• The Journal of Natural Sciences
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• v.12 no.1
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• pp.41-48
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• 2002

Atomic coherences can be induced via atom-light interaction and can exhibit new interesting phenomena. Electromagnetically-induced-absorption (EIA) is one of such phenomena where the absorption of probe beam is increased due to the presence of strong coupling beam. EIA can be observed in multiple-V type atomic systems. This paper present a method to study EIA when the frequencies of probe beam and coupling beam are both near resonant to the same transition line. Time-varying interaction Hamiltonian was introduced and density matrix equations were solved and the amplitude of oscillations was used to calculate the EIA.

• Bulletin of the Korean Mathematical Society
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• v.58 no.5
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• pp.1279-1300
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• 2021

Let P be a finite point set in ℝ² with the set of distance n-chains defined as ∆_n(P) = {(|p₁ - p₂|, |p₂ - p₃|, …, |p_n - p_n+1|) : p_i ∈ P}. We show that for 2 ⩽ n = O_|P|(1) we have ${\mid}{\Delta}_n(P){\mid}{\gtrsim}{\frac{{\mid}P{\mid}^n}{{\log}^{\frac{13}{2}(n-1)}{\mid}P{\mid}}}$. Our argument uses the energy construction of Elekes and a general version of Rudnev's rich-line bound implicit in [28], which allows one to iterate efficiently on intersecting nested subsets of Guth-Katz lines. Let G is a simple connected graph on m = O(1) vertices with m ⩾ 2. Define the graph-distance set ∆_G(P) as ∆_G(P) = {(|p_i - p_j|)_{i,j}∈E(G) : p_i, p_j ∈ P}. Combining with results of Guth and Katz [17] and Rudnev [28] with the above, if G has a Hamiltonian path we have ${\mid}{\Delta}_G(P){\mid}{\gtrsim}{\frac{{\mid}P{\mid}^{m-1}}{\text{polylog}{\mid}P{\mid}}}$.

• Journal of Power Electronics
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• v.19 no.6
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• pp.1527-1535
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• 2019

Because of the shortcomings of the PID controllers and traditional drive systems of permanent magnet synchronous motors (PMSMs), a PMSM passivity-based control (PBC) drive system based on a quasi-Z source matrix converter (QZMC) is proposed in this paper. The traditional matrix converter is a buck converter with a maximum voltage transmission ratio of only 0.866, which limits the performance of the driven motor. Therefore, in this paper a quasi-Z source circuit is added to the input side of the two-stage matrix converter (TSMC) and its working principle has also been verified. In addition, the controller of the speed loop and current loop in the conventional vector control of a PMSM is a PID controller. The PID controller has the problem since its parameters are difficult to adjust and its anti-interference capability is limited. As a result, a port controlled dissipative Hamiltonian model (PCHD) of a PMSM is established. Thereafter a passivity-based controller based on the interconnection and damping assignment (IDA) of a QZMC-PMSM is designed, and the stability of the equilibrium point is theoretically verified. Simulation and experimental results show that the designed PBC control system of a PMSM based on a QZMC can make the PMSM run stably at the rated speed. In addition, the system has strong robustness, as well as good dynamic and static performances.

• Steel and Composite Structures
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• v.44 no.2
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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.

• Steel and Composite Structures
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• v.45 no.5
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• pp.697-713
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• 2022

In the context of the finite elements method, the dynamic behavior of porous functionally graded double wishbone vehicle suspension structural system incorporating joints flexibility constraints under road bump excitation is studied and analyzed. The functionally graded material properties distribution through the thickness direction is simulated by the power law including the porosity effect. To explore the porosity effects, both classical and adopted porosity models are considered based on even porosity distribution pattern. The dynamic equations of motion are derived based on the Hamiltonian principle. Closed forms of the inertia and material stiffness components are derived. Based on the plane frame isoparametric Timoshenko beam element, the dynamic finite elements equations are developed incorporating joint flexibilities constraints. The Newmark's implicit direct integration methodology is utilized to obtain the transient vibration time response under road bump excitation. The presented procedure is validated by comparing the computational model results with the available numerical solutions and an excellent agreement is observed. Obtained results show that the decrease of porosity percentage and material graduation tends to decrease the deflection as well as the resulting stresses of the control arms thus improving the dynamic performance and increasing the service lifetime of the control arms.

• Journal of the Korean Society for Precision Engineering
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• v.12 no.5
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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.

• Journal of Astronomy and Space Sciences
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• v.41 no.2
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• pp.87-106
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• 2024

The objective of this research is to address the issue of frozen orbits in charged satellites by incorporating geopotential zonal harmonics up to J6 and the initial tesseral harmonics. The employed model starts from the first normalized Hamiltonian to calculate specific sets of long-term frozen orbits for charged satellites. To explore the frozen orbits acquired, a MATHEMATICA CODE is developed. The investigation encompasses extensive variations in orbit altitudes by employing the orbital inclination and argument of periapsis as freezing parameters. The determined ranges ensuring frozen orbits are derived from the generated figures. Three-dimensional presentations illustrating the freezing inclination in relation to eccentricity, argument of periapsis, and semi-major axis parameters are presented. Additional three-dimensional representations of the phase space for the eccentricity vector and its projection onto the nonsingular plane are examined. In all investigated scenarios, the impacts of electromagnetic (EM) field perturbations on the freezing parameters of a charged satellite are demonstrated.

• Bulletin of the Korean Chemical Society
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• v.33 no.5
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• pp.1675-1680
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• 2012

Three new cyanide-bridged $Cr^{III}Mn^{II}$ binuclear complexes, $[Mn(phen)_2Cl][Cr(bpmb)(CN)_2]{\cdot}H_2O$ ($\mathbf{1}$) (phen = 1,10-phenanthroline, $bpdmb^{2-}$ = 1,2-bis(pyridine-2-carboxamido)-4-methyl-benzenate), $[Mn(phen)_2Cl][Cr(bpmb)-(CN)_2]{\cdot}H_2O$ ($\mathbf{2}$) ($bpdmb^{2-}$ = 1,2-bis(pyridine-2-carboxamido)-4,5-dimethyl-benzenate), and $[Mn(phen)_2Cl]-[Cr(bpClb)(CN)_2]{\cdot}CH_3OH{\cdot}H_2O$ ($\mathbf{3}$) ($bpClb^{2-}$ = 1,2-bis(pyridine-2-carboxamido)-4-chloro-benzenate) were obtained based on $Mn(phen)_2Cl_2$ and a series of dicyanidechromate(III) building blocks. Single crystal X-ray diffraction analysis shows the structures of the three complexes are dimeric type with two different metal centers linked by a cyanide group from corresponding dicyanidechromate(III) building block. Magnetic investigations indicate the existence of relatively weak antiferromagnetic coupling between Cr(III) and Mn(II) ions with best-fit constants $J_{CrMn}=-2.78(5)cm^{-1}$ for $\mathbf{1}$, $J_{CrMn}=-3.02(2)cm^{-1}$ for $\mathbf{2}$ and $J_{CrMn}=-2.27(3)cm^{-1}$ for $\mathbf{3}$ based on the spin exchange Hamiltonian = $-2J_{CrMn}\hat{S}_{Cr}\hat{S}_{Mn}$. The magneto-structural correlation of cyanide-bridged $Cr^{III}Mn^{II}$ complexes has been discussed at last.

• Bulletin of the Korean Chemical Society
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• v.33 no.3
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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.

• Proceedings of the Korea Contents Association Conference
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• 2007.11a
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• pp.209-211
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• 2007

The computational time of Stocahstic Diagonalization (SD) calculation for 2-dimensional interacting fermion systems is reduced by using several methods including symmetry operations. First, each lattice is subdivided into spin-up and spin-down lattices separately, thus allowing a bi-partite lattice. A valid basis state is then obtained from stacking up an up-spin configuration on top of a down-spin configuration. As a consequence, the memory space to be used in saving the trial basis state reduces significantly. Secondly, the matrix elements of a Hamiltonianin are reconrded in a look-up table when making basis state set. Thus the repeated calculation of the matrix elements of the Hamiltonian are avoided during SD process. Thirdly, by applying symmetry operations to the basis state set the original basis state is transformed to a new basis state whose elements are the eigenvectors of the symmetry operations. The ground state wavefunction is constructed from the elements of symmetric - bonding state - basis state set. As a result, the total number of basis states involved in SD calculation is reduced upto 50 percentage by using symmetry operations.