• Applied Chemistry for Engineering
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• v.9 no.7
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• pp.1079-1084
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• 1998

Reaction kinetics between 4,4'-dihexyl methane diisocyanate($H_{12}MDI$) and n-hexanol in toluene with dibutyltin dilaurate(DBTDL) as catalyst was studied by experimental measurements and mathematical modeling. Experiments were carried out at various temperatures, catalyst concentrations and [NCO]/[OH] ratios, and the reaction kinetics were described by two second-order reactions, the one between NCO and OH leading to urethane and the other between urethane and NCO leading to allophanate. The rate constants were estimated by the Runge-Kutta 4th-order method. Experiments and mathematical simulations showed a good agreement for various experimental conditions. The [allophanate]/[urethane] ratios at 90% conversion of initial NCO were estimated to be over 20% for most conditions employed in the present study, indicating that allophanate formation might significantly affect the properties of urethane polymers.

• The KIPS Transactions:PartB
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• v.13B no.1 s.104
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• pp.15-20
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• 2006

This paper describes research on intelligent game character through performance enhancements of physics engine in computer games. The algorithm that recognizes the physics situation uses momentum back-propagation neural networks. Also, we present an experiment and its results, integration methods that display optimum performance based on the physics situation. In this experiment on integration methods, the Euler method was shown to produce the best results in terms of fps in a simulation environment with collision detection. Simulation with collision detection was shown similar fps for all three methods and the Runge-kutta method was shown the greatest accuracy. In the experiment on physics situation recognition, a physics situation recognition algorithm where the number of input layers (number of physical parameters) and output layers (destruction value for the master car) is fixed has shown the best performance when the number of hidden layers is 3 and the learning count number is 30,000. Since we tested with rigid bodies only, we are currently studying efficient physics situation recognition for soft body objects.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.41 no.2
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• pp.95-101
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• 2017

In this study, we derived theoretical equations for the zigzag movement of a leading vehicle, which is the most frequent behavior in train accidents, by using a simplified spring-mass model for the rolling stock. In order to solve the equations of motion, we applied the Runge-Kutta method, which is the typical numerical analysis method used for differential equations. Furthermore, the lateral displacement of the wheel-set at the wheel-rail interface was estimated using kinetic energy. In order to verify the derived equations, we compared the theoretical and simulated results under various collision conditions. The maximum relative deviations of the lateral displacements were 0.8 [%] ~ 4.7 [%] in light collisions and 0.6 [%] ~ 5.1 [%] under derailment conditions. When an accident is simulated, these theoretical equations can be used to predict the overall behavior and obtain the offset of the body-to-body link as the initial perturbation.

• Journal of the Institute of Convergence Signal Processing
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• v.9 no.1
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• pp.82-88
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• 2008

In this paper, Runge-Kutta (RK)-Butcher algorithm is proposed to study the periodic and oscillatory problems. Simulation results obtained using RK-Butcher algorithms and the classical fourth order Runge-Kutta (RK(4)) methods are compared with the exact solutions of a few periodic and oscillatory problems to confirm the performance of the proposed algorithm. The simulation results from RK-Butcher algorithms are always found to be very close to the exact solutions of these problems. Further, it is found that the RK-Butcher algorithm is superior when compared to RK(4) methods in terms of accuracy. The RK-Butcher algorithm can be easily implemented in a programming language and a more accurate solution may be obtained for any length of time. RK-Butcher algorithm is applicable as a good numerical algorithm for studying the problems of orbit and two body as it gives the nearly identical solutions.

• Journal of the Korea Institute of Military Science and Technology
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• v.25 no.4
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• pp.364-371
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• 2022

Surface state change of ammunition generated during the storage period increases the surface roughness and this affects the flight of ammunition, but there are no research results quantitatively indicating this. In this study, the drag force for each Mach number of howitzer shells was calculated through CFD to which the surface data of the howitzer shell was applied, and analysis of trajectory was performed using drag force values as an input of the 4th Runge-Kutta method, and the degree of decrease of the maximum range caused by the surface roughness of the howitzer shell was estimated. As a result, it was confirmed that the maximum range of howitzer shell with high surface roughness was 1.12 % shorter than that of howitzer shell without roughness. It was confirmed that the effect of surface roughness on the trajectory is not negligible.

• Journal of Korea Water Resources Association
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• v.39 no.7 s.168
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• pp.593-603
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• 2006

The basin response to storm is regarded as nonlinearity inherently. In addition, the consistent nonlinearity of hydrologic system response to rainfall has been very tough and cumbersome to be treated analytically. The thing is that such nonlinear models have been avoided because of computational difficulties in identifying the model parameters from recorded data. The parameters of nonlinear system considered as dynamic effects in the conceptual model are optimized as the sum of errors between the observed and computed runoff is minimized. For obtaining the optimal parameters of functions, the historical data for the Bocheong watershed in the Geum river basin were tested by applying the numerical methods, such as quasi-linearization technique, Runge-Kutta procedure, and pattern-search method. The estimated runoff carried through from the storage function with dynamic effects was compared with the one of 1st-order differential equation model expressing just nonlinearity, and also done with Nash model. It was found that the 2nd-order model yields a better prediction of the hydrograph from each storm than the 1st-order model. However, the 2nd-order model was shown to be equivalent to Nash model when it comes to results. As a result, the parameters of nonlinear 2nd-order differential equation model performed from the present study provided not only a considerable physical meaning but also a applicability to Korean watersheds.

• Journal of the Korea institute for structural maintenance and inspection
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• v.15 no.4
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• pp.204-211
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• 2011

A dynamic analysis procedure is developed to provide a better estimation of the dynamic responses of bridge during the passage of high speed railway vehicles. Particularly, a three dimensional numerical model including the structural interaction between high speed vehicles, bridges and railway endures to analyse accurately and evaluate with in-depth parametric studies for dynamic responses of various bridge span lengths running KTX railway locomotive up to increasing maximum speed(450km/h). Three dimensional frame element is used to model the simply supported pre-stressed concrete (PSC) box bridges for four span lengths(40~25m). Track irregularity employed as a stationary random process from the given spectral density functions and irregularities of both sides of the track are assumed to have high correlation. The high-speed railway vehicle (KTX) is used as 38-degree of freedom system. Three displacements (Vertical, lateral, and longitudinal) as well as three rotational components (Pitching, rolling, and yawing) are considered in the 38-degree of freedom model. The dynamic amplification factors are evaluated by the developed procedure under various traveling conditions, such as track irregularity camber, train speed and ballast. The dynamic analysis such as Newmark-${\beta}$ and Runge-Kutta methods which are able to analyse considering the dynamic impact factors are compared and contrasted.

• Proceedings of the KIEE Conference
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• 2003.07a
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• pp.107-109
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• 2003

전력계통의 과도 안정도 해석의 접근방법에는 SI(Simultaneous Implicit)법과 PE(Partitioned Explicit)법 두 가지방법을 사용해오고 있다. SI법에는 Trapezoidal법 등이 있고, PE법에는 Runge-Kutta법, Euler법등이 사용되고 있다. SI법인 Trapezoidal법은 PE법의 Runge-Kutta법 또는 Euler법에 비해 시간간격을 크게 해서 계산속도를 줄일 수 있다는 장점이 있지만, 정화도면에서는 신뢰한 수 없는 단점이 있다. 이 논문에서는 포물선 사법을 이용하여 Trapezoidal법의 정확도를 개선학 수 있는 방법을 제시하고 명확한 수학적 증명을 통해 타당성을 보여준다. 연속함수와 불연속함수에 대해서 Runge-Kutta법과 Trapezoidal법과 제안한 방법을 적용시켜서 제안한 방법의 정화함을 보여준다.

• Transactions of the Korean Society of Mechanical Engineers
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• v.14 no.4
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• pp.981-989
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• 1990

본 연구에서는 유한체적법에 의한 4단계 Runge-Kutta방법으로 2차원 익열에 대한 비점성 천음속 유동장에 대한 해석을 수행하기로 하는데 이는 경계층방정식에 대 한 경계조건으로 이용될 수 있고 3차원 계산시 그 기초자료가 될 수 있을 것이다.

• The Journal of Korean Medicine
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• v.34 no.1
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• pp.136-145
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• 2013

Objectives: Recently, Korean medicine has been explored by employing mathematical methods, which is an effort to raise Korean medicine to a higher level of scientific research. In that vein, we propose a mathematical model, analyzing the effects of seasonal cycle as an external factor in addition to the internal interactions of five-states, the engendering and the restraining. Methods: Some modified differential equations with 5-state variables were given to describe the interactions of the engendering and the restraining, and effect of seasonal cycle, and are numerically analyzed by Runge-Kutta method. We then simulated it along with time and dynamically analyzed it by Moran's I, a spatial autocorrelation. Results: We showed the effects of seasonal cycle on yin-yang five-states and applied it to the human life cycle. Conclusions: Our result is comparable to previous results in the respect that we consider the seasonal cycle and its effect on five-states, unlike others' mainly focusing on internal interaction. Furthermore, we suggest some follow-up study taking into consideration the complexity and diversity of external factors.