids in patch or pattern slot coating process, which is employed in manufacturing IT products such as secondary batteries, has been investigated for the purpose of optimal process designs. As a matter of fact, the flow control in this system is more difficult than in continuous case because od its transient or time-dependent nature. The internal die and die lip designs for patterned uniform coating products have been obtained by controlling flow behaviors of coating liquids issuing from slot. Numerical simulations have been performed using Fluent and Flow-3D packages. Flow behavior and pressure distribution inside the slot die has been compared with various die internal shapes and geometries. In the coating bead region, efforts to reduce irregular coating defects in head and tail parts of one patterned coating unit have been tried by changing die lip shapes. It has been concluded that optimal die internal design gas been developed, guaranteeing uniform velocity distribution of both Newtonian and shear thinning fluids at the die exit. And also optimal die lip design has been established, providing the longer uniform coating layer thickness within one coating unit.