• 대한기계학회:학술대회논문집
• /
• 대한기계학회 2004년도 추계학술대회
• /
• pp.1213-1218
• /
• 2004

The present article reports extensive numerical results on the non-local characteristics of ultra-short pulsed laser-induced breakdowns of fused silica ($SiO_{2}$) by using the multivariate Fokker-Planck equation. The nonlocal type of multivariate Fokker-Planck equation is modeled on the basis of the Boltzmann transport formalism to describe the ultra-short pulsed laser-induced damage phenomena in the energy-position space, together with avalanche ionization, three-body recombination, and multiphoton ionization. Effects of electron avalanche, recombination, and multiphoton ionization on the electronic transport are examined. From the results, it is observed that the recombination becomes prominent and contributes to reduce substantially the rate of increase in electron number density when the electron density exceeds a certain threshold. With very intense laser irradiation, a strong absorption of laser energy takes place and an initially transparent solid is converted to a metallic state, well known as laser-induced breakdown. It is also found that full ionization is provided at intensities above threshold, all further laser energy is deposited within a thin skin depth.

• 한국지진공학회논문집
• /
• 제9권6호
• /
• pp.53-58
• /
• 2005

본 연구에서는 지진하중을 받는 교량의 거동을 확률밀도함수를 통하여 분석할 수 있는 기법을 개발하였다. 확률밀도함수의 전개는 추계론적 이론을 이용한 반해석적 방법을 통하여 구하였으며, 반해석적 방법은 교량운동방정식으로부터 상응하는 Fokker-Planck equation을 구한 후, path-integral solution을 유도하여 이를 수치적으로 해석함으로써 구할 수 있다. 교량거동의 확률밀도 함수전개로부터 교량거동의 확률적 특성을 파악하고 확률밀도함수의 범위로부터 교량응답거동의 포락선을 얻을 수 있으며 이를 이용하여 최대응답의 범위를 결정할 수 있다는 것을 밝혔다.

• The Journal of the Acoustical Society of Korea
• /
• 제17권4E호
• /
• pp.3-10
• /
• 1998

This paper concerns the dynamical behavior, in probabilistic sense, of a feedforward neural network performing auto association for novelty. Networks of retinotopic topology having a one-to-one correspondence between and output units can be readily trained using back-propagation algorithm, to perform autoassociative mappings. A novelty filter is obtained by subtracting the network output from the input vector. Then the presentation of a "familiar" pattern tends to evoke a null response ; but any anomalous component is enhanced. Such a behavior exhibits a promising feature for enhancement of weak signals in additive noise. As an analysis of the novelty filtering, this paper shows that the probability density function of the weigh converges to Gaussian when the input time series is statistically characterized by nonsymmetrical probability density functions. After output units are locally linearized, the recursive relation for updating the weight of the neural network is converted into a first-order random differential equation. Based on this equation it is shown that the probability density function of the weight satisfies the Fokker-Planck equation. By solving the Fokker-Planck equation, it is found that the weight is Gaussian distributed with time dependent mean and variance.

• 한국지하수토양환경학회:학술대회논문집
• /
• 한국지하수토양환경학회 2000년도 창립총회 및 춘계학술발표회
• /
• pp.163-163
• /
• 2000

• Ocean Systems Engineering
• /
• 제1권3호
• /
• pp.249-261
• /
• 2011

The stochastic nonlinear dynamic behavior and probability density function of ship rolling are studied using the nonlinear dynamical systems approach and probability theory. The probability density function of the rolling response is evaluated through solving the Fokker Planck Equation using the path integral method based on a Gauss-Legendre interpolation scheme. The time-dependent probability of ship rolling restricted to within the safe domain is provided and capsizing is investigated from the probability point of view. The random differential equation of ships' rolling motion is established considering the nonlinear damping, nonlinear restoring moment, white noise and colored noise wave excitation.

• 한국소음진동공학회:학술대회논문집
• /
• 한국소음진동공학회 1997년도 추계학술대회논문집; 한국과학기술회관; 6 Nov. 1997
• /
• pp.145-153
• /
• 1997

Dynamic characteristics are investigated when a nonlinear system showing periodic and chaotic responses under harmonic excitation is exposed to random perturbation. About two well potential problem, probability of homoclinic bifurcation is estimated using stochastic generalized Meinikov process and quantitive characteristics are investigated by calculation of Lyapunov exponent. Critical excitaion is calculated by various assumptions about Gaussian Melnikov process. To verify the phenomenon graphically Fokker-Planck equation is solved numerically and the original nonlinear equation is numerically simulated. Numerical solution of Fokker-Planck equation is calculated on Poincare section and noise induced chaos is studied by solving the eigenvalue problem of discretized probability density function.

• Ocean Systems Engineering
• /
• 제1권1호
• /
• pp.1-15
• /
• 2011

Offshore structures are subjected to wind loads, wind generated wave excitations, and current forces. In this paper we focus on the wind generated wave excitations as the main source for the external forces on the structure. The main objective of the paper is to provide a tool for using deck acceleration measurements to predict the value of the force and moment acting on the offshore structure foundation. A change in these values can be used as an indicator of the health of the foundation. Two methods of analysis are used to determine the relationship between the force and moment acting on the foundation and deck acceleration. The first approach uses neural networks while the other uses a Fokker-Planck formulation. The Fokker-Plank approach was used to relate the variance of the excitation to the variance of the deck acceleration. The total virtual mass of the equivalent SDOF of the structure was also determined at different deck masses.

• 한국방재학회:학술대회논문집
• /
• 한국방재학회 2008년도 정기총회 및 학술발표대회
• /
• pp.237-240
• /
• 2008

Numerical Analysis for exchanging seawater experiment is carried out in Do-Jang fish port. The change of tidal velocity and water level is derived by the two-dimensional nonlinear shallow-water numerical model. To calculate exchange rate of seawater with the change of tidal velocity and water level, a two-dimensional numerical model is employed which governing equations are Fokker-Plank equations. The calculated exchange rates of each time are described in tables and figures.

• 충청수학회지
• /
• 제27권1호
• /
• pp.35-37
• /
• 2014

We examine a question raised in [1] regarding existence and uniqueness of the steady-state solution of certain type of Kolmogorov forward equation in this paper, and prove that the question holds for $S^1$ by giving an explicit solution.

• 호남수학학술지
• /
• 제35권4호
• /
• pp.679-681
• /
• 2013

In this paper, we raise a question regarding existence and uniqueness of the steady-state solution of a type of Kolmogorov forward equation. We prove that the question has a positive answer for trivial vector fields, and also provide examples which show that the compactness assumption is necessary.