• 대한수학회지
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• 제38권2호
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• pp.275-281
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• 2001

The trajectory of a classical dynamics is determined by the least action principle. As soon as we come to quantum dynamics, we have to consider all possible trajectories which are proposed to be a sum of the classical trajectory and Brownian fluctuation. Thus, the action involves the square of the derivative B(t) (white noise) of a Brownian motion B(t). The square is a typical example of a generalized white noise functional. The Feynman propagator should therefore be an average of a certain generalized white noise functional. This idea can be applied to a large class of dynamics with various kinds of Lagrangians.

• Bulletin of the Korean Chemical Society
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• 제21권7호
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• pp.727-733
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• 2000

Analytical potential energy surfaces have been constructed for the four-center elimination of HCI from 1,1-dichloroethylene.The potential functions are Morse-type functions which are modified by appropriate switching and attenuating functions with adjustable parameters. The parameters have been found by fitting the calculated vibrational frequencies, reaction endothermicity, equlibrium geometries of the reactant and products to those of experiments and ab initio calculations. The translational energy release obtained from classical trajectory calculations on this surface is in good agreement with the experiment.

• Bulletin of the Korean Chemical Society
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• 제32권5호
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• pp.1527-1533
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• 2011

The reaction of gas-phase atomic hydrogen with oxygen atoms chemisorbed on a silicon surface is studied by use of the classical trajectory approach. We have calculated the probability of the OH formation and energy deposit of the reaction exothermicity in the newly formed OH in the gas-surface reaction H(g) + O(ad)/Si${\rightarrow}$ OH(g) + Si. All reactive events occur in a single impact collision on a subpicosecond scale, following the Eley-Rideal mechanism. These events occur in a localized region around the adatom site on the surface. The reaction probability is dependent upon the gas temperature and shows the maximum near 1000 K, but it is essentially independent of the surface temperature. The reaction probability is also independent upon the initial excitation of the O-Si vibration. The reaction energy available for the product state is carried away by the desorbing OH in its translational and vibrational motions. When the initial excitation of the O-Si vibration increases, translational and vibrational energies of OH rise accordingly, while the energy shared by rotational motion varies only slightly. Flow of energy between the reaction zone and the solid has been incorporated in trajectory calculations, but the amount of energy propagated into the solid is only a few percent of the available energy released in the OH formation.

• Bulletin of the Korean Chemical Society
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• 제33권9호
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• pp.2873-2877
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• 2012

Quasi-classical trajectory (QCT) calculations of H+HLi reaction have been carried out on a new potential energy surface of the ground state reported by Prudente et al. [Chem. Phys. Lett. 2009, 474, 18]. The four polarization-dependent differential cross sections have been carried out in the center of mass (CM) frame at various collision energies. The reaction probability for the depletion channel has been studied over a wide collision energy range. It has been found that the collision energy decreases remarkably reaction probability, which shows the expected behavior of the title reaction belonging to an exothermic barrierless reaction. The results are in good agreement with previous RMP results. The P(${\theta}_r$), P(${\phi}_r$) and P(${\theta}_r,\;{\phi}_r$) distributions, the k-k'-j' correlation and the angular distribution of product rotational vectors are presented in the form of polar plots. The average rotational alignment factor <$P_2(j{\prime}{\cdot}k)$> as a function of collision energy is also calculated. The results indicate that the collision energy has a great influence on the polarization of the product rotational angular momentum vector j'.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1988년도 한국자동제어학술회의논문집(국내학술편); 한국전력공사연수원, 서울; 21-22 Oct. 1988
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• pp.41-44
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• 1988

This paper represents the study of an effective self-tuning PID control for a robot manipulator to track a reference trajectory in spite of the presence of nonlinearities and parameters uncertainties in robot dynamic models. In this control scheme, an error model of the manipulator is established, for the first time, by difference between joint reference trajectory and tracked trajectory. It's model Parameters are estimated by the recursive least-square identification algorithm, and classical controller parameters are determined by pole placement method. A computer simulation study was conducted to demonstrate performance of the proposed self-tuning PID control in joint-based coordinates for a robot with payload.

• Bulletin of the Korean Chemical Society
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• 제33권2호
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• pp.589-596
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• 2012

In this paper, the reactive dynamics properties of the reactions Ba + $C_6H_5Br$ and Ba + m-$C_6H_4CH_3Br$ were studied by means of the quasi-classical trajectory method based on the London-Eyring-Polanyi-Sato potential energy surfaces. The vibrational distributions, reaction cross sections, rotational alignments of the products BaBr all were obtained. The peak values of the vibrational distributions are located at $\nu$ = 0 for the reactions Ba + $C_6H_5Br$ and Ba + m-$C_6H_4CH_3Br$ when the collision energies are 1.09 and 1.10 eV, respectively. The reaction cross sections increase with the increasing collision energy, which changes from 0.6 to 1.5 eV. The product rotational alignments deviate from -0.5 and firstly increase and then decrease while the collision energy is increasing, just like that of Heavy+Light-Light system.

• Bulletin of the Korean Chemical Society
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• 제34권11호
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• pp.3350-3356
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• 2013

Quasi-classical trajectory calculations have been carried out for the reaction H+HS by using the newest triplet 3A" potential energy surface (PES). The effects of the collision energy and reagent initial rotational excitation are studied. The cross sections and thermal rate constants for the title reaction are calculated. The results indicate that the integral cross sections (ICSs) are sensitive to the collision energy and almost independent to the initial rotational states. The ro-vibrational distributions for the product $H_2$ at different collision energies are presented. The investigations on the vector correlations are also performed. It is found that the collision energies play a postive role on the forward scatter of the product molecules. There is a negative influence on both the alignment and orientation of the product angular momentum for low collision energy at low energy region. Whereas the influence of collision energy is not obvious at high energy region.

• Bulletin of the Korean Chemical Society
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• 제23권12호
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• pp.1737-1743
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• 2002

We have studied the dynamics of energy-rich hydrogen molecules produced on a graphite surface through H(g) + H(ad)/C(gr) → $H_2$ + C(gr) at thermal conditions mimicking the interstellar medium using a classical trajectory procedure. The recombination reaction of gaseous H atom at 100 K and the adsorbed H atom on the interstellar graphite grains at 10 K efficiently takes place on a subpicosecond time scale with most of the reaction exothermicity depositing in the product vibration, which leads to a strong vibrational population inversion. The molecules produced in nearly end-on geometry where H(g) is positioned below H(ad) rotate clockwise and are more highly rotationally excited. but in low-lying vibrational levels. The rotational axis of most of the molecule rotating clockwise is tilted from the surface normal by more than 30°, the intensity peaking at 35°. The molecules produced when H(ad) is close to the surface rotate counter-clockwise and are weakly rotationally excited, but highly vibrationally excited. These molecules tend to align their rotational axes parallel to the surface. The number of molecules rotating clockwise is eight times larger than that rotating counter-clockwise.

• Bulletin of the Korean Chemical Society
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• 제26권9호
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• pp.1369-1380
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• 2005

The reaction of methyl radical with iodine molecule on an attractive potential energy surface is studied by classical trajectory procedures. The reaction occurs over a wide range of impact parameters with the majority of reactive events occurring in the backward rebound region on a subpicosecond scale. A small fraction of reactive events take place in the forward hemisphere on a longer time scale. The ensemble average of reaction times is 0.36 ps. The occurrence of reactive events is strongly favored when the incident radical and the target molecule align in the neighborhood of collinear geometry. Since the rotational velocity of I2 is slow, the preferential occurrence of reactive events at the collinear configuration of $CH_3{\ldots}I{\ldots}$I leads to the reaction exhibiting an anisotropic dependence on the orientation of $I_2$. During the collision, there is a rapid flow of energy from the $H_3C{\ldots}$I interaction to the I-I bond. The $CH_3I$ translation and $H_3C$-I vibration share nearly all the energy released in the reaction, and the distribution of the vibrational energy is statistical. The reaction probability is $\cong$0.4 at the $CH_3$ and I2 temperatures maintained at 1000 K and 300 K, respectively. The probability is weakly dependent on the $CH_3\;and\;I_2$ temperatures between 300 K and 1500 K.

• 호남수학학술지
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• 제39권4호
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• pp.637-647
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• 2017

Elastica is known as classical curve that is a solution of variational problem, which minimize a thin inextensible wire's bending energy. Studies on elastica has been conducted in Euclidean space firstly, then it has been extended to Riemannian manifold by giving different characterizations. In this paper, we focus on energy of the elastic curve in a Lie group. We attepmt to compute its energy by using geometric description of the curvature and the torsion of the trajectory of the elastic curve of the trajectory of the moving particle in the Lie group. Finally, we also investigate the relation between energy of the elastic curve and energy of the same curve in Frenet vector fields in the Lie group.