• 충청수학회지
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• 제26권3호
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• pp.501-516
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• 2013

The well-known Vlasov-Poisson equation describes plasma physics as nonlinear first-order partial differential equations. Because of the nonlinear condition from the self consistency of the Vlasov-Poisson equation, many problems occur: the existence, the numerical solution, the convergence of the numerical solution, and so on. To solve the problems, a viscosity term (a second-order partial differential equation) is added. In a viscosity term, the Vlasov-Poisson equation changes into a parabolic equation like the Fokker-Planck equation. Therefore, the Schauder fixed point theorem and the classical results on parabolic equations can be used for analyzing the Vlasov-Poisson equation. The sequence and the convergence results are obtained from linearizing the Vlasove-Poisson equation by using a fixed point theorem and Gronwall's inequality. In numerical experiments, an implicit first-order scheme is used. The numerical results are tested using the changed viscosity terms.

• Bulletin of the Korean Chemical Society
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• 제6권5호
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• pp.295-299
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• 1985

An approximate solution of the Fokker-Planck equation with the nonlinear drift term due to a Schlogl model is obtained and the result is compared with the methods proposed by Suzuki. Also the effect of nonlinearity on the correlation length at the stable steady state is studied.

• 전자공학회논문지D
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• 제35D권10호
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• pp.29-38
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• 1998

본 논문에서는 CZ 방법으로 성장된 실리콘에서 임의의 열처리 과정 또는 VLSI 공정중에 발생하는 산소석출물(oxygen precipitates)의 성장 및 감소에 대한 모델을 유도하고 수치해석법으로 시뮬레이션을 수행하여 모델에 대한 타당성을 검증하였다. 확산제한 성장법칙(diffusion-limited growth law)과 DBET(detailed balance equilibrium theory)를 이용하여 산소 석출물의 성장률과 감소율을 유도하고 이를 CREs(chemical rate equations)와 PFE (Fokker-Planck equation)이 결합된 식에 적용하여 수치해석법으로 풀었다. 또한 어닐링 분위기에 따라 표면에서 일어나는 현상을 달리 고려해야 하는데, 특히 O₂가스 분위기에서는 산화막이 성장되는 조건을 고려해야 하므로 산화막 성장 모델과 산소 용해도 증가등의 영향을 고려하였다. 이 방법으로 기존의 결과보다 더 정확하게 깊이에 따른 산소 농도의 분포와 산소 석출물의 밀도분포 함수를 계산할 수 있었다.

• 한국물환경학회지
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• 제25권1호
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• pp.112-119
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• 2009

Based on the study of soil water dynamics, this study is to suggest an advanced stochastic soil water model for future study for drought application. One distinguishable remark of this study is the derivation of soil water dynamic controling equation for 3-stage loss functions in order to understand the temporal behaviour of soil water with reaction to the precipitation. In terms of modeling, a model with rather simpler structure can be applied to regenerate the key characteristics of soil water behavior, and especially the probabilistic solution of the derived soil water dynamic equation can be helpful to provide better and clearer understanding of soil water behavior. Moreover, this study will be the future cornerstone of applying to more realistic phenomenon such as drought management.

• 대한수학회논문집
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• 제26권4호
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• pp.709-720
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• 2011

We obtain special type of differential equations which their solution are random variable with known continuous density function. Stochastic differential equations (SDE) of continuous distributions are determined by the Fokker-Planck theorem. We approximate solution of differential equation with numerical methods such as: the Euler-Maruyama and ten stages explicit Runge-Kutta method, and analysis error prediction statistically. Numerical results, show the performance of the Rung-Kutta method with respect to the Euler-Maruyama. The exponential two parameters, exponential, normal, uniform, beta, gamma and Parreto distributions are considered in this paper.

• 한국산업융합학회 논문집
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• 제3권1호
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• pp.43-51
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• 2000

The response statistics of a hinged-clamped beam under broad-band random excitation is investigated. The random excitation is applied at the nodal point of the second mode. By using Galerkin's method the governing equation is reduced to a system of nonautonomous nonlinear ordinary differential equations. A method based upon the Markov vector approach is used to generate a general first-order differential equation in the dynamic moment of response coordinates. By means of the Gaussian and non-Gaussian closure methods the dynamic moment equations for the random responses of the system are reduced to a system of autonomous ordinary differential equations. The case of two mode interaction is considered in order to compare it with the case of three mode interaction. The analytical results for two and three mode interactions are also compared with results obtained by Monte Carlo simulation.

• Journal of the Korean Physical Society
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• 제73권9호
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• pp.1219-1224
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• 2018

We investigate the evolutionary dynamics and the phase transitions of the island model which consists of subdivided populations of individuals confined to two islands. In the island model, the population is subdivided so that migration acts to determine the evolutionary dynamics along with selection and genetic drift. The individuals are assumed to be haploid and to be one of two species, X or Y. They reproduce according to their fitness values, die at random, and migrate between the islands. The evolutionary dynamics of an individual based model is formulated in terms of a master equation and is approximated by using the diffusion method as the multidimensional Fokker-Planck equation (FPE) and the coupled non-linear stochastic differential equations (SDEs) with multiplicative noise. We analyze the infinite population limit to find the phase transitions from the monomorphic state of one type to the polymorphic state to the monomorphic state of the other type as we vary the ratio of the fitness values in two islands and complete the phase diagram of our island model.

• 한국수자원학회논문집
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• 제42권6호
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• pp.433-443
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• 2009

토양수분에 관한 관심이 급증하면서 토양수분의 시공간적 특성을 이해하고자 하는 연구가 최근 꾸준히 일어나고 있다. 토양수분의 보다 나은 이해를 위해, 본 연구에서는 이에 대한 동역학을 추계학적 기법을 이용하여 기후변화에 따른 영향평가에 대한 적용을 염두에 둔 추계학적 토양수분모형을 제시하고자 하였다. 보다 현실적인 적용을 위하여 손실항을 세 가지로 구분하여 고려하였고 강우의 추계학적인 특성 역시 고려하였다. 모의 결과 본 연구에서 유도한 토양수분 모형으로 관측 자료를 적절하게 재현 할 수 있으며 토양수분이 계절별로 강수의 패턴에 따라 일정한 순환의 형태를 가짐을 재현하였다. 또한 CGCM3.1 자료를 이용한 미래 토양수분 상태 예측으로, 토양수분의 변동성이 현재보다 커질 것으로 예측되었다.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 1996년도 춘계학술대회논문집; 부산수산대학교, 10 May 1996
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• pp.125-129
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• 1996

This paper deals with the problem of placement/sizing of distributed piezo actuators to achieve the control objective of vibration suppression. Using the mean square response as a performance index in optimization, we obtain optimal placement and sizing of the actuator. The use of genetic algorithms as a technique for solving optimization problems of placement and sizing is explored. Genetic algorithms are also used for the control strategy. The analysis of the system and response moment equations are carried out by using the Fokker-Planck equation. This paper presents the design and analysis of an active controller and optimal placement/sizing of distributed piezo actuators based on genetic algorithms for a flexible structure under random disturbance, shows numerical example and the result.

• Journal of Astronomy and Space Sciences
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• 제8권1호
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• pp.11-23
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• 1991

The dynamical evolution of globular clusters is studied using the orbit-averaged multicomponent Fokker-Planck equation. The original code developed by Cohn(1980) is modi-fied to include the effect of stellar evolutions. Plommer's model is chosen as the initial density distribution with the initial mass function index $\alpha$=0.25, 0.65, 1.35, 2.35, and 3.35. The mass loss rate adopted in this work follows that of Fusi-Pecci and Renzini(1976). The stellar mass loss acts as the energy source, and thus affects the dynamical evolution of globular clusters by slowing down the evolution rate and extending the core collapse time Tcc. And the dynamical length scale $$R_c, $$R_h is also extended. This represents the expansion of cluster due to the stellar mass loss.