• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2000년도 춘계학술대회논문집
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• pp.1292-1297
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• 2000

외부로부터 불규칙 교란을 받는 동력학계에 대해 '허-확률 제어기법'을 이용하여 설계된 제어기의 성능을 수치모사를 통하여 검증하였다. 압전소자를 알루미늄 보에 부착하여 다중입출력의 복합재료보로 만들고, 기반에 불규칙한 외부교란을 받는계에 대한 모델링을 수행하였으며, Ito의 확률미분방정식과 F-P-K방정식을 이용하여 동적 모멘트 방정식을 유도하여 시스템의 확률영역에서의 특성을 알아보았다. 본 연구에서 제어기의 목표는 외부교란의 입력에 의해 발생하는 시스템의 모멘트 응답크기를 줄이는 방향으로 전개하였고, 확률영역에서의 MIMO PI제어기('허-확률 MIMO PI 제어기')를 설계하여 시간영역에서의 응답형태를 관찰하였다.

• Structural Engineering and Mechanics
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• 제28권4호
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• pp.373-386
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• 2008

In this study stochastic analysis of non-linear dynamical systems under ${\alpha}$-stable, multiplicative white noise has been conducted. The analysis has dealt with a special class of ${\alpha}$-stable stochastic processes namely sub-Gaussian white noises. In this setting the governing equation either of the probability density function or of the characteristic function of the dynamical response may be obtained considering the dynamical system forced by a Gaussian white noise with an uncertain factor with ${\alpha}/2$- stable distribution. This consideration yields the probability density function or the characteristic function of the response by means of a simple integral involving the probability density function of the system under Gaussian white noise and the probability density function of the ${\alpha}/2$-stable random parameter. Some numerical applications have been reported assessing the reliability of the proposed formulation. Moreover a proper way to perform digital simulation of the sub-Gaussian ${\alpha}$-stable random process preventing dynamical systems from numerical overflows has been reported and discussed in detail.

• Journal of the Korean Physical Society
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• 제73권11호
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• pp.1774-1786
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• 2018

Phenotypic variation among clones (individuals with identical genes, i.e. isogenic individuals) has been recognized both theoretically and experimentally. We investigate the effects of phenotypic variation on evolutionary dynamics of a population. In a population, the individuals are assumed to be haploid with two genotypes : one genotype shows phenotypic variation and the other does not. We use an individual-based Moran model in which the individuals reproduce according to their fitness values and die at random. The evolutionary dynamics of an individual-based model is formulated in terms of a master equation and is approximated as the Fokker-Planck equation (FPE) and the coupled non-linear stochastic differential equations (SDEs) with multiplicative noise. We first analyze the deterministic part of the SDEs to obtain the fixed points and determine the stability of each fixed point. We find that there is a discrete phase transition in the population distribution when the probability of reproducing the fitter individual is equal to the critical value determined by the stability of the fixed points. Next, we take demographic stochasticity into account and analyze the FPE by eliminating the fast variable to reduce the coupled two-variable FPE to the single-variable FPE. We derive a quasi-stationary distribution of the reduced FPE and predict the fixation probabilities and the mean fixation times to absorbing states. We also carry out numerical simulations in the form of the Gillespie algorithm and find that the results of simulations are consistent with the analytic predictions.

• Wind and Structures
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• 제36권2호
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• pp.133-147
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• 2023

The random vibration of saddle membrane structures under wind load is studied theoretically and experimentally. First, the nonlinear random vibration differential equations of saddle membrane structures under wind loads are established based on von Karman's large deflection theory, thin shell theory and potential flow theory. The probabilistic density function (PDF) and its corresponding statistical parameters of the displacement response of membrane structure are obtained by using the diffusion process theory and the Fokker Planck Kolmogorov equation method (FPK) to solve the equation. Furthermore, a wind tunnel test is carried out to obtain the displacement time history data of the test model under wind load, and the statistical characteristics of the displacement time history of the prototype model are obtained by similarity theory and probability statistics method. Finally, the rationality of the theoretical model is verified by comparing the experimental model with the theoretical model. The results show that the theoretical model agrees with the experimental model, and the random vibration response can be effectively reduced by increasing the initial pretension force and the rise-span ratio within a certain range. The research methods can provide a theoretical reference for the random vibration of the membrane structure, and also be the foundation of structural reliability of membrane structure based on wind-induced response.

• Journal of applied mathematics & informatics
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• 제11권1_2호
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• pp.215-241
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• 2003

In this paper, solute transport in heterogeneous aquifers using a modified Fokker-Planck equation (MFPE) is investigated. This newly developed mathematical model is characterised with a time-, scale-dependent dispersivity. A two-dimensional finite volume quadrilateral mesh method (FVQMM) based on a quadrilateral background interpolation mesh is developed for analysing the model. The FVQMM transforms the coupled non-linear partial differential equations into a system of differential equations, which is solved using backward differentiation formulae of order one through five in order to advance the solution in time. Three examples are presented to demonstrate the model verification and utility. Henry's classic benchmark problem is used to show that the MFPE captures significant features of transport phenomena in heterogeneous porous media including enhanced transport of salt in the upper layer due to its parameters that represent the dependence of transport processes on scale and time. The time and scale effects are investigated. Numerical results are compared with published results on the some problems.

• Interaction and multiscale mechanics
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• 제1권3호
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• pp.369-379
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• 2008

A combined stochastic diffusion and mean-field model is developed for a systematic study of the grain growth in a pure single-phase polycrystalline material. A corresponding Fokker-Planck continuity equation is formulated, and the interplay/competition of stochastic and curvature-driven mechanisms is investigated. Finite difference results show that the stochastic diffusion coefficient has a strong effect on the growth of small grains in the early stage in both two-dimensional columnar and three-dimensional grain systems, and the corresponding growth exponents are ~0.33 and ~0.25, respectively. With the increase in grain size, the deterministic curvature-driven mechanism becomes dominant and the growth exponent is close to 0.5. The transition ranges between these two mechanisms are about 2-26 and 2-15 nm with boundary energy of 0.01-1 J $m^{-2}$ in two- and three-dimensional systems, respectively. The grain size distribution of a three-dimensional system changes dramatically with increasing time, while it changes a little in a two-dimensional system. The grain size distribution from the combined model is consistent with experimental data available.

• 한국항해항만학회지
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• 제26권5호
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• pp.563-569
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• 2002

오염물질 확산모델링시 기존의 유한차분모델의 단점을 보완하기 위해 입자추적법이 사용되고 있다. 본 연구에서는 Princeton Ocean Model에 결합하여 사용할 수 있는 3차원 입자추적모델을 개발하였으며 이를 다양한 수치실험을 통해 검증하였다. 또한 미국 플로리다 주 템파만의 해양방류구 모델링에 적용하므로써 모델의 유용성을 확인하였다. 예상대로 입자추적모델은 기존의 유한차분모델에 비해 적은 확산범위를 나타내었으며, 이는 기존의 유한차분모델이 안고 있는 수치확산에 따른 오차로 추정된다. 새로이 개발된 모델은 다양한 해양확산모델링에 유용하게 응용될 것으로 기대된다.