• Korean Journal of Mathematics
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• v.17 no.3
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• pp.283-291
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• 2009

We investigate the existence of multiple solutions (${\xi},{\eta}$) for perturbations of the parabolic system with Dirichlet boundary condition $$(0.1)\;\begin{array}{lcr}{\xi}_t=-L{\xi}+g_1(3{\xi}+{\eta})-s{\phi}_1-h_1(x,t)\;in\;{\Omega}{\times}(0,\;2{\pi}),\\{\eta}_t=-L{\eta}+g_2(3{\xi}+{\eta})-s{\phi}_1-h_2(x,t)\;in\;{\Omega}{\times}(0,\;2{\pi}).\end{array}$$ We show the existence of multiple solutions (${\xi},{\eta}$) for perturbations of the parabolic system when the nonlinearity $g^{\prime}_1,\;g^{\prime}_2$ are bounded and $3g^{\prime}_1(-{\infty})+g^{\prime}_2(-{\infty})<{\lambda}_1,\;{\lambda}_n<3g^{\prime}_1(+{\infty})+g^{\prime}_2(+{\infty})<{\lambda}_{n+1}$.

• Journal of the Korean Chemical Society
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• v.21 no.5
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• pp.330-338
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• 1977

In order to elucidate the plastic deformation of solids, the following assumptions were made: (1) the plastic deformation of solids is classified into two main types, the one which is caused by dislocation movement and the other caused by grain boundary movement, each movement being restricted on a different shear surface, (2) the dislocation movement is expressed by a mechanical model of a parallel connection of various kinds of Maxwell dislocation flow units whereas the grain boundary movement is also expressed by a parallel connection of various kinds of Maxwell grain boundary flow units; the parallel connection in each type of movements indicates that all the flow units on each shear surface flow with the same shear rate, (3) the latter model for grain boundary movement is connected in series to the former for dislocation movement, this means physically that the applied stress distributes homogeneously in the flow system while the total strain rate distributes heterogeneously on the two types of shear planes (dislocation or grain boundary shear plane), (4) the movement of dislocation flow units and grain boundary units becomes possible when the atoms or molecules near the obstacles, which hinder the movement of flow units, diffuse away from the obstacles.Using the above assumptions in conjunction with the theory of rate processes, generalized equations of shear stress and shear rate for plastic deformation were derived. In this paper, four cases important in practice were considered.ted N${\cdot}{\cdot}{\cdot}$O hydrogen bond and the second of two normal N${\cdot}{\cdot}{\cdot}$O hydrogen bonds, both of which exist between the amino group and the perchlorate, groups. A p-phenylenediamine group is approximately planar within an experimental error and bonded to twelve perchlorates: ten perchlorates forming hydrogen bonds and two being contacted with the van der Waals forces. A perchlorate group is surrounded by six p-phenylenediamines and four perchlorates; among the six p-phenylenediamines, five of them are hydrogen-bonded, and the rest contacted with the van der Waals force.

• Journal of Animal Environmental Science
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• v.11 no.1
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• pp.45-54
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• 2005

A field survey was conducted to determine the concentration of odor compounds from pig buildings and that were 20 meters within the boundary area. The odor compounds were measured from large, medium and small farms with enclosed and open housing systems and slurry and sawdust manure fermentation treatment methods. Among the odor compounds investigated, ammonia ($NH_3$) had the highest concentration at 0.9 ${\~}$ 21.0 ppm followed by Hydrogen Sulfide($H_2S$) with a wide variation concentration of 51.9 ${\~}$ 6,712.4 pub, Uethylmercaptan($CH_3SH$) with non-detectable (N. D.) ${\~}$ 12.9 ppb, Dimethylsulphide($(CH_3)_2S$), with N. D. ${\~}$ 5.2 ppb and Dimethyldisulphide($(CH_3)_2S_2$) with N. D. ${\~}$ 2.6 ppb. Considering the prevailing wind direction and air velocity ranging from 0.23 to 0.73 m/s within the boundary area, the odorous matters; $NH_3$, $H_2S$, $CH_3SH$, $(CH_3)_2S_2$ and $(CH_3)_2S$ were 0.2${\~}$4.5 ppm, 0.01 ${\~}$0.06 ppb, N. D. ${\~}$0.009ppb, N. D.${\~}$0.002ppb and N. D. for $(CH_3)_2S$ respectively. These findings suggested that the Odor compounds $(CH_3)_2S_2$ had the lower detection in the boundary area whilst $(CH_3)_2S$ had no detection level within a 20-meter distance only. However, with these results odor compounds from pig buildings has to be further investigated under more controlled environmental factors.

• Proceedings of the KSME Conference
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• 2003.11a
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• pp.103-108
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• 2003

In this paper, the current lead for superconducting device is studied by numerical method. The current lead is cooled by surrounded $N_{2}$ gas by natural convection. The heat conduction equation for current lead and boundary layer equation for $N_{2}$ gas must be solved simultaneously. The boundary layer equation for $N_{2}$ gas is highly nonlinear for varied temperature of current lead. So the linearization method is adopted for simplicity. Numerical results using natural convection cooling are compared with the conventional cooling methods such as conduction cooling and vapor cooling methods. The main difference of natural convection cooing is the non-zero temperature gradient at the top of current lead for the minimum heat dissipation into superconducting devices. For the optimized conduction-cooling and vapor-cooling current leads, the temperature gradient at the top of current lead is zero. Also, the heat flow at the cold end is much smaller than conduction cooling case.

• Structural Engineering and Mechanics
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• v.5 no.4
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• pp.433-450
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• 1997

The objective of this work is to predict the failure loads, associated maximum transverse displacements, locations and the modes of failure, including the onset of delamination, of thin, flat, square symmetric laminates under the action of uni-axial compression. Two progressive failure analyses, one using Hashin criterion and the other using Tensor polynomial criteria, are used in conjunction with the finite element method. First order shear deformation theory and geometric nonlinearity in the von Karman sense have been employed. Five different types of lay-up sequence are considered for laminates with all edges simply supported. In addition, two boundary conditions, one with all edges fixed and other with mixed boundary conditions for $(+45/-45/0/90)_{2s}$ quasi-isotropic laminate have also been considered to study the effect of boundary restraints on the failure loads and the corresponding modes of failure. A comparison of linear and nonlinear results is also made for $({\pm}45/0/90)_{2s}$ quasi-isotropic laminate. It is observed that the maximum difference between the failure loads predicted by various criteria depend strongly on the laminate lay-ups and the flexural boundary restraints. Laminates with clamped edges are found to be more susceptible to failure due to the transverse shear and delamination, while those with the simply supported edges undergo total collapse at a load slightly higher than the fiber failure load.

• Journal of applied mathematics & informatics
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• v.40 no.1_2
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• pp.99-115
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• 2022

The problem of Benard double diffusive Marangoni convection is investigated in a horizontally infinite composite layer system consisting of a two component fluid layer above a porous layer saturated with the same fluid, using Darcy-Brinkman model with constant heat sources/sink in both the layers. The lower boundary of the porous region is rigid and upper boundary of the fluid region is free with Marangoni effects. The system of ordinary differential equations obtained after normal mode analysis is solved in closed form for the eigenvalue, thermal Marangoni number for two types of thermal boundary combinations, Type (I) Adiabatic-Adiabatic and Type (II) Adiabatic -Isothermal. The corresponding two thermal Marangoni numbers are obtained and the essence of the different parameters on non-Darcy-Benard double diffusive Marangoni convection are investigated in detail.

• Journal of the Society of Naval Architects of Korea
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• v.32 no.3
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• pp.62-71
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• 1995

In the numerical analysis of incompressible unsteady Navier-stokes equation, large time is required for solving the pressure Poisson equation of the elliptic type at each time step. In this paper, a numerical analysis by the direct method is carried out to solve the pressure Poisson equation and the computing time is analyzed as mesh size increases. The pressure Poisson equation can be transformed to the boundary value problem by the Green theorem. The computing time for the convolution type of the domain integral can be reduced by using F.F.T. and the computing time in the direct method depends entirely on obtaining the solution of the boundary value problem. The numerical analysis on the known solutions is carried out and compared for the verification of the direct method. And the numerical analysis on the body boundary and domain decomposition problem are carried out with the computing time less than O($n^{3}$) in the (n.n) mesh.

• Bulletin of the Korean Mathematical Society
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• v.51 no.4
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• pp.1195-1204
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• 2014

We newly define the volume integral means of harmonic functions to characterize the weighted harmonic Bergman spaces. It is based on Xiao and Zhu's results on holomorphic Bergman spaces [5].

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2000.05a
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• pp.779-782
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• 2000

This paper aimes to clarify the effects of tool geometry on the tool life in machining of STS 304. The main conclusions obtained were as follows. The lift of TiN coated cermet tool was the longest, exhibiting shorter life in the order of P2O, cermet, TiCN coated carbide and TiAIN coated carbide tools. S-type tool showed the best performance of all tools used in this tests due to preventing the boundary wear of the side cutting edge.

• Korean Journal of Mathematics
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• v.5 no.1
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• pp.29-33
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• 1997

In this paper we investigate the existence of positive solutions of a nonlinear biharmonic equation under Dirichlet boundary condition in a bounded open set ${\Omega}$ in $\mathbf{R}^n$, i.e., $${\Delta}^2u+c{\Delta}u=bu^{+}+s\;in\;{\Omega},\\u=0,\;{\Delta}u=0\;on\;{\partial}{\Omega}$$.