• 한국임상약학회지
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• 제31권2호
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• pp.125-135
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• 2021

Background: Generally, pharmacokinetics (PK) models could be stratified into two models. The compartment PK model uses the concept of simple compartmentalization to describe complex bodies, and the physiologically based pharmacokinetic (PBPK) model describes the body using multi-compartment networking. Notwithstanding sharing a theoretical background in both models, there was still a lack of knowledge to enhance compatibility in both models. Objective: This study aimed to evaluate the compatibility among PBPK, lumping model and compartment PK model with voriconazole PK case study. Methods: The number of compartments and blood flow on each tissue in the PBPK model were modified using the lumping method, considering physiological similarities. The concentration-time profiles and area under the concentration-time curve (AUC) parameters were simulated at each model, assuming taken voriconazole oral 400 mg single dose. After that, those mentioned PK parameters were compared. Results: The PK profiles and parameters of voriconazole in the three models were similar that proves their compatibility. The AUC of central compartment in the PBPK and lumping model was within a 2-fold range compared to those in the 2- compartment model. The AUC of non-eliminating tissues compartment in the PBPK model was similar to those in the lumping model. Conclusion: Regarding the compatibility of the three PK models, the utilization of the lumping method was confirmed by suggesting its reliable PK parameters with PBPK and compartment PK models. Further case studies are recommended to confirm our findings.

• Steel and Composite Structures
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• 제23권6호
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• pp.683-690
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• 2017

In the stability and sensitivity design and diagnosis approaches, there are various methodologies available. Bond graph modeling by lumping technique is one of the universal methodologies in methodical analysis used by many researchers in all over the world. The accuracy of the method is validated in different arenas. Bond graphs are a concise, pictorial representation of the energy storage, dissipation and exchange mechanisms of interacting dynamic systems, subsystems and components. This paper proposes a bond graph modeling for distributed parameter systems using lumping techniques. Therefore, a steel frame structure was modeled to analyze employing bond graph modeling of distributed system using lumping technique. In the analytical part, the effectiveness of bond graphs to model this system is demonstrated. The dynamic responses of the system were computed and compared with those computed from the finite element analysis. The calculated maximum deflection time histories were found to be comparable. The sensitivity and the stability of the steel frame structure was also studied in different aspects. Thus, the proposed methodology, with its simplicity, can be used for stability and sensitivity analyses as alternative to finite element method for steel structures. The major value brought in the practical design is the simplicity of the proposed method for steel structures.

• Journal of Welding and Joining
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• 제11권3호
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• pp.34-47
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• 1993

용접에서 발생하는 열응력 및 잔류응력을 해석하기 위한 유한요소용 모델을 개발하였다. 여러 가 지 변수의 연구를 통하여 Ramp heat input function과 Lumped모델을 제시하였다. 용접부에 열입 력을 점차적으로 주기 위하여 Ramp heat input을 이용하였으며 Ramp input을 통하여 이차원 모 델에서의 이동열원의 영향을 고려하였고 실험치와 비교에서 최적 ramp시간을 결정하였다. 다층용 접에서는 용접 pass 에 비례하여 계산시간이 증가한다. 따라서 후판용접의 잔류응력계산에는 막 대한 계산시간이 필요하며 이를 줄이기 위하여 Lumped 모델을 개발하였다. 이 Lumped모델에서 는 각 용접층에 들어있는 용접 pass들을 하나의 lumped pass으로 이용하였으며 각 pass를 따로 계산한 모델 및 시험치와의 비교를 통하여 최적 lumped technique을 제시하였다. *****Finite element models were developed for thermal and residual stress analysis for the specific welding problems. They were used to evaluate the effectiveness of the various welding heat input models, such as ramp heat input function and lumped pass models. Through the parametric studies, thermal-mechanical modeling sensitivity to the ramp function and lumping techniques was determined by comparing the predicted results with experimental data. The kinetics for residual stress formation during welding can be developed by iteration of various proposed mechanisms in the parametric study. A ramp heat input function was developed to gradually apply the heat flux with variable amplitude to the model. This model was used to avoid numerical convergence problems due to an instantaneous increase in temperature near the fusion zone. Additionally, it enables the model to include the effect of a moving arc in a two-dimensional plane. The ramp function takes into account the variation in the out of plane energy flow in a 2-D model as the arc approaches, travels across, and departs from each plane under investigation. A lumped pass model was developed to reduce the computation cost in the analysis of multipass welds. Several weld passes were assumed as one lumped pass in this model. Recommendations were provided about ramp lumping techniques and the optimum number of weld passes that can be combined into a single thermal input.

• 한국해안·해양공학회논문집
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• 제22권1호
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• pp.47-57
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• 2010

Woo and Liu (2004)의 확장형 Boussinesq FEM 수치모형에서 한계점으로 지적되었던 수치진동현상과 계산 효율성이 크게 개선되었다. 수치진동을 해결하기 위해 subgrid scale stabilization method를 사용하였고, 계산효율성을 높이기 위해서 Hessian 연산자를 도입하였으며, 유속벡터에 대한 행렬 구성을 하나의 행렬로 구성하였다. 또한 추가변수에 대한 행렬은 mass lumping technique을 사용하여 대각행렬로 구성하였다. Vincent and Briggs(1989)의 파랑 굴절 및 회절에 대한 수치실험 결과 수치진동현상이 확연히 줄어 들은 것을 관찰할 수 있었으며, 수리실험 결과와도 상당히 일치하는 결과를 보였다. 이전 모형에 비해 약 10배의 계산소요시간이 줄어 향후 항만부진동이나 퇴적물 이동과 같은 현실적인 문제에 적용이 가능할 것으로 기대된다.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제20권3호
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• pp.243-259
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• 2016

The Richards equation for water movement in unsaturated soil is highly nonlinear partial differential equations which are not solvable analytically unless unrealistic and oversimplifying assumptions are made regarding the attributes, dynamics, and properties of the physical systems. Therefore, conventionally, numerical solutions are the only feasible procedures to model flow in partially saturated porous media. The standard Finite element numerical technique is usually coupled with an Euler time discretizations scheme. Except for the fully explicit forward method, any other Euler time-marching algorithm generates nonlinear algebraic equations which should be solved using iterative procedures such as Newton and Picard iterations. In this study, lumped mass and distributed mass in the frame of Picard and Newton iterative techniques were evaluated to determine the most efficient method to solve the Richards equation with finite element model. The accuracy and computational efficiency of the scheme and of the Picard and Newton models are assessed for three test problems simulating one-dimensional flow processes in unsaturated porous media. Results demonstrated that, the conventional mass distributed finite element method suffers from numerical oscillations at the wetting front, especially for very dry initial conditions. Even though small mesh sizes are applied for all the test problems, it is shown that the traditional mass-distributed scheme can still generate an incorrect response due to the highly nonlinear properties of water flow in unsaturated soil and cause numerical oscillation. On the other hand, non oscillatory solutions are obtained and non-physics solutions for these problems are evaded by using the mass-lumped finite element method.

• 한국해안·해양공학회논문집
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• 제21권2호
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• pp.108-116
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• 2009

유한요소법에 사용되어 효율적으로 파랑변형을 해석할 수 있는 (Legendre 보간 함수) 방법을 소개하였다. 고차의 보간함수를 사용하는 유한요소모형은 대부분이 Lagrangian 보간 함수를 사용한다. 이 경우, 적은 수의 요소를 사용하고도 정확한 결과를 얻을 수 있다는 장점이 있지만 결과를 얻기 위해 소요되는 시간이 증가한다는 단점이 있다. Mass lumping을 통하여 계산 시간을 절약할 수는 있지만 이 경우에는 해의 정확성이 떨어진다는 단점이 있어 정확도를 향상시키기 위하여 요소의 수를 증가시켜 다시 계산시간이 증대되는 문제가 생기게 된다. 본 연구에서 Lagrangian 보간 함수의 변형된 형태인 Legendre 보간함수에 수치적분을 사용하여 mass lumping을 수행한 것과 같이 대각 행렬을 만들어 시간 절약의 효과를 얻으면서도 정확도가 어느 정도 유지되는 방법을 소개하였다. Boussinesq 방정식을 이용한 다양한 수치 계산을 통하여 본 연구에서 제안하는 방법의 우수성을 검증하였다.

• KSBB Journal
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• 제14권5호
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• pp.550-560
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• 1999

There have been many research efforts on biofilter modeling including Ottengraf et al. who derived a model equation for the concentration profile of pollutants(e.g., VOCs) in the biolayer and solved their outlet concentration of the waste gas stream through biofilter. However, for most of research works done so far, the effects to explain the effect of adsorption of organic particles to medium(i.e., adsorbent) have been ignored. In this work biofilter modeling accompanying process lumping has been proposed and the theoretical effect of adsorption property of the medium, on the biofilter performance of eliminating organic components in waste gas stream, is intensively discussed.

• 한국국방경영분석학회지
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• 제11권1호
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• pp.111-129
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• 1985

Markov chains with large transition probability matrices occur in many applications such as manpowr models. Under certain conditions the state space of a stationary discrete parameter finite Markov chain may be partitioned into subsets, each of which may be treated as a single state of a smaller chain that retains the Markov property. Such a chain is said to be 'lumpable' and the resulting lumped chain is a special case of more general functions of Markov chains. There are several reasons why one might wish to lump. First, there may be analytical benefits, including relative simplicity of the reduced model and development of a new model which inherits known or assumed strong properties of the original model (the Markov property). Second, there may be statistical benefits, such as increased robustness of the smaller chain as well as improved estimates of transition probabilities. Finally, the identification of lumps may provide new insights about the process under investigation.

• Korean Chemical Engineering Research
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• 제50권1호
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• pp.155-161
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• 2012

바이오필터에서 폐가스에 포함된 유기오염물을 제거하는 효율에 대한 미디움 흡착능력의 영향을 포괄하는 강인한 동적 바이오필터 모델링을 수행하였다. 특히 비정상상태의 운전 조건 하에서도 바이오필터에 의해 처리된 폐가스 내의 유기오염물 농도를 구하기 위한 바이오막, 가스상, 수착(sorption) 부피 및 흡착상의 네가지 모델요소로 구성된 독창적인 모델인 개선된 프로세스럼핑 모델을 제시하였다. 이전의 프로세스럼핑모델에서는 담체에 대한 VOC의 평형 흡착량이 담체의 수착부피 내의 용존 VOC 농도에 선형적으로 비례한다는 가정 하에서 식을 유도하였으므로, 폐가스 처리에 적용이 제한적이었다. 따라서 실제 적용을 위해서 Freundlich 식과 같은 흡착관계식을 프로세스럼핑 모델에 접합하여 모든 농도의 VOC의 경우에 유효한 강인한 프로세스럼핑 모델을 구축하였다. 프로세스럼핑 모델 파라미터 중에서 바이오필터 미디움의 흡착과 관련한 파라미터 값들을 선행논문의 동적 흡착칼럼실험 및 문헌을 통하여 구하였다. 또한 에탄올을 포함한 폐가스처리를 위한 비정상상태의 바이오필터실험을 수행하였고, 그 실험결과와 여러 가지 Thiele modulus(${\phi}$) 값을 가지는 동적 바이오필터모델링 예측 값과 비교하였다. 이때에 구하여진 Thiele modulus(${\phi}$) 값은 0.03에 근접하였다.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2003년도 춘계학술대회
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• pp.2043-2047
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• 2003

The distributions of blood pressure, blood flow, and blow volume in the left common artery (LCCA) were determined using the lumping parameter method. In order to develop a mathematical model for microcirculation in LCCA, the present study adopted preexisted set of measured morphological data on anatomy, mechanical properties of the coronary vessels, viscosity of blood, the basic laws of physics, and the appropriate boundary condition. Pressures and volumes of blood and flow resistance were expressed in terms of electrical voltages, current, and resistances, respectively, in the electrical analog model. The results of two mathematical models, symmetrical and asymmetrical models, were compared with other investigator's data. The present results were in good agreement with previous studies. It was found that the mean pressure profiles were similar in both models.