• Bulletin of the Korean Chemical Society
• /
• 제27권10호
• /
• pp.1659-1663
• /
• 2006

A many-body master equation is constructed by incorporating stochastic terms responsible for chemical reactions into the many-body Smoluchowski equation. Two forms of Langevin-type of memory equations describing the time evolution of dynamical variables under the influence of time-independent perturbation with an arbitrary intensity are derived. One form is convenient in obtaining the dynamics approaching the steady-state attained by the perturbation and the other in describing the fluctuation dynamics at the steady-state and consequently in obtaining the linear response of the system at the steady-state to time-dependent perturbation. In both cases, the kinetics of statistical averages of variables is found to be obtained by analyzing the dynamics of time-correlation functions of the variables.

• 한국추진공학회:학술대회논문집
• /
• 한국추진공학회 2003년도 제21회 추계학술대회 논문집
• /
• pp.65-70
• /
• 2003

본 연구에서는 섭동가속도의 변화식으로 주어지는 궤도 섭동 방정식으로부터 지구 편원현상과 대기저항에 의해 기인하는 궤도요소들의 변화를 표현하고 궤도 일회전당 변화량을 근거로 하여 대기저항에 의한 속도 보정과 그에 필요한 연료소모량을 효과적으로 예측하는 방법을 제시하고 그 기법을 다목적위성 궤도해석에 적용하였다. 그리고 궤도 해석을 위해 위성에 영향을 미치는 섭동력을 비대칭 중력장, 대기 저항력, 태양과 달의 인력, 태양 복사압에 의한 영향을 계산하여 정량적으로 비교 분석하였다.

• KSTLE International Journal
• /
• 제10권1_2호
• /
• pp.6-12
• /
• 2009

In this study, the effect of oil supply conditions on the dynamic performance of a hydrodynamic journal bearing is analyzed numerically. Axial length, circumferential length and location of oil grooves are considered as oil supply conditions. The perturbation equations of the perturbed film contents are obtained by applying Elrod's universal equation implementing JFO film rupture / reformation boundary conditions to Lund's infinitesimal perturbation method. The dynamic coefficients of a hydrodynamic journal bearing are calculated by solving the perturbation equations, and the linear stability analysis is carried out by using those for a variety of oil supply conditions.

• Journal of applied mathematics & informatics
• /
• 제28권3_4호
• /
• pp.845-862
• /
• 2010

In a recent paper, M.A. Noor et al. (Hindawi publishing corporation, Mathematical Problems in Engineering, Volume 2008, Article ID 696734, 11 pages, doi:10.1155/2008/696734) proposed the variational homotopy perturbation method (VHPM) for solving higher dimentional initial boundary value problems. In this paper, we consider the proposed method for analytic treatment of the linear and nonlinear ordinary differential equations, homogeneous or inhomogeneous. The results reveal that the proposed method is very effective and simple and can be applied for other linear and nonlinear problems in mathematical.

• Biomaterials and Biomechanics in Bioengineering
• /
• 제5권1호
• /
• pp.51-64
• /
• 2020

In this study, the mathematical model that describes blood cell development in the bone marrow (i.e., hematopoiesis) has been studied via the Homotopy Perturbation Method (HPM). The results from the present work compared very well with the numerical solutions from published literature. This work has shown that the HPM is viable for solving delay differential equations born from hematopoiesis problem. The influence of the proliferating cells loss rate, time delay rate and the phase re-entry rate on the population densities of both the proliferating and resting cells were also determined through the underlined procedure.

• Bulletin of the Korean Chemical Society
• /
• 제10권6호
• /
• pp.529-535
• /
• 1989

A general perturbation series solution of the Smoluchowski equation is applied to investigate the rate of recombination and the remaining probability of a pair of particles in liquids. The radiative boundary condition is employed and the convergence of the perturbation series is analyzed in terms of a convergene factor in time domain. The upper bound to the error introduced by the n-th order perturbation scheme is also evaluated. The long time behaviors of the rate of recombination and the remaining probability are found to be expressed in closed forms if the perturbation series is convergent. A new and efficient method of purely numerical integration of the Smoluchowski equation is proposed and its results are compared with those obtained by the perturbation method. For the two cases where the interaction between the particles is given by (i) the Coulomb potential and (ii) the shielded Coulomb potential, the agreement between the two results is found to be excellent.

• 대한기계학회논문집B
• /
• 제36권9호
• /
• pp.907-913
• /
• 2012

연속적으로 누출되면서 원형으로 퍼져가고 있는 액체에 대한 모델에 대한 고차 섭동 해를 구하여 1차 섭동 해를 개선하였다. 일반적인 해를 얻기 위하여 무차원화된 지배방정식을 유도하고 무차원 지배 변수를 도출하였다. 무차원 증발계수를 섭동 변수로 이용하였다. 계산 결과 부피 및 확산 반경에 관해서 고차 섭동해가 1차 섭동 해를 개선시키고 있으며, 섭동해의 차수가 증가함 따라 오차를 감소시키는 경향을 보였다. 3차 섭동 해는 수치 해와 거의 일치하고 있어 3차 섭동해의 타당성을 보여주고 있다.

• East Asian mathematical journal
• /
• 제34권5호
• /
• pp.549-570
• /
• 2018

We establish existence and bifurcation of global positive solutions for parametrized nonhomogeneous elliptic equations involving critical Sobolev-Hardy exponents and Hardy terms. The main approach to the problem is the variational method.

• Structural Engineering and Mechanics
• /
• 제16권6호
• /
• pp.731-748
• /
• 2003

In this paper a thick cylindrical shell with varying thickness which is subjected to static non-uniform internal pressure is analyzed. At first, equilibrium equations of the shell have been derived by the energy principle and by considering the first order theory of Mirsky-Herrmann which includes transverse shear deformation. Then the governing equations which are, a system of differential equations with varying coefficients have been solved analytically with the boundary layer technique of the perturbation theory. In spite of complexity of modeling the conditions near the boundaries, the method of this paper is very capable of providing a closed form solution even near the boundaries. Displacement predictions are in a good agreement with the calculated finite elements and other analytical results. The convergence of solution is very fast and the amount of calculations is less than the Frobenius method.

• 한국항공우주학회지
• /
• 제31권4호
• /
• pp.8-15
• /
• 2003

본 연구는 적분 방정식과 반복 "오차-수정" 개념을 이용하는 Takanashi의 이론에 기초한 초음속 실용적인 설계방법의 개발 결과로서, 형상의 수정량은 목표 압력분포와 설계대상의 압력분포와의 차를 경계조건으로 이용해 LSP 방정식을 풀므로써 계산되어진다. 이 연구에서는 Green의 정리를 이용하여 편미방정식 형태의 LSP 방정식을 적분방정식으로 변환하여 계산하는 방법을 이용하고 있다. 여기서는 Isolated wing과 wign-nacelles 두가지 경우의 설계를 예로 들었다.