• Journal of KSNVE
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• v.11 no.1
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• pp.156-166
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• 2001

This work uses tensor calculus to derive a complete set of three-dimensional field equations well-suited for determining the behavior of thick shells of revolution having arbitrary curvature and variable thickness. The material is assumed to be homogeneous, isotropic and linearly elastic. The equations are expressed in terms of coordinates tangent and normal to the shell middle surface. The relationships are combined to yield equations of motion in terms of orthogonal displacement components taken in the meridional, normal and circumferential directions. Strain energy and kinetic energy functionals are also presented. The equations of motion and energy functionals may be used to determine the static or dynamic displacements and stresses in shells of revolution, including free and forced vibration and wave propagation.

• Coupled systems mechanics
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• v.6 no.3
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• pp.369-376
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• 2017

Intermolecular interaction energies and conformer geometries of the hydrogen bonded acrylamide dimers have been studied by using the second-order Møller-Plesset (MP2) perturbation theory and the density functional theory (DFT) with 17 density functionals. Dunning's correlation consistent basis sets (up to aug-cc-pVTZ) have been used to study the basis set effects. The DFT calculated interaction energies are compared to the reference energy data calculated by the MP2 method and the coupled cluster method at the complete basis set (CCSD(T)/CBS) limit in order to determine the relative performance of the studied density functionals. Overall, dispersion-energy-corrected density functionals outperform uncorrected ones. The ${\omega}B97XD$ density functional is particularly effective in terms of both accuracy and computational cost in estimating the reference energy values using small basis sets and is highly recommended for similar calculations for larger systems.

• Interaction and multiscale mechanics
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• v.2 no.1
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• pp.31-44
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• 2009

While the classical theory of Griffith is the foundation of modern understanding of brittle fracture, it has a number of significant shortcomings: Griffith theory does not predict crack initiation and path and it suffers from the presence of unphysical stress singularities. In 1998, Francfort and Marigo presented an energy functional minimization method, where the crack (or its absence) as well as its path are part of the problem's solution. The energy functionals act on spaces of functions of bounded variations, where the cracks are related to the discontinuity sets of such functions. The new model presented here uses modified energy functionals to account for molecular interactions in the vicinity of crack tips, resulting in Barenblatt cohesive forces, such that the model becomes free of stress singularities. This is done in a physically consistent way using recently published concepts of Sinclair. Here, for the consistency of the model, it becomes necessary to allow for crack reversibility and to consider local minimizers of the energy functionals. The latter is achieved by introducing different time scales. The model is solved in its global as well as in its local version for a simple one-dimensional example, showing that local minimization is necessary to yield a physically reasonable result.

• 한국신재생에너지학회:학술대회논문집
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• 2005.11a
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• pp.634-637
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• 2005

Hydrogen adsorption mechanism onto the porous metal-organic frameworks (MOFs) has been studied by density functional theory calculation. The selected functionals for the predict ion of interact ion energies between hydrogen and potential adsorption sites of MOF was utilized after the evaluation with the various functionals for interaction energy of $H_2C_6H_6$ model system the adsorption energy of hydrogen molecule into MOF was investigated with the consideration of the favorable adsorption sites and the orientations. We also calculated the second favorable adsorption sites by geometry optimization using every combination of two first absorbed hydrogen molecules. Based on the calculation of first and second adsorption sites and energies, the hydrogen adsorption into MOF follows a cooperative mechanism in which the initial metal sites initiate the propagation of the hydrogen adsorption on the whole frameworks. In addition, it was found that the interaction strength between the simple benzene ring with hydrogen is significantly reinforced when the benzene ring has been incorporated into the framework of MOFs.

• Journal of the Korean Chemical Society
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• v.68 no.2
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• pp.65-73
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• 2024

The halide-acetylene anions, X^--HCCH (X = F, Cl, and Br) have been studied by using several different ab initio and DFT methods to determine structures, hydrogen-bond energies, vibrational frequencies of the anion complexes. Although the halide-acetylene complexes all have linear equilibrium structures, it is found that the fluoride complex is characterized with distinctively different structure and interactions compared to those of the chloride and bromide complexes. The performance of various density functionals on describing ionic hydrogen-bonded complexes is assessed by examining statistical deviations with respect to high level ab initio CCSD(T) results as reference. The density functionals employed in the present work show considerably varying degrees of performance depending on the properties computed. The performances of each density functional on geometrical parameters related with the hydrogen bond, hydrogen-bond energies, and scaled harmonic frequencies of the anion complexes are examined and discussed based on the statistical deviations.

• The Pure and Applied Mathematics
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• v.30 no.2
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• pp.109-129
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• 2023

In this paper, we introduce a second order linear differential operator ^T□: C^∞ (M) → C^∞ (M) as a natural generalization of Cheng-Yau operator, [8], where T is a (1, 1)-tensor on Riemannian manifold (M, h), and then we show on compact Riemannian manifolds, divT = divT^t, and if divT = 0, and f be a smooth function on M, the condition ^T□ f = 0 implies that f is constant. Hereafter, we introduce T-energy functionals and by deriving variations of these functionals, we define T-harmonic maps between Riemannian manifolds, which is a generalization of L_k-harmonic maps introduced in [3]. Also we have studied fT-harmonic maps for conformal immersions and as application of it, we consider fL_k-harmonic hypersurfaces in space forms, and after that we classify complete fL₁-harmonic surfaces, some fL_k-harmonic isoparametric hypersurfaces, fL_k-harmonic weakly convex hypersurfaces, and we show that there exists no compact fL_k-harmonic hypersurface either in the Euclidean space or in the hyperbolic space or in the Euclidean hemisphere. As well, some properties and examples of these definitions are given.

• Bulletin of the Korean Mathematical Society
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• v.52 no.3
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• pp.907-914
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• 2015

In this paper, we consider a viscoelastic plate equation with p-Laplacian $u^{{\prime}{\prime}}+{\Delta}^2u-div({\mid}{\nabla}u{\mid}^{p-2}{\nabla}u)+{\sigma}(t){\int}_{0}^{t}g(t-s){\Delta}u(s)ds-{\Delta}u^{\prime}=0$. By introducing suitable energy and Lyapunov functionals, we establish a general decay estimate for the energy, which depends on the behavior of both ${\sigma}$ and g.

• Current Applied Physics
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• v.18 no.12
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• pp.1528-1533
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• 2018

The trajectories of adsorption and dissociation process of $O_2$ on the Al (111) surface were studied by the spinpolarized ab initio molecular dynamics method, and the adsorption activation energy was clarified by the NEB method with hybrid functionals. Three typical dissociation trajectories were found through simulation of $O_2$ molecule at different initial positions. When vertically approaches to the Al surface, the $O_2$ molecule tends to rotate, and the activation energy is 0.66eV. If $O_2$ molecule does not rotate, the activation energy will increase to 1.43 eV, and it makes the O atom enter the Al sublayer eventually. When the $O_2$ molecules parallel approach to the Al surface, there is no activation energy, due to the huge energy released during the adsorption process.

• Bulletin of the Korean Chemical Society
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• v.24 no.6
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• pp.859-863
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• 2003

We report on the theoretical positron affinities of closed-shell atomic anions. The second-order many-body perturbation theory is applied taking the positron-electron interaction as a perturbation. The corrections for the complete basis set effects to the second order affinity are calculated based on the variational and nonvariational energy functionals of explicitly correlated geminals. It is shown that the explicitly correlated methods accelerate the convergence of the expansion significantly giving the account of the cusp behavior outside the orbital space.

• Communications of the Korean Mathematical Society
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• v.12 no.2
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• pp.293-303
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• 1997

The existence theorem for the operator valued function space integral has been studied, when the wave function was in $L_1(R)$ class and the potential energy function was represented as a double integra [4]. Johnson and Lapidus established the existence theorem for the operator valued function space integral, when the wave function was in $L_2(R)$ class and the potential energy function was represented as an integral involving a Borel measure [9]. In this paper, we establish the existence theorem for the operator valued function we establish the existence theorem for the operator valued function space integral as an operator from $L_1(R)$ to $L_\infty(R)$ for certain potential energy functions which involve double integrals with some Borel measures.