• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2000.11a
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• pp.649-654
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• 2000

The non-linear differential equations of motion of a fluid conveying curved pipe are derived by making use of Hamiltonian approach. The extensible dynamics of the pipe is based on the Euler-Bernoulli beam theory. Some significant differences between linear and nonlinear equations and the basic analysis results are discussed. Using eigenfrequency analysis, it can be shown that the natural frequencies are changed with flow velocity.

• Bulletin of the Korean Chemical Society
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• v.11 no.2
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• pp.85-88
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• 1990

The electron paramagnetic resonance (EPR) spectrum of the copper (II) complex with the 2-methylamino-1-cyclo-pentene-1-dithiocarboxylate (acdc) anion, $Cu(N-CH_3acdc)_2$ has been studied in the diamagnetic host lattices afforded by the corresponding divalent nickel, zinc, cadmium and mercury complexes. EPR parameters of the complex support the exclusive use of sulfur atoms by the ligand in metal binding. A combination of host lattice structure and covalency effects can be account for the observed spin-Hamiltonian parameters.

• Bulletin of the Korean Chemical Society
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• v.16 no.5
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• pp.427-432
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• 1995

A model based on two coupled generalized Langevin equations is proposed to investigate the trans-stilbene photoisomerization dynamics. In this model, a system which has two independent coordinates is considered and these two system coordinates are coupled to the same harmonic bath. The direct coupling between the system coordinates is assumed negligible and these two coordinates influence each other through the frictional coupling mediated by solvent molecules. From the Hamiltonian which is equivalent to the coupled generalized Langevin equations, we obtain the transition state theory rate constants of the stilbene photoisomerization. The rates obtained from this model are compared to experimental results in n-alkane solvents.

• Journal of the Korean Mathematical Society
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• v.60 no.2
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• pp.375-393
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• 2023

Rabinowitz action functional is the Lagrange multiplier functional of the negative area functional to a constraint given by the mean value of a Hamiltonian. In this note we show that on a symplectization there is a one-to-one correspondence between gradient flow lines of Rabinowitz action functional and gradient flow lines of the restriction of the negative area functional to the constraint. In the appendix we explain the motivation behind this result. Namely that the restricted functional satisfies Chas-Sullivan additivity for concatenation of loops which the Rabinowitz action functional does in general not do.

• Journal of the Korean Vacuum Society
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• v.21 no.3
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• pp.171-177
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• 2012

The computer program (EPR-NMR program version 6.2) employed here sets up the spin Hamiltonian matrices and determines their eigenvalues using exact diagonalization. We study the electron spin resonance for $Mn^{2+}$ in ferroelectric $LiNbO_3$ single crystals. The self-energy is obtained using the projection operator method developed by Argyres and Sigel. The self-energy is calculated to be axially symmetric about the by the spin Hamiltonian. The line-widths decreased as the temperature increased; we assume that the hyperfine structure transition is a more dominant scattering than the other transitions. We conclude that the calculation process presented in this study is useful for quantum optical transitions.

• Journal of KSNVE
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• v.9 no.1
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• pp.196-205
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• 1999

The existence. bifurcation. and the orbital stability of periodic motions, which is called nonlinear normal mode, in a nonlinear dual mass Hamiltonian system. which has 6th order homogeneous polynomial as a nonlinear term. are studied in this paper. By direct integration of the equations of motion. Poincare Map. which is a mapping of a phase trajectory onto 2 dimensional surface in 4 dimensional phase space. is obtained. And via the Birkhoff-Gustavson canonical transformation, the analytic expression of the invariant curves in the Poincare Map is derived for small value of energy. It is found that the nonlinear system. which is considered in this paper. has 2 or 4 nonlinear normal modes depending on the value of nonlinear parameter. The Poincare Map clearly shows that the bifurcation modes are stable while the mode from which they bifurcated out changes from stable to unstable.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.21 no.1
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• pp.20-27
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• 2020

In general, a nonlinear system is linearized in the form of a multiplication of the 1st and 2nd order system. This paper reports a design method of a weighting matrix and control law of LQ control to move the double poles that have a Jordan block to a pair of complex conjugate poles. This method has the advantages of pole placement and the guarantee of stability, but this method cannot position the poles correctly, and the matrix is chosen using a trial and error method. Therefore, a relation function (𝜌, 𝜃) between the poles and the matrix was derived under the condition that the poles are the roots of the characteristic equation of the Hamiltonian system. In addition, the Pole's Moving-range was obtained under the condition that the state weighting matrix becomes a positive semi-definite matrix. This paper presents examples of how the matrix and control law is calculated.

• Journal of the Korean Chemical Society
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• v.22 no.4
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• pp.202-220
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• 1978

Uniform semiclassical (WKB) solutions are obtained for nonseparable systems without using a close coupling formalism and are given explicitly in terms of well known analytic functions for various physically interesting and realistic cases. They do not become singular at turning points or surfaces and when taken in their asymptotic forms, they reduce to the usual WKB solutions that could be obtained if the Stokes phenomenon was properly taken care of for solutions. In obtaining such uniform solutions, the Schroedinger equations for nonseparable systems are suitably "renormalized" to solvable "normal" forms through certain transformations. Ehrenfest's adiabatic principle plays an important guiding role for obtaining such "renormalized" uniform solutions for nonseparable systems. The eigenvalues of the Hamiltonian can be calculated from the extended Bohr-Sommerfeld quantization rules when appropriate classical trajectories are obtained. An application is made to many-electron systems and for one of the simplest examples to show the utility of the method the approximate wavefunction is calculated of the ground state helium atom.

• Advances in nano research
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• v.7 no.3
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• pp.209-221
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• 2019

Graphene, with impressive electronic properties, have high potential in the microelectronic field. However, graphene itself is a zero bandgap material which is not suitable for digital logic gates and its application. Thus, much focus is on graphene nanoribbons (GNRs) that are narrow strips of graphene. During GNRs fabrication process, the occurrence of defects that ultimately change electronic properties of graphene is difficult to avoid. The modelling of GNRs with defects is crucial to study the non-idealities effects. In this work, nearest-neighbor tight-binding (TB) model for GNRs is presented with three main simplifying assumptions. They are utilization of basis function, Hamiltonian operator discretization and plane wave approximation. Two major edges of GNRs, armchair-edged GNRs (AGNRs) and zigzag-edged GNRs (ZGNRs) are explored. With single vacancy (SV) defects, the components within the Hamiltonian operator are transformed due to the disappearance of tight-binding energies around the missing carbon atoms in GNRs. The size of the lattices namely width and length are varied and studied. Non-equilibrium Green's function (NEGF) formalism is employed to obtain the electronics structure namely band structure and density of states (DOS) and all simulation is implemented in MATLAB. The band structure and DOS plot are then compared between pristine and defected GNRs under varying length and width of GNRs. It is revealed that there are clear distinctions between band structure, numerical DOS and Green's function DOS of pristine and defective GNRs.

• Advances in nano research
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• v.15 no.5
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• pp.385-399
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• 2023

Hexagonal boron nitride (h-BN), commonly referred to as Boron Nitride Nanoribbons (BNNRs), is an electrical insulator characterized by high thermal stability and a wide bandgap semiconductor property. This study delves into the electronic properties of two BNNR configurations: Armchair BNNRs (ABNNRs) and Zigzag BNNRs (ZBNNRs). Utilizing the nearest-neighbour tight-binding approach and numerical methods, the electronic properties of BNNRs were simulated. A simplifying assumption, the Hamiltonian matrix is used to compute the electronic properties by considering the self-interaction energy of a unit cell and the interaction energy between the unit cells. The edge perturbation is applied to the selected atoms of ABNNRs and ZBNNRs to simulate the electronic properties changes. This simulation work is done by generating a custom script using numerical computational methods in MATLAB software. When benchmarked against a reference study, our results aligned closely in terms of band structure and bandgap energy for ABNNRs. However, variations were observed in the peak values of the continuous curves for the local density of states. This discrepancy can be attributed to the use of numerical methods in our study, in contrast to the semi-analytical approach adopted in the reference work.