• Journal of the Korean Mathematical Society
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• v.44 no.5
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• pp.1065-1078
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• 2007

We consider initial value problems for the semirelativistic Hartree type equations with cubic convolution nonlinearity $F(u)=(V*{\mid}u{\mid}^2)u$. Here V is a sum of two Coulomb type potentials. Under a specified decay condition and a symmetric condition for the potential V we show the global existence and scattering of solutions.

• Bulletin of the Korean Chemical Society
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• v.30 no.11
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• pp.2617-2620
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• 2009

Using Coulomb-Yukawa like correlated interaction potentials of integer and noninteger indices the series expansion formulae in terms of multicenter overlap integrals of three complete orthonormal sets of ${\psi}^{\alpha}$‒exponential type orbitals and linear combination coefficients of molecular orbitals are established for the potential of electrostatic field produced by the charges of molecule, where $\alpha$ = 1, 0, ‒1, ‒2,${\cdots}$. The formulae obtained can be useful for the study of interaction between atomic--molecular systems containing any number of closed and open shells when the ${\psi}^{\alpha}$‒exponential type basis functions and Coulomb-Yukawa like correlated interaction potentials are used in the Hartree-Fock-Roothaan and explicitly correlated approximations. The final results are valid for the arbitrary values of parameters of correlated interaction potentials and orbitals. As an example of application, the calculations have been performed for the potential energy of interaction between electron and molecule $H_2O$ using combined Hartree-Fock-Roothaan equations suggested by the author.

• Bulletin of the Korean Chemical Society
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• v.30 no.7
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• pp.1539-1542
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• 2009

Using one-range addition theorems for Slater type orbitals (STOs) and Coulomb-Yukawa like correlated interaction potentials (CIPs) introduced by the author, the series expansion formulae are derived for the multicenter multielectron integrals. The expansion coefficients occurring in these relations are presented through the overlap integrals of two STOs. The convergence of series expansion relations is tested by calculating concrete cases. The accuracy of the results is quite high for quantum number, screening constants and location of orbitals. The final results are especially useful in the calculation of multielectron properties for atoms and molecules when Hartree-Fock-Roothaan (HFR) and explicitly correlated methods are employed.

• Journal of Institute of Control, Robotics and Systems
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• v.6 no.5
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• pp.356-366
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• 2000

In this paper, a nonlinear $H_2/H_\infty/LTR$ control for the flexible inverted pendulum of a parallel type with Coulomb friction is presented. The dynamic equation for this system is derived by the Hamilton's principle and assumed-mode method. This hard nonlinear system can be modeled by a the quasi-linear state space model using the REF method. It is shown that the $H_2/H_\infty$ control can be applied to the nonlinear controller design of the system having Coulomb frictions if the proper LTR conditions are satisfied. In order to present the usefulness of the suggested control method, the nonlinear $H_2/H_\infty/LTR$ controller is designed to control the Position of the end point of the flexible inverted pendulum that has Coulomb frictions present in actuator parts. The results are given via computer simulations.

• Proceedings of the IEEK Conference
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• 2000.07b
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• pp.596-599
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• 2000

A natural admittance control system design is presented for a particular type of interaction controller that achieve high-performance and guarantees stability. The admittance control Significantly improves performance when Coulomb friction is present in the one link robot system. The technique requires a careful choice of the target impedance. Experimental performance results are presented for a two-mass system with internal Coulomb friction. Results demonstrate that the admittance control law is successful in rejecting internal Coulomb friction force disturbances. The controller was designed and implemented on our system that we set up one link robot system and hardware configuration system, and performance results are presented.

• 제어로봇시스템학회:학술대회논문집
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• 1994.10a
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• pp.512-517
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• 1994

The control system of a precise positioning mechanism with resonance and Coulomb friction has been designed using H$_{\infty}$ control theory, and the control performance has been verified by computer simulation and experimental analysis. The DGKF type H$_{\infty}$ control theory with scalar weighting factors was utilized for designing the control system. The followings have been confirmed from the present study: (1) The system with H$_{\infty}$ control presents better convergence and stability than the system with conventional control (PI-notch filter control). (2) The H$_{\infty}$ control system have good robustness properties for a wide range of operating conditions in the presence of external disturbances such as Coulomb friction and changing mechanical resonant frequency.ncy.

• Structural Engineering and Mechanics
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• v.60 no.5
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• pp.809-828
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• 2016

In deep open pit mines, slope stability is very important. Particularly, increasing the depths increase the risks in mines having weak rock mass. Blasting operations in this type of open pits may have a negative impact on slope stability. Several or combination of methods can be used in order to enable better analysis in this type of deep open-pit mines. Numerical modeling is one of these options. Many complex problems can be integrated into numerical methods at the same time and analysis, solutions can be performed on a single model. Rock failure criterions and rock models are used in numerical modeling. Hoek-Brown and Mohr-Coulomb terms are the two most commonly used rock failure conditions. In this study, mine planning and discontinuity conditions of a lignite mine facing two big landslides previously, has been investigated. Moreover, the presence of some damage before starting the study was identified in surrounding structures. The primary research of this study is on slope study. In slope stability analysis, numerical modeling methods with Hoek-Brown and Mohr-Coulomb failure criterions were used separately. Preparing the input data to the numerical model, the outcomes of patented-blast vibration minimization method, developed by co-author was used. The analysis showed that, the model prepared by applying Hoek-Brown failure criterion, failed in the stage of 10. However, the model prepared by using Mohr-Coulomb failure criterion did not fail even in the stage 17. Examining the full research field, there has been ongoing production in this mine without any failure and damage to surface structures.

• Advances in nano research
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• v.12 no.1
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• pp.25-35
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• 2022

Within the framework of the density functional theory combined with the method of non-equilibrium Green's functions (DFT + NEGF), the features of electron transport in fullerene nanojunctions, which are «core-shell» nanoobjects made of a combination of fullerenes of different diameters C₂₀, C₈₀, C₁₈₀, placed between gold electrodes (in a nanogap), are studied. Their transmission spectra, the density of state, current-voltage characteristics and differential conductivity are determined. It was shown that in the energy range of -0.45-0.45 eV in the transmission spectrum of the "Au-C₁₈₀-Au" nanojunction appears a HOMO-LUMO gap with a width of 0.9 eV; when small-sized fullerenes C₂₀, C₈₀ are intercalation into the cavity C₁₈₀ the gap disappears, and a series of resonant structures are observed on their spectra. It has been established that distinct Coulomb steps appear on the current-voltage characteristics of the "Au-C₁₈₀-Au" nanojunction, but on the current-voltage characteristics "Au-C₈₀@C₁₈₀-Au", "Au-(C₂₀@C₈₀)@C₁₈₀-Au" these step structures are blurred due to a decrease in Coulomb energy. An increase in the number of Coulomb features on the dI/dV spectra of core-shell fullerene nanojunctions was revealed in comparison with nanojunctions based on fullerene C₆₀, which makes it possible to create high-speed single-electron devices on their basis. Models of single-electron transistors (SET) based on fullerene nanojunctions "Au-C₁₈₀-Au", "Au-C₈₀@C₁₈₀-Au" and "Au-(C₂₀@C₈₀)@C₁₈₀-Au" are considered. Their charge stability diagrams are analyzed and it is shown that SET based on C₈₀@C₁₈₀-, (C₂₀@C₈₀)@C₁₈₀- nanojunctions is output from the Coulomb blockade mode with the lowest drain-to-source voltage.

• Bulletin of the Korean Chemical Society
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• v.13 no.3
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• pp.317-324
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• 1992

Structure and dynamics of $Na^+$ ions are investigated by molecular dynamics simulations of rigid dehydrated zeolite-A at several temperatures using a simple Lennard-Jones potential plus Coulomb potential. A best-fitted set of electrostatic charges is chosen from the results of simulation at 298.15 K and Ewald summation technique is used for the long-ranged character of Coulomb interaction. The calculated x, y, and z coordinates of $Na^+$ ions are in good agreement with the positions determined by X-ray crystallography within statistical errors, their random movings in different types of closed cages are well described by time-correlation functions, and $Na_Ⅰ$ type ions are found to be less diffusive than $Na_Ⅱ$ and $Na_{III}$. At 600.0 K, the unstable $Na_{III}$ type ion pushes down one of nearest $Na_{I}$ ions into the $\beta-cage$ and sits on the stable site Ⅰ, and the captured ion in the $\beta-cage$ wanders over and attacks one of 8 $Na_{I}$ type ions.

• Coupled systems mechanics
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• v.7 no.5
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• pp.583-610
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• 2018

This paper discusses the issues associated with modeling frictional contact between solid bodies undergoing large deformations. The most common model for friction on contact interfaces in solid mechanics is the Coulomb friction model, in which two distinct responses are possible: stick and slip. Handling the transition between these two phases computationally has been a source of algorithmic instability, lack of convergence and non-unique solutions, particularly in the presence of large deformations. Most computational models for frictional contact have used penalty or updated Lagrangian approaches to enforce frictional contact conditions. These two approaches, however, present some computational challenges due to conditioning issues in penalty-type implementations and the iterative nature of the updated Lagrangian formulation, which, particularly in large simulations, may lead to relatively slow convergence. Alternatively, a plasticity-inspired implementation of frictional contact has been shown to handle the stick-slip conditions in a local, algorithmically efficient manner that substantially reduces computational cost and successfully avoids the issues of instability and lack of convergence often reported with other methods (Laursen and Simo 1993). The formulation of this approach, however, has been limited to the small deformations realm, a fact that severely limited its application to contact problems where large deformations are expected. In this paper, we present an algorithmically consistent formulation of this method that preserves its key advantages, while extending its application to the realm of large-deformation contact problems. We show that the method produces results similar to the augmented Lagrangian formulation at a reduced computational cost.