• Journal of the Chungcheong Mathematical Society
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• v.26 no.3
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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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• v.6 no.5
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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.

• Journal of the Korean Institute of Telematics and Electronics D
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• v.35D no.10
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• pp.29-38
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• 1998

In this paper, we have induced a model for the growth and dissolution of oxygen precipitates which is generated during arbitrary thermal treatments or VLSI processes in CZ-grown silicon. Based on diffusion-limited growth law and detailed balance equilibrium theory, growth and dissolution rates are induced and inserted into a set of chemical rate equations and a Fokker-Planck equation. Then this is solved by numerical analysis. And because phenomenon at the silicon surface must be considered differently in various annealing conditions, in particular in $O_2$ ambient we have considered the growth model of SiO$_2$ at the surface of silicon wafer and the enhancement of oxygen solubility. By this method, oxygen depth profile and density distribution of oxygen precipitates are calculated more accurately than the other simulation results.

• Journal of Korean Society on Water Environment
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• v.25 no.1
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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.

• Communications of the Korean Mathematical Society
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• v.26 no.4
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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.

• Journal of the Korean Society of Industry Convergence
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• v.3 no.1
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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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• v.73 no.9
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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.

• Journal of Korea Water Resources Association
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• v.42 no.6
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• pp.433-443
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• 2009

For the better understanding of the temporal characteristics of soil water, this study is to suggest a stochastic soil water model and to apply it for impact assessment of climate change. The loss function is divided into 3 stages for more specified comprehension of the probabilistic behavior of soil water, and especially, the soil water model considering the stochastic characteristics of precipitation is developed in order to consider the variation of climatic factors. The simulation result of soil water model confirms that the proposed soil water model can re-generate the observation properly, and it also proves that the soil water behaves with consistent cycle based on the precipitation pattern. Moreover, with the simulation results with a climate change scenario, it can be predicted that the future soil water will have higher variations than present soil water.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 1996.04a
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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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• v.8 no.1
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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.