• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• 제3권1호
• /
• pp.1-15
• /
• 1999

Gradient recovery techniques for the second order elliptic boundary value problem are well known. In particular, the Midpoint and the Vertex Recovery Operator have been studied by various authors and under suitable assumptions on the regularity of the unknown solution superconvergence property of these recovered gradients have been proved. In this paper we extend these results to the recovered gradient of the finite element approximation to a model initial-boundary value problem, and go on to prove superconvergence result for this recovered gradient in a discrete (in time) error norm.

• Korean Journal of Mathematics
• /
• 제19권3호
• /
• pp.309-319
• /
• 2011

We give sufficient conditions that the homogeneous differential equations : for $t{\geq}t_0$(> 0), $$x^{{\prime}{\prime}}(t)+q(t)x^{\prime}(t)+p(t)x(t)=0,\\x^{{\prime}{\prime}}(t)+q(t)x^{\prime}(t)+F(t,x({\phi}(t)))=0$$, are oscillatory where $0{\leq}{\phi}(t)$, 0 < ${\phi}^{\prime}(t)$, $\lim_{t\to{\infty}}{\phi}(t)={\infty}$. and $F(t,u){\cdot}sgn$ $u{\leq}p(t)|u|$. We obtain comparison theorems.

• Korean Journal of Mathematics
• /
• 제19권4호
• /
• pp.391-402
• /
• 2011

We give necessary and sufficient conditions such that the homogeneous differential equations of the type: $$(r(t)x^{\prime}(t))^{\prime}+q(t)x^{\prime}(t)+p(t)x(t)=0$$ are nonoscillatory where $r(t)$ > 0 for $t{\in}I=[{\alpha},{\infty})$, ${\alpha}$ > 0. Under the suitable conditions we show that the above equation is nonoscillatory if and only if for ${\gamma}$ > 0, $$(r(t)x^{\prime}(t))^{\prime}+q(t)x^{\prime}(t)+p(t)x(t-{\gamma})=0$$ is nonoscillatory. We obtain several comparison theorems.

• Journal of applied mathematics & informatics
• /
• 제19권1_2호
• /
• pp.179-190
• /
• 2005

We deal with the Cauchy problem for the space-time fractional diffusion equation, which is obtained from standard diffusion equation by replacing the second-order space derivative with a Caputo (or Riemann-Liouville) derivative of order ${\beta}{\in}$ (0, 2] and the first-order time derivative with Caputo derivative of order ${\beta}{\in}$ (0, 1]. The fundamental solution (Green function) for the Cauchy problem is investigated with respect to its scaling and similarity properties, starting from its Fourier-Laplace representation. We derive explicit expression of the Green function. The Green function also can be interpreted as a spatial probability density function evolving in time. We further explain the similarity property by discussing the scale-invariance of the space-time fractional diffusion equation.

• Structural Engineering and Mechanics
• /
• 제65권1호
• /
• pp.91-98
• /
• 2018

Three structure-dependent integration methods with no numerical dissipation have been successfully developed for time integration. Although these three integration methods generally have the same numerical properties, such as unconditional stability, second-order accuracy, explicit formulation, no overshoot and no numerical damping, there still exist some different numerical properties. It is found that TLM can only have unconditional stability for linear elastic and stiffness softening systems for zero viscous damping while for nonzero viscous damping it only has unconditional stability for linear elastic systems. Whereas, both CEM and CRM can have unconditional stability for linear elastic and stiffness softening systems for both zero and nonzero viscous damping. However, the most significantly different property among the three integration methods is a weak instability. In fact, both CRM and TLM have a weak instability, which will lead to an adverse overshoot or even a numerical instability in the high frequency responses to nonzero initial conditions. Whereas, CEM possesses no such an adverse weak instability. As a result, the performance of CEM is much better than for CRM and TLM. Notice that a weak instability property of CRM and TLM might severely limit its practical applications.

• 대한기계학회:학술대회논문집
• /
• 대한기계학회 2008년도 추계학술대회A
• /
• pp.1692-1696
• /
• 2008

In this paper, we characterize the mechanical properties of PCL strand which is made by oscillating nozzle for tissue engineering scaffold. In order to increase the mechanical properties of the PCL strand, we designed an oscillating nozzle system for the 3D plotting system. First, we check the effect of the nozzle speed (3 to 8 mm/sec), frequency (0 or 300 Hz) and the oscillating amplitude (0 or 100 V) on the diameter of the PCL strand. Second, we observe the effect of the frequency (0, 100, 200 and 300 Hz) and the oscillating amplitude (0, 50 and 100 V) on the mechanical property of PCL strand. The mechanical properties and surface morphology of PCL strand made by oscillating nozzle are compared with the PCL strand made by normal nozzle using Nano-UTM and SEM.

• Nuclear Engineering and Technology
• /
• 제34권1호
• /
• pp.90-103
• /
• 2002

The thermal and mechanical properties of compacted bentonite and bentonite-sand mixture were collected from the literatures and compiled. The thermal conductivity of bentonite is found to increase almost linearly with increasing dry density and water content of the bentonite. The specific heat can also be expressed as a function of water ontent, and the coefficient of thermal expansion is almost independent on the dry density. The logarithm of unconfined compressive strength and Young’s modulus of elasticity increase linearly with increasing dry density, and in the case of constant dry density, it can be fitted to a second order polynomial of water content. Also the unconfined compressive strength and Young’s modulus of elasticity of the bentonite-sand mixture decreases with increasing sand content. The Poisson’s ratio remains constant at the dry density higher than 1.6 Mg/m$_3$, and the shear strength increases with increasing dry density.

• Structural Engineering and Mechanics
• /
• 제87권4호
• /
• pp.363-373
• /
• 2023

Since the first family of structure-dependent methods can simultaneously integrate unconditional stability and explicit formulation in addition to second order accuracy, it is very computationally efficient for solving inertial problems except for adopting auto time-stepping techniques due to no nonlinear iterations. However, an unusual stability property is first found herein since its unconditional stability interval is drastically different for zero and nonzero damping. In fact, instability might occur for solving a damped stiffness hardening system while an accurate result can be obtained for the corresponding undamped stiffness hardening system. A technique of using a stability factor is applied to overcome this difficulty. It can be applied to magnify an unconditional stability interval. After introducing this stability factor, the formulation of this family of structure-dependent methods is changed accordingly and thus its numerical properties must be re-evaluated. In summary, a large stability factor can result in a large unconditional stability interval but also lead to a large relative period error. As a consequence, a stability factor must be appropriately chosen to have a desired unconditional stability interval in addition to an acceptable period distortion.

• Carbon letters
• /
• 제14권1호
• /
• pp.27-33
• /
• 2013

An increase in population initiating rapid industrialization was found to consequently increase the effluents and domestic wastewater into the aquatic ecosystem. In this research the potentialities of Sambucus nigra L. (SNL) plant in the remediation of water, contaminated with methylene blue (MB), a basic dye were investigated. SNL was chemically impregnated with $KHCO_3$. Operating variables studied were pH, amount of adsorbent and contact time. In general, pH did not have any significant effect on colour removal and the highest adsorption capacity was obtained in 0.035 g MB/g-activated carbon. The Langmuir, Freundlich, Temkin and Dubinin-Radushkevich adsorption models were applied to describe the equilibrium isotherms. The adsorption isotherm data were fitted to the Temkin isotherm. The mass transfer property of the sorption process was studied using Lagergren pseudo-first-order and chemisorption pseudo-second-order kinetic models. The sorption process obeyed the pseudo-second-order kinetic model. The surface area, pores volume and diameter were assessed by the Brunauer-Emmett-Teller and Barrett-Joyner-Halenda methods. The results were compared to those from activated carbon (Merck) and an actual sample. The results indicate that SNL can be employed as a natural and eco-friendly adsorbent material for the removal of dye MB from aqueous solutions.

• 멤브레인
• /
• 제9권4호
• /
• pp.209-214
• /
• 1999

본 연구의 목적은 냉연공장 폐수재이용을 위해 3단 역삼투시스템 사용시 각단에서의 투과특성을 조사하는 것이다 판틀형 모듈 7개를 사용하여 회수율이 75% 가 되도록 3단 (배열 : 4+2+1) 으로 구성하여 장기간에 걸친 pilot test를 통해 막오염 진행에 따른 각 단에서의 유량 및 수질변화를 조사하였다 실험결과 각 단 모듈 1개당 평균 투과수량은 운전초기에는 1단, 2단, 3단의 순서로 많았으나 운전시간이 경과하며 막오염이 진행됨에 따라 1단은 감소하는 반면 2단은 거의 변화가 없고 3단의 투과수량은 증가하였다 즉 막오염은 주로 1단에서 발생하며 점차 2단. 3단으로 진행되는 것을 확인할수 있었다. 한편 투과수 수질은 예상한 것과 같이 1단이 가장 우수하였고 다음으로는 2단, 3단의 순서였으며 막오염에 영향을 받지않았다.