• Title/Summary/Keyword: Differential equations

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Biaxial Buckling Analysis of Magneto-Electro-Elastic(MEE) Nano Plates using the Nonlocal Elastic Theory (비국소 탄성이론을 이용한 자기-전기-탄성 나노 판의 2방향 좌굴 해석)

  • Han, Sung-Cheon;Park, Weon-Tae
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.30 no.5
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    • pp.405-413
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    • 2017
  • In this paper, we study the biaxial buckling analysis of nonlocal MEE(magneto-electro-elastic) nano plates based on the first-order shear deformation theory. The in-plane electric and magnetic fields can be ignored for MEE(magneto-electro-elastic) nano plates. According to magneto-electric boundary condition and Maxwell equation, the variation of magnetic and electric potentials along the thickness direction of the MME plate is determined. In order to reformulate the elastic theory of MEE(magneto-electro-elastic) nano-plate, the nonlocal differential constitutive relations of Eringen is used. Using the variational principle, the governing equations of the nonlocal theory are discussed. The relations between nonlocal and local theories are investigated by computational results. Also, the effects of nonlocal parameters, in-plane load directions, and aspect ratio on structural responses are studied. Computational results show the effects of the electric and magnetic potentials. These computational results can be useful in the design and analysis of advanced structures constructed from MEE(magneto-electro-elastic) materials and may be the benchmark test for the future study.

Dissolution of Oxygen in Water by Nonporous Hollow Fiber Membrane Contactor (비다공성 분리막을 이용한 수용액 내 용존 산소 조절)

  • Lee, Yong-Taek;Jeong, Heon-Kyu;Ahn, Hyo-Seong;Song, In-Ho;Jeon, Hyun-Soo;Jeong, Dong-Jae
    • Membrane Journal
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    • v.17 no.4
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    • pp.352-358
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    • 2007
  • A nonporous hollow fiber membrane contactor was used to control the concentration of oxygen dissolved in an aqueous solution, which was predicted along the hollow fiber membrane using a computer simulation. The governing ordinary differential equations were derived for the occurrent flows of the feed aqueous solution and the feed gas mixture in a membrane contactor and they were numerically solved using the 5th Runge-Kutta-Verner method with a personal computer, where the program was coded utilizing a software of the Compaq Visual Fortran 6.6. It is found that the concentration of oxygen dissolved in water increases from 30 to 64 ppm as the length of the hollow fiber increases from 0.4 to 1.2 m when the membrane of fibers are equal to be 16,000; the flow rate of the feed gas is kept to be 0.536 mol/sec; its pressure is maintained to be 486 kPa; the flow rate of the water is 16.69 mol/sec. As the flow rate of the water increases from 9.26 to 26.85 mol/sec, the concentration of oxygen decreases from 40 to 20 ppm with the constant fiber length of 0.4 m. Finally, it is observed that the concentration of oxygen increases from 33 to 69 ppm as the pressure of the feed gas increases from 298 to 847 kPa.

Studies of Solid-Liquid Phase Equilibria for Mixtures of N-vinyl-2-pyrrolidone+2-pyrrolidone and Growth Rate of N-vinyl-2-pyrrolidone Crystal Using Melt Crystallization (N-vinyl-2-pyrrolidone과 2-pyrrolidone 혼합물의 고-액 상평형 및 용융결정화를 이용한 N-vinyl-2-pyrrolidone의 결정성장속도 연구)

  • Kim, Sun Hyung;Seo, Myoung Do;Tak, Moon Seon;Kim, Woo Sik;Yang, Dae Ryuk;Kang, Jeong Won
    • Korean Chemical Engineering Research
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    • v.51 no.5
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    • pp.587-590
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    • 2013
  • Solid-liquid equilibria for mixtures composed of n-vinyl-2-pyrrolidone (NVP) and 2-pyrrolidone were measured as a basic study for the melt crystallization process to remove 2-pyrrolidone as impurity included in NVP. A differential scanning calorimeter (DSC) and a crystallizer were used and the experimental results obtained from two methods were similar. The mixture showed a eutectic system which has a single composition at the minimum melting temperature. Calculation results from simple thermodynamic equations were found in general agreements with present data. To determine the growth rate of NVP crystal which is important for the design of crystallization process, thicknesses of the crystal were measured with the time using a layer melt crystallizer. The growth rates increased as cooling temperatures decreased. Heat transfer coefficient correlated from present data was found to successfully describe the crystal growth behavior.

A Comic Facial Expression Method for Intelligent Avatar Communications in the Internet Cyberspace (인터넷 가상공간에서 지적 아바타 통신을 위한 코믹한 얼굴 표정의 생성법)

  • 이용후;김상운;청목유직
    • Journal of the Institute of Electronics Engineers of Korea CI
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    • v.40 no.1
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    • pp.59-73
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    • 2003
  • As a means of overcoming the linguistic barrier between different languages in the Internet, a new sign-language communication system with CG animation techniques has been developed and proposed. In the system, the joint angles of the arms and the hands corresponding to the gesture as a non-verbal communication tool have been considered. The emotional expression, however, could as play also an important role in communicating each other. Especially, a comic expression is more efficient than real facial expression, and the movements of the cheeks and the jaws are more important AU's than those of the eyebrow, eye, mouth etc. Therefore, in this paper, we designed a 3D emotion editor using 2D model, and we extract AU's (called as PAU, here) which play a principal function in expressing emotions. We also proposed a method of generating the universal emotional expression with Avatar models which have different vertex structures. Here, we employed a method of dynamically adjusting the AU movements according to emotional intensities. The proposed system is implemented with Visual C++ and Open Inventor on windows platforms. Experimental results show a possibility that the system could be used as a non-verbal communication means to overcome the linguistic barrier.

Experimental and FEMLAB Simulation Study of Ibuprofen Racemate Separation in HPLC (Ibuprofen Racemate의 HPLC 분리실험과 FEMLAB 전산모사 연구)

  • Lee, Eun;Chang, Sang-Mork;Kim, Jong-Min;Kim, Woo-Shick;Kim, In-Ho
    • KSBB Journal
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    • v.21 no.3
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    • pp.224-229
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    • 2006
  • FEMLAB is a powerful interactive environment for modeling, solving all kinds of scientific and engineering problems based on partial differential equations(PDEs). Separation process of chiral compound in HPLC columns was simulated by FEMLAB. To study change of elution profile with isotherm models, non-competitive and competitive Langmuir adsorption isotherm were adopted. Separated material was (R, S)-ibuprofen [(R, S)-2-(4-isobutyl phenyl) propionic acid], an anti-inflammatory agent, which retain the pharmacological activity in the (S)-(+)-enantiomer. Sample concentrations were changed from 0.5 mg/ml to 2.0 mg/ml at a flow rate of 1 ml/min and flow rate varied from 1 ml/min to 3 ml/min at an ibuprofen concentration of 2.0 mg/ml and $20{\mu}l$ of injection volume. Simulated results were well fitted with experimental data.

Kinetic Behavior of Immobilized Tyrosinase on Carbon in a Simulated Packed-Bed Reactor (충전층에서 탄소에 고정시킨 Tyrosinase의 반응속도에 관한 연구)

  • Shin, Sun Kyoung;Kim, Kyeo-Keun
    • Analytical Science and Technology
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    • v.10 no.1
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    • pp.66-74
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    • 1997
  • Influence of the axial dispersion on immobilized enzyme catalytic bed was investigated in order to examine the kinetic behavior of the biocatalysis. The enzyme employed in this study was the tyrosinase(EC 1.14.18.1) immobilized on carbon support : this system requires two substrates of phenol and oxygen. This enzyme has potential application for phenol degradation in waste water. A simulated reactor was a packed-bed reactor of 2.54cm in diameter and 10cm long, loaded with the immobilized carbon particle with an average diameter of $550{\mu}m$. A phenol feed in the strength of 55.5mM(5220ppm) was used to observe the behavior of the immobilized enzyme column at three different dissolved oxygen levels of 0.08445mM(2.7ppm), 0.1689mM(5.4ppm) and 0.3378mM(9.5ppm) with the flow rates in the range of 60(1mL/s) to 180mL/min(3mL/s). Examination of the Biot number and Damkolher numbers of the immobilized system enables us to eliminate the contribution of external mass transfer to set of differential equations derived from the dispersion model. Solution of the equation was finally obtained numerically with the application of the Danckwert boundary conditions and the assumed zero-and first order rates on the non-linear two substrate enzyme kinetics. Higher conversion of phenol was observed at the low flow rates and at the higher oxygen concentration. Comparison of axial dispersion and plug flow model showed that no detectable difference was observed in the column outlet conversion between the axial and the plug flow models which was in complete agreement with the previous studies.

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Fundamentals of Tight fitted Contact Lens Movement (Tight Fit 콘택트렌즈 운동의 기초)

  • Kim, Dae Soo
    • Journal of Korean Ophthalmic Optics Society
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    • v.14 no.3
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    • pp.17-27
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    • 2009
  • Purpose: This review article was written to determine the effects of parameters characterizing a hard contact lens (RGP included), such as BCs, diameters, edge angles, on the time interval for tight fitted lens to return to the equilibrium when it was decentered from blinking. Methods: A mathematical formulation was established to relate or calculate the restoring forces and thickness of lacrimal layer beneath the cornea with the various lens parameters when the tight fitted lens was decentered from blinking. Based on this formulation the differential equations and their numerical solution program were set up to describe the time dependence of the lens on the position and to estimate the time for the lens's return to the equilibrium after blink. Results: It is found that the time interval for the tight fitted lens to return to the equilibrium decreases as either the BC decreases or the diameter increases because both the reduction in BC and increase in diameter result in the increase in the lacrimal layer thickness between the lens and cornea increase which yielded the lowering of the viscous friction in the lens motion. As the edge angle of tight fitted lens increases the time for recentering decreases due to the increase in restoring force without change in lacrimal thickness beneath the lens. In the case of flat fitted hard lens (RGP included), the lacrimal layer thickness under the lens increases as either BC or diameter increases which results in reduction in viscous friction so that the time for the lens's return to the equilibrium were to decrease. The edge angle of flat fitted lens does not affect the lens motion. Conclusions: The effect of BCs on the lens motion (time to approach the equilibrium) was concluded to be significant with both tight and flat fitted lens where its results are contrary with each other. The edge angle of lens only affects the motion in tight fitted lenses.

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Is Backwards Causation Possible? (후향적인 인과성은 가능한가?)

  • Ahn, Gan-Hun
    • Journal of Korean Philosophical Society
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    • v.105
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    • pp.269-290
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    • 2008
  • The purpose of this paper is to explore the possibility of backwards causation. For study, this paper was divided into four views as follows: The first view was sometimes suggested by the people such as M. Dummett who distinguished observers from behaviors. According to observers' view, backwards causation is impossible, whereas behaviors' view possible. However, in a real or genuine sense, it is incorrect for us to argue for impossibility of backwards causation from the observer aspect. The second view was supported by J. H. Schmidt. He analyzed the possibility of backwards causation in terms of macro and micro level analysis about the causal events. According to micro level analysis, backwards causation is possible, but macro level analysis impossible. Usually the latter makes the former something miraculous. Under the macro level analysis, backwards causation, at first, seems to be miraculous phenomena which belongs to the micro level analysis. The third view had to do with physical equation, and the fourth view physical phenomena, respectively. John Earman argued for the backwards causation by the transformation from Lorentz­-Dirac equation to a second-order integro-differential one in the field of electrodynamic acceleration. His argument was criticized because of his misunderstanding about the relationship between two equations. On the other hand, Phil Dowe defended a version of Reichenbach's own theory about the direction of causation founded on the fork asymmetrical causal relation. However his view was different from Reichenbach's because the former defended the backwards causation model of Bell phenomena in quantum mechanics. On the contrary, Reichenbach put stressed on the priority of cause in the causal process. Subjectivism has recently been defended by H. Price, under the label of perspectivism. According to him, in a certain sense causal asymmetry is not in the world, but is rather a product of our own asymmetric perspective on the world. He also suggested causal net, the symmetry of microphysics, and so on. As mentioned above, there are many kind of suggestions of backwards causation. However none of them replaced objectively the main streams of the direction of causal process. The main stream has been usually defended by pragmatical ground. That is, effects do not precede their causes although causes cannot be without their effects.

Development of Optimal Chlorination Model and Parameter Studies (최적 염소 소독 모형의 개발 및 파라미터 연구)

  • Kim, Joonhyun;Ahn, Sooyoung;Park, Minwoo
    • Journal of Environmental Impact Assessment
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    • v.29 no.6
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    • pp.403-413
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    • 2020
  • A mathematical model comprised with eight simultaneous quasi-linear partial differential equations was suggested to provide optimal chlorination strategy. Upstream weighted finite element method was employed to construct multidimensional numerical code. The code was verified against measured concentrations in three type of reactors. Boundary conditions and reaction rate were calibrated for the sixteen cases of experimental results to regenerate the measured values. Eight reaction rate coefficients were estimated from the modeling result. The reaction rate coefficients were expressed in terms of pH and temperature. Automatic optimal algorithm was invented to estimate the reaction rate coefficients by minimizing the sum of squares of the numerical errors and combined with the model. In order to minimize the concentration of chlorine and pollutants at the final usage sites, a real-time predictive control system is imperative which can predict the water quality variables from the chlorine disinfection process at the water purification plant to the customer by means of a model and operate the disinfection process according to the influent water quality. This model can be used to build such a system in water treatment plants.

The Effect Analysis of COVID-19 vaccination on social distancing (코로나19 백신접종이 사회적 거리두기 효과에 미치는 영향분석)

  • Moon, Su Chan
    • Journal of the Korea Convergence Society
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    • v.13 no.2
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    • pp.67-75
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    • 2022
  • The purpose of this study is to present an appropriate management plan as a supplement to the scientific evidence of the currently operated distancing system for preventing COVID-19. The currently being used mathematical models are expressed as simultaneous ordinary differential equations, there is a problem in that it is difficult to use them for the management of entry and exit of small business owners. In order to supplement this point, in this paper, a method for quantitatively expressing the risk of infection by people who gather is presented in consideration of the allowable risk given to the gathering space, the basic infection reproduction index, and the risk reduction rate due to vaccination. A simple quantitative model was developed that manages the probability of infection in a probabilistic level according to a set of visitors by considering both the degree of infection risk according to the vaccination status (non-vaccinated, primary inoculation, and complete vaccination) and the epidemic status of the virus. In a given example using the model, the risk was reduced to 55% when 20% of non-vaccinated people were converted to full vaccination. It was suggested that management in terms of quarantine can obtain a greater effect than medical treatment. Based on this, a generalized model that can be applied to various situations in consideration of the type of vaccination and the degree of occurrence of confirmed cases was also presented. This model can be used to manage the total risk of people gathered at a certain space in a real time, by calculating individual risk according to the type of vaccine, the degree of inoculation, and the lapse of time after inoculation.