• Korean Journal of Optics and Photonics
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• v.29 no.4
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• pp.166-172
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• 2018

In this paper, we propose a new method to predict a mirror's surface deformation due to the stress of moisture release by a coating in the environment of outer space. We measured the surface deformation of circular samples 50 mm in diameter and 1.03 mm thick, using an interferometer. The results were analyzed using Zernike fringe polynomials. The coating stress caused by moisture release was calculated to be 152.7 MPa. This value was applied to an analytic model of a 1.25 mm thickness sample mirror, confirming that the change of surface deformation could be predicted within the standard deviation of the measurement result ($78.9{\pm}5.9nm$). Using this methodology, we predicted the surface deformation of 600 mm hyperbolic mirror for the Compact Advanced Satellite, which will be launched in 2019. The result is only $2.005{\mu}m$ of focal shift, leading to 2.3% degradation of modulation transfer function (MTF) at the Nyquist frequency, which satisfies the requirement.

• Journal of the Korean Mathematical Society
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• v.54 no.2
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• pp.599-612
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• 2017

If ${\psi}$ is analytic on the open unit disk $\mathbb{D}$ and ${\varphi}$ is an analytic self-map of $\mathbb{D}$, the weighted composition operator $C_{{\psi},{\varphi}}$ is defined by $C_{{\psi},{\varphi}}f(z)={\psi}(z)f({\varphi}(z))$, when f is analytic on $\mathbb{D}$. In this paper, we study normal, cohyponormal, hyponormal and normaloid weighted composition operators on the Hardy and weighted Bergman spaces. First, for some weighted Hardy spaces $H^2({\beta})$, we prove that if $C_{{\psi},{\varphi}}$ is cohyponormal on $H^2({\beta})$, then ${\psi}$ never vanishes on $\mathbb{D}$ and ${\varphi}$ is univalent, when ${\psi}{\not\equiv}0$ and ${\varphi}$ is not a constant function. Moreover, for ${\psi}=K_a$, where |a| < 1, we investigate normal, cohyponormal and hyponormal weighted composition operators $C_{{\psi},{\varphi}}$. After that, for ${\varphi}$ which is a hyperbolic or parabolic automorphism, we characterize all normal weighted composition operators $C_{{\psi},{\varphi}}$, when ${\psi}{\not\equiv}0$ and ${\psi}$ is analytic on $\bar{\mathbb{D}}$. Finally, we find all normal weighted composition operators which are bounded below.

• Journal of applied mathematics & informatics
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• v.15 no.1_2
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• pp.29-51
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• 2004

In this paper, we propose a new mixed finite element method, called the characteristics-mixed method, for approximating the solution to Burgers' equation. This method is based upon a space-time variational form of Burgers' equation. The hyperbolic part of the equation is approximated along the characteristics in time and the diffusion part is approximated by a mixed finite element method of lowest order. The scheme is locally conservative since fluid is transported along the approximate characteristics on the discrete level and the test function can be piecewise constant. Our analysis show the new method approximate the scalar unknown and the vector flux optimally and simultaneously. We also show this scheme has much smaller time-truncation errors than those of standard methods. Numerical example is presented to show that the new scheme is easily implemented, shocks and boundary layers are handled with almost no oscillations. One of the contributions of the paper is to show how the optimal error estimates in $L^2(\Omega)$ are obtained which are much more difficult than in the standard finite element methods. These results seem to be new in the literature of finite element methods.

• Geomechanics and Engineering
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• v.29 no.6
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• pp.615-626
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• 2022

The soft clays are widely distributed, and one of the prominent engineering problems is the creep behavior. In order to predict the creep deformation of soft clays in an easier and more acceptable way, a simple creep constitutive model has been proposed in this paper. Firstly, the triaxial creep test data indicated that, the strain-time (𝜀-t) curve showing in the 𝜀-lgt space can be divided into two lines with different slopes, and the time referring to the demarcation point is named as t_EOP. Thereafter, the strain increments occurred after the time t_EOP are totally assumed to be the creep components, and the elastic and plastic strains had occurred before t_EOP. A hyperbolic equation expressing the relationship between creep volumetric strain, stress and time is proposed, with several triaxial creep test data of soft clays verifying the applicability. Additionally, the creep flow law is suggested to be similar with the plastic flow law of the modified Cam-Clay model, and the proposed volumetric strain equation is used to deduced the scaling factor for creep strains. Therefore, a creep constitutive model is thereby established, and verified by successfully predicting the creep principal strains of triaxial specimens.

• Horticultural Science & Technology
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• v.29 no.3
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• pp.201-210
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• 2011

This experiment was conducted to investigate physical and chemical characteristics by volume fractions of root media using peatmoss, perlite, and vermiculite, along with effects on the growth of pot chrysanthemums (Dendranthema ${\times}$ grandiflorum 'Vemini') in a C-channel mat irrigation system. To evaluate the physico-chemical properties of 20 root media, the bulk density, particle density, total pore space, pore space, ash content, organic matter, pH, and electrical conductivity were measured and data were analyzed using principal component analysis (PCA). PCA scores revealed that physico-chemical properties changed by the blending of peatmoss, perlite, and vermiculite. The 20 root media were divided into three main groups by hierarchical cluster analysis. At the end of the experiment, the pH and EC of the root media were measured from media divided into four layers. The pH of root media without plants showed a strong linear relationship and the pH of root media with plants increased exponentially. The change of EC in the root medium was indicated as a hyperbolic curve. Plant growth characteristics according to growth in the 20 root media were analyzed by PCA. It was found that the mixing ratios of the root media affected plant growth characteristics. Therefore, mixing ratio is an important factor for pot-plant production in a subirrigation system.

• Journal of Astronomy and Space Sciences
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• v.33 no.4
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• pp.323-333
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• 2016

In this study, the uncertainty requirements for orbit, attitude, and burn performance were estimated and analyzed for the execution of the $1^{st}$ lunar orbit insertion (LOI) maneuver of the Korea Pathfinder Lunar Orbiter (KPLO) mission. During the early design phase of the system, associate analysis is an essential design factor as the $1^{st}$ LOI maneuver is the largest burn that utilizes the onboard propulsion system; the success of the lunar capture is directly affected by the performance achieved. For the analysis, the spacecraft is assumed to have already approached the periselene with a hyperbolic arrival trajectory around the moon. In addition, diverse arrival conditions and mission constraints were considered, such as varying periselene approach velocity, altitude, and orbital period of the capture orbit after execution of the $1^{st}$ LOI maneuver. The current analysis assumed an impulsive LOI maneuver, and two-body equations of motion were adapted to simplify the problem for a preliminary analysis. Monte Carlo simulations were performed for the statistical analysis to analyze diverse uncertainties that might arise at the moment when the maneuver is executed. As a result, three major requirements were analyzed and estimated for the early design phase. First, the minimum requirements were estimated for the burn performance to be captured around the moon. Second, the requirements for orbit, attitude, and maneuver burn performances were simultaneously estimated and analyzed to maintain the $1^{st}$ elliptical orbit achieved around the moon within the specified orbital period. Finally, the dispersion requirements on the B-plane aiming at target points to meet the target insertion goal were analyzed and can be utilized as reference target guidelines for a mid-course correction (MCC) maneuver during the transfer. More detailed system requirements for the KPLO mission, particularly for the spacecraft bus itself and for the flight dynamics subsystem at the ground control center, are expected to be prepared and established based on the current results, including a contingency trajectory design plan.

• Tunnel and Underground Space
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• v.21 no.2
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• pp.117-127
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• 2011

The purpose of this study is to demonstrate the effect of in-situ rock stresses on the deformability and permeability of fractured rocks. Geological data were taken from the site investigation at Forsmark, Sweden, conducted by Swedish Nuclear Fuel and Waste Man-agement Company (SKB). A set of numerical experiments was conducted to determine the equivalent mechanical properties (essentially, elastic moduli and Poisson's ratio) and permeability, using a Discrete Fracture Network-Discrete Element Method (DFN-DEM) approach. The results show that both mechanical properties and permeability are highly dependent on stress because of the hyperbolic nature of the stiffness of fractures, different closure behavior of fractures, and change of fluid pathways caused by deformation. This study shows that proper characterization and consideration of in-situ stress are important not only for boundary conditions of a selected site but also for the understanding of the mechanical and hydraulic behavior of fractured rocks.

• Journal of Korean Association for Spatial Structures
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• v.2 no.3 s.5
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• pp.81-92
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• 2002

The objective of this paper is to help to make decision of the appropriate structural types in long span structured building due to range of span. For the intention, based on 7 forces of structural element, it is analized the relationships among 6 configurations of structural element(d/1), 25 structural types, 4 materials, and span-length known with 186 sample from 1850 to 1996. 1) bending forces: $club(1/100{\sim}1/10),\;plate(1/100{\sim}1/10),\;rahmen(steel,\;10{\sim}24m)\;simple\;beam(PC,\;10{\sim}35m)$ 2) shearing forces: $shell(1/100{\sim}1/1000)\;hyperbolic\;paraboloids(RC,25{\sim}97m)$ 3) shearing+bending forces: plate, folded $plate(RC21{\sim}59m)$ 4) compression axial forces: club, $arch(RC,\;32{\sim}65m)$ 5) compression+tension forces: shell, braced dome $shell(RC,\;40{\sim}201m),\;vault\;shell(RC,\;16{\sim}103m)$ 6) compression+tension axial forces: $rod(1/1000{\sim}1/100)$, cable(below 1/1000)+rod, coble+rod+membrane(below 1/1000), planar $truss(steel,\;31{\sim}134m),\;arch\;truss(31{\sim}135m),\;horizontal\;spaceframe(29{\sim}10\;8m),\;portal\;frame(39{\sim}55m),\;domical\;space\;truss(44{\sim}222m),\;framed\;\;membrane(45{\sim}110m),\;hybrid\;\;membrane\;(42{\sim}256m)$ 7) tension forces: cable, membrane, $suspension(60{\sim}150m),\;cable\;\;beam(40{\sim}130m),\;tensile\;membrane(42{\sim}136m),\;cable\;-slayed(25{\sim}90m),\;suspension\;membrane(24{\sim}97m),\;single\;layer\;pneumatic\;structure(45{\sim}231m),\;double\;layer\;pneumatic\;structures(30{\sim}44m)$

• Computers and Concrete
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• v.19 no.4
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• pp.419-427
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• 2017

With the rising global environmental awareness on energy saving and carbon reduction, as well as the environmental transition and natural disasters resulted from the greenhouse effect, waste resources should be efficiently used to save environmental space and achieve environmental protection principle of "sustainable development and recycling". This study used recycled cement mortar and adopted the volumetric method for experimental design, which replaced cement (0%, 10%, 20%, 30%) with recycled materials (fly ash, slag, glass powder) to test compressive strength and ultrasonic pulse velocity (UPV). The hyperbolic function for nonlinear multivariate regression analysis was used to build prediction models, in order to study the effect of different recycled material addition levels (the function of $R_m$(F, S, G) was used and be a representative of the content of recycled materials, such as fly ash, slag and glass) on the compressive strength and UPV of cement mortar. The calculated results are in accordance with laboratory-measured data, which are the mortar compressive strength and UPV of various mix proportions. From the comparison between the prediction analysis values and test results, the coefficient of determination $R^2$ and MAPE (mean absolute percentage error) value of compressive strength are 0.970-0.988 and 5.57-8.84%, respectively. Furthermore, the $R^2$ and MAPE values for UPV are 0.960-0.987 and 1.52-1.74%, respectively. All of the $R^2$ and MAPE values are closely to 1.0 and less than 10%, respectively. Thus, the prediction models established in this study have excellent predictive ability of compressive strength and UPV for recycled materials applied in cement mortar.

• Proceedings of the Korea Association of Crystal Growth Conference
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• 1996.06b
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• pp.285-309
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• 1996

Non oxide ceramics such as nitrides of transition metals have shown significant potential for future economic impact, in diverse applications in ceramic, aerospace and electronic industries, as refractory products, abrasives and cutting tools, aircraft components, and semi-conductor substrates amid others. Combustion synthesis has become an attractive alternative to the conventional furnace technology to produce these materials cheaply, faster and at a higher level of purity. However he process os highly exothermic and manifests complex dynamics due to its strongly non-linear nature. In order to develop an understanding of this process and to study the effect of operational parameters on the final outcome, numerical modeling is necessary, which would generated essential knowledge to help scale-up the process. the model is based on a system of parabolic-hyperbolic partial differential equations representing the heat, mass and momentum conservation relations. The model also takes into account structural change due to sintering and volumetric expansion, and their effect on the transport properties of the system. The solutions of these equations exhibit steep moving spatial gradients in the form of reaction fronts, propagating in space with variable velocity, which gives rise to varying time scales. To cope with the possibility of extremely abrupt changes in the values of the solution over very short distances, adaptive mesh techniques can be applied to resolve the high activity regions by ordering grid points in appropriate places. To avoid a control volume formulation of the solution of partial differential equations, a simple orthogonal, adaptive-mesh technique is employed. This involves separate adaptation in the x and y directions. Through simple analysis and numerical examples, the adaptive mesh is shown to give significant increase in accuracy in the computations.