• 대한수학회논문집
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• 제31권4호
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• pp.869-878
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• 2016

This paper presents an ecient fractional shifted Legendre polynomial method to solve the fractional Volterra's model for population growth model. The fractional derivatives are described based on the Caputo sense by using Riemann-Liouville fractional integral operator. The theoretical analysis, such as convergence analysis and error bound for the proposed technique has been demonstrated. In applications, the reliability of the technique is demonstrated by the error function based on the accuracy of the approximate solution. The numerical applications have provided the eciency of the method with dierent coecients of the population growth model. Finally, the obtained results reveal that the proposed technique is very convenient and quite accurate to such considered problems.

• 한국자기공명학회논문지
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• 제27권4호
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• pp.28-34
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• 2023

We study the linear-nonlinear quantum transport theory of Wannier-Landau transition system in the confinement of electrons by a square well confinement potential. We use the projected Liouville equation method with the ensemble density projection technique. We select the dynamic value under a linearly oscillatory external field. We derive the dynamic value formula and the memory factor functions in three electron phonon coupling systems and electron impurity coupling systems of two transition types, the intra-band transitions and inter-band transitions. We obtain results that can be applied directly to numerical analyses. For simple example of application, we analyze the absorption power and line-widths of ZnO, through the numerical calculation of the theoretical result in the Landau system.

• 한국해안해양공학회지
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• 제4권2호
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• pp.91-107
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• 1992

Heaps(1972)가 사용한 천해균질류에 대한 선형 기본방정식을 수심평균류속과 해수면변리를 계산하는 External mode와 수심변이 유속을 계산하는 Internal mode로 분리시킨 다음, Internal mode식에 Galerkin Method를 적용하였다. Internal mode유속을 수평좌표, 시간에 따라 변하는 계수와 대직좌표에 따라 변하는 Basis function들의 곱의 형태로 선형전개하며, 난류확산계수를 포함하는 2차미분항으로부터 해수면에 Homogeneous boundary condition과 해저면에 Sheared boundary condition이 가해지는 Sturm-Liouville system을 구성, Eigenfunctions 해를 구하여 Basis function으로 사용하였다. 모델의 성능을 검토하기 위하여 수립된 모델을 정상균일풍이 가해지는 1차원 수노에 적용하여 Cooper and Pearce(1977)가 제시한 해저면 비활동조건하의 무한 및 유한수노 연직류원분포에 대한 해석각와 비교하였으며, North Sea 규모의 등수심 장방형 Basin(Heaps' Basin)에 적용하여 정상균일풍에 대한 Heaps(1972)의 계산결과와 비교하였다.

• Bulletin of the Korean Chemical Society
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• 제33권3호
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• pp.933-940
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• 2012

Recently, it has been shown that quantum coherence appears in energy transfers of various photosynthetic lightharvesting complexes at from cryogenic to even room temperatures. Because the photosynthetic systems are inherently complex, these findings have subsequently interested many researchers in the field of both experiment and theory. From the theoretical part, simplified dynamics or semiclassical approaches have been widely used. In these approaches, the quantum-classical Liouville equation (QCLE) is the fundamental starting point. Toward the semiclassical scheme, approximations are needed to simplify the equations of motion of various degrees of freedom. Here, we have adopted the Poisson bracket mapping equation (PBME) as an approximate form of QCLE and applied it to find the time evolution of the excitation in a photosynthetic complex from marine algae. The benefit of using PBME is its similarity to conventional Hamiltonian dynamics. Through this, we confirmed the coherent population transfer behaviors in short time domain as previously reported with a more accurate but more time-consuming iterative linearized density matrix approach. However, we find that the site populations do not behave according to the Boltzmann law in the long time limit. We also test the effect of adding spurious high frequency vibrations to the spectral density of the bath, and find that their existence does not alter the dynamics to any significant extent as long as the associated reorganization energy is changed not too drastically. This suggests that adopting classical trajectory based ensembles in semiclassical simulations should not influence the coherence dynamics in any practical manner, even though the classical trajectories often yield spurious high frequency vibrational features in the spectral density.

• 전기학회논문지P
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• 제66권3호
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• pp.129-134
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• 2017

We investigated theoretically the quantum optical transition properties of Si, in quasi 2-Dimensinal Landau splitting system, based on quantum transport theory. We apply the quantum transport theory (QTR) to the system in the confinement of electrons by square well confinement potential under linearly polarized oscillating field. We use the projected Liouville equation method with Equilibrium Average Projection Scheme (EAPS). In order to analyze the quantum transition, we compare the temperature and the magnetic field dependencies of the QTLW and the QTLS on four transition processes, namely, the intra-leval transition process, the inter-leval transition process, the phonon emission transition process and the phonon absorption transition process.