• 한국세라믹학회지
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• 제23권1호
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• pp.1-6
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• 1986

The shrinkage rate of solid state sintering has been theoretically derived by combining the rate equation of material transport and the net free energy change resulting from the decrease of solid-vapor interface and the increase of grain boundary during sintering. For a sinteing model an idealized situation of the spherical particles with BCC packing was taken as the initial condition and the shrinkage was assumed to occur by forming the flat circualr grain boundaries on each particle. The plotted shrinkage rates as a function of grain boundary to surface energy ratio $(gamma_g/gamma_s)$ have shown that the relative density increases linearly at the initial stage of sintering but the shrinkage rate is decreased upon further sintering due to a decrease in driving force for densificaton. It has been also shown that the densification is critically affected by the $gamma_g/gamma_s$ ratio. In order to get the complete densificatin the ratio should be less than $sqrt{3}$. Any additive or atmospheric condition causing the decrease of$_g/gamma_s$ ratio will enhance sintering.

• 충청수학회지
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• 제30권4호
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• pp.397-409
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• 2017

In this paper, we investigated the extinction, positivity, and decay estimates of the solutions to the initial-boundary value problem of the semilinear parabolic equation with nonlinear gradient source and interior absorption terms by using the integral norm estimate method. We found that the decay estimates depend on the choices of initial data, coefficients and domain, and the first eigenvalue of the Laplacean operator with homogeneous Dirichlet boundary condition plays an important role in the proofs of main results.

• 대한수학회지
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• 제53권5호
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• pp.1133-1148
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• 2016

In this paper, we first discuss a representation of solutions to the initial value problem and the initial-boundary value problem for discrete evolution equations $${\sum\limits^l_{n=0}}c_n{\partial}^n_tu(x,t)-{\rho}(x){\Delta}_{\omega}u(x,t)=H(x,t)$$, defined on networks, i.e. on weighted graphs. Secondly, we show that the weight of each link of networks can be uniquely identified by using their Dirichlet data and Neumann data on the boundary, under a monotonicity condition on their weights.

• Tribology and Lubricants
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• 제16권6호
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• pp.477-483
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• 2000

Rolling contact fatigue (RCF) tests were performed for two kinds of commercial silicon nitride balls using 4-Ball rolling contact fatigue life tester under EHL condition (Λ=8.9) and boundary lubrication condition (Λ=0.2). All the test balls were finished up to the dimensional accuracy of Grade 5 defined in KS B 2001 (Steel Balls for Ball Bearings) with a size of 8.731 mm. RCF tests were then conducted under the initial theoretical maximum contact stress 6.63 GPa and the spindle speed 10,000 rpm. All the test balls were not failed until 3.75 $\times$ 107 contact cycles and wear tracks of test balls were not conspicuous under EHL condition (Λ= 8.9). In the operations of low lambda regime (Λ= 0.2), all the test balls were surface damaged and high rolling wear resistance was achievable in fully densified using MgO 1 wt% and HIPed balls. Rolling wear of silicon nitride balls under boundary lubrication condition depend mainly on grain size and intergranular phase content of silicon nitride balls.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1997년도 한국자동제어학술회의논문집; 한국전력공사 서울연수원; 17-18 Oct. 1997
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• pp.1520-1523
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• 1997

A rigorous dynamic simulation was performed in binary gas mixture H$_{2}$/CO (70:30 vol.%) to determinate start-up operating conditions of PSA(Pressure Swing Adsorption) processes. The rigorous dynamic model for the PSA process contains an Ergun equation for expressing the pressure drop in a bed, and valve equations to compute the boundary pressure change of the bed. As the result of the continuous dynamic simulation of 100 operating cyles in various initial conditions, the unsteady-state appeared in the early period and the cyclic steady-state came out about 20th cycle in feed condition and vaccum condition, and 30th cycle in pure H$_{2}$ condition. As time goes by valve equations made change the pressure at each end of the bed in ressurization, countercurrunt-depressurization and pressure equalization steps. The H$_{2}$ purity and the recovery is 99.99% and 86.73% respectively, which is slightly higher than the experimental data. Main contributiion of this study includes supplying fundamental technologies of handling combined variables PSA processes by developing rigorous models.

• 대한수학회지
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• 제47권6호
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• pp.1317-1328
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• 2010

In this paper, we study the properties of positive solutions for the reaction-diffusion equation $u_t$ = $\Delta_u+{\int}_\Omega u^pdx-ku^q$ in $\Omega\times(0,T)$ with nonlocal nonlinear boundary condition u (x, t) = ${\int}_{\Omega}f(x,y)u^l(y,t)dy$ $\partial\Omega\times(0,T)$ and nonnegative initial data $u_0$ (x), where p, q, k, l > 0. Some conditions for the existence and nonexistence of global positive solutions are given.

• 전기학회논문지
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• 제68권1호
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• pp.129-139
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• 2019

In order for a gun-launched guided projectile to glide to the maximum range, when to deploy the fin and start flight with guidance and control should be considered in range optimization process. This study suggests a solution to the optimal guidance problem for flight range maximization of the flight model of a guided projectile in vertical plane considering the aerodynamic properties. After converting the nonlinear Multi-Phase Optimal Control Problem to Two-Point Boundary Value Problem, the optimized guidance command and the best fin deployment timing are calculated by the proposed numerical method. The optimization results of the multiple flight rounds with various initial velocity and launch angle indicate that determining specific launch condition incorporated with the guidance scheme is of importance in terms of mechanical energy consumption.

• 한국공간구조학회:학술대회논문집
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• 한국공간구조학회 2006년도 춘계 학술발표회 논문집 제3권1호(통권3호)
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• pp.227-232
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• 2006

This paper investigate the optimum thickness distribution of plate structure with different essential boundary conditions in the fundamental natural frequency maximization problem. In this study, the fundamental natural frequency is considered as the objective function to be maximized and the initial volume of structures is used as the constraint function. The computer-aided geometric design (CAGD) such as Coon's patch representation is used to represent the thickness distribution of plates. A reliable degenerated shell finite element is adopted calculate the accurate fundamental natural frequency of the plates. Robust optimization algorithms implemented in the optimizer DoT are adopted to search optimum thickness values during the optimization iteration. Finally, the optimum thickness distribution with respect to different boundary condition

• 대한수학회보
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• 제50권3호
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• pp.753-760
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• 2013

We consider the global existence of strong solutions of the 3D incompressible Navier-Stokes equations in a bounded Lipschitz do-main under Dirichlet boundary condition. We present by a very simple argument that a strong solution exists globally when the product of $L^2$ norms of the initial velocity and the gradient of the initial velocity and $L^{p,2}$, $p{\geq}4$ norm of the forcing function are small enough. Our condition is scale invariant and implies many typical known global existence results for small initial data including the sharp dependence of the bound on the volumn of the domain and viscosity. We also present a similar result in the whole domain with slightly stronger condition for the forcing.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제16권4호
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• pp.235-242
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• 2012

In this paper, we investigate a nonlocal semilinear heat equation with homogeneous Dirichlet boundary condition in a bounded domain, and prove that there exist solutions with positive initial energy that blow up in finite time.