• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2001년도 추계학술대회논문집 II
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• pp.799-804
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• 2001

Nonlinear normal mode (NNM) vibration, in a nonlinear dual mass Hamiltonian system, which has 6th order homogeneous polynomial as a nonlinear term, is studied in this paper. The existence, bifurcation, and the orbital stability of periodic motions are to be studied in the phase space. In order to find the analytic expression of the invariant curves in the Poincare Map, which is a mapping of a phase trajectory onto 2 dimensional surface in 4 dimensional phase space, Whittaker's Adelphic Integral, instead of the direct integration of the equations of motion or the Birkhotf-Gustavson (B-G) canonical transformation, is derived for small value of energy. It is revealed that the integral of motion by Adelphic Integral is essentially consistent with the one obtained from the B-G transformation method. The resulting expression of the invariant curves can be used for analyzing the behavior of NNM vibration in the Poincare Map.

• 자연과학논문집
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• 제12권1호
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• pp.41-48
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• 2002

원자와 빛과의 상호작용으로 인해 원자에 결맞음이 유도될 수 있는데, 이 결맞음은 새로운 현상을 보여 줄 수 있다. 그 중 전자기 유도 흡수는 결합광의 영향으로 조사광의 흡수가 증가하는 현상인데, 다중-V 타입 원자계에서 관측될 수 있다. 본 논문에서는 주파수가 다른 조사광이 결합광과 같은 천이선에 인가되는 경우 전자기 유도 흡수현상을 이론적으로 연구하기 위한 방법을 제시하였다. 조사광과 원자의 상호작용을 시간의존 해밀토니안으로 표시하였으며, 밀도 행렬요소의 변화는 밀도행렬방정식을 풀어서 조사하였고, 행렬 요소 변화의 진폭으로부터 전자기 유도 흡수를 계산하였다.

• Steel and Composite Structures
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• 제44권2호
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• pp.255-270
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• 2022

This manuscript illustrates the dynamic response of nanoscale carbon nanotubes (CNTs) embedded in an elastic media under moving load using doublet mechanics theory, which not considered before. CNTs are modelled by Timoshenko beam theory (TBT) and a bottom to up modelling nano-mechanics is simulated by doublet mechanics theory to capture the size effect of CNTs. To explore the influence of the CNTs configurations on the dynamic behaviour, both armchair and zigzag configurations are considered. The governing equations of motion and the associated boundary conditions are obtained using the Hamiltonian principle. The Navier solution methodology is applied to obtain the solutions for both orientations. Free vibration and forced response under moving loads are considered. The accuracy of the developed procedure is verified by comparing the obtained results with available previous algorithms and good agreement is observed. Parametric studies are conducted to demonstrate effects of doublet length scale, CNTs configurations, moving load velocities as well as the elastic media parameters on the dynamic behaviours of CNTs. The developed procedure is supportive in the design and manufacturing of MEMS/NEMS made from CNTs.

• 한국정밀공학회지
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• 제12권5호
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• pp.57-68
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• 1995

A general procedure for the numerical solution of coupled, nonlinear, differential two-point boundary-value problems, solutions of which are crucial to the controller design, has been developed and demonstrated. A fixed-end-points, free-terminal-time, optimal-control problem, which is derived from Pontryagin's Maximum Principle, is solved by an extension of Davidenko's method, a differential form of Newton's method, for algebraic root finding. By a discretization process like finite differences, the differential equations are converted to a nonlinear algebraic system. Davidenko's method reconverts this into a pseudo-time-dependent set of implicitly coupled ODEs suitable for solution by modern, high-performance solvers. Another important advantage of Davidenko's method related to the time-optimal problem is that the terminal time can be computed by treating this unkown as an additional variable and sup- plying the Hamiltonian at the terminal time as an additional equation. Davidenko's method uas used to produce optimal trajectories of a single-degree-of-freedom problem. This numerical method provides switching times for open-loop control, minimized terminal time and optimal input torque sequences. This numerical technique could easily be adapted to the multi-point boundary-value problems.

• 한국정보통신학회논문지
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• 제20권8호
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• pp.1487-1493
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• 2016

최근 SNS (Social Networking Services)를 통한 사용자들 간 정보 확산이 폭발적으로 증가하고 있다. SEIR (Susceptible-Exposed-Infectious-Recovered model)모델은 전염병 예측에 널리 사용되는 수학적 모델로, 이러한 정보 확산은 SEIR를 이용하여 모델링 할 수 있다. 본 논문에서는 SEIR모델을 이용하여 최적 제어 이론의 관점에서 SNS의 정보 확산 모델을 도출하였다. 본 논문에서는 PMP (Pontryagin's Minimum Principle)에 기반한 forward-backward algorithm을 제안하였다. 이 알고리즘은 전방과 후방으로 가면서 state와 adjoint equation들을 통합하면서 동작한다. 수치해석을 통해 정보 내용의 impact value와 birth rate이 작으면 작을수록 더 많은 노드들이 해로운 정보를 필터링하는 것을 보였다.

• 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.

• Steel and Composite Structures
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• 제49권4호
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• pp.361-380
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• 2023

A size dependent bending behavior of piezoelectrical flexoelectric layered perforated functionally graded (FG) composite nanobeam rested on an elastic foundation is investigated analytically. The composite beam is composed of regularly cutout FG core and two piezoelectric face sheets. The material characteristics is graded through the core thickness by power law function. Regular squared cutout perforation pattern is considered and closed forms of the equivalent stiffness parameters are derived. The modified nonlocal strain gradient elasticity theory is employed to incorporate the microstructure as well as nonlocality effects into governing equations. The Winkler as well as the Pasternak elastic foundation models are employed to simulate the substrate medium. The Hamiltonian approach is adopted to derive the governing equilibrium equation including piezoelectric and flexoelectric effects. Analytical solution methodology is developed to derive closed forms for the size dependent electromechanical as well as mechanical bending profiles. The model is verified by comparing the obtained results with the available corresponding results in the literature. To demonstrate the applicability of the developed procedure, parametric studies are performed to explore influences of gradation index, elastic medium parameters, flexoelectric and piezoelectric parameters, geometrical and peroration parameters, and material parameters on the size dependent bending behavior of piezoelectrically layered PFG nanobeams. Results obtained revealed the significant effects both the flexoelectric and piezoelectric parameters on the bending behavior of the piezoelectric composite nanobeams. These parameters could be controlled to improve the size dependent electromechanical as well as mechanical behaviors. The obtained results and the developed procedure are helpful for design and manufacturing of MEMS and NEMS.