• Journal of the Korean Mathematical Society
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• v.58 no.5
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• pp.1181-1209
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• 2021

In the present paper, we are concerned with the existence of ground state sign-changing solutions for the following Schrödinger-Poisson-Kirchhoff system $$\;\{\begin{array}{lll}-(1+b{\normalsize\displaystyle\smashmargin{2}{\int\nolimits_{{\mathbb{R}}^3}}}{\mid}{\nabla}u{\mid}^2dx){\Delta}u+V(x)u+k(x){\phi}u={\lambda}f(x)u+{\mid}u{\mid}^4u,&&\text{in }{\mathbb{R}}^3,\\-{\Delta}{\phi}=k(x)u^2,&&\text{in }{\mathbb{R}}^3,\end{array}$$ where b > 0, V (x), k(x) and f(x) are positive continuous smooth functions; 0 < λ < λ₁ and λ₁ is the first eigenvalue of the problem -∆u + V(x)u = λf(x)u in H. With the help of the constraint variational method, we obtain that the Schrödinger-Poisson-Kirchhoff type system possesses at least one ground state sign-changing solution for all b > 0 and 0 < λ < λ₁. Moreover, we prove that its energy is strictly larger than twice that of the ground state solutions of Nehari type.

• Bulletin of the Korean Mathematical Society
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• v.56 no.6
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• pp.1601-1615
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• 2019

We show the existence of ground state and orbital stability of standing waves of nonlinear $Schr{\ddot{o}}dinger$ equations with singular linear potential and essentially mass-subcritical power type nonlinearity. For this purpose we establish the existence of ground state in $H^1$. We do not assume symmetry or monotonicity. We also consider local and global well-posedness of Strichartz solutions of energy-subcritical equations. We improve the range of inhomogeneous coefficient in [5, 12] slightly in 3 dimensions.

• Bulletin of the Korean Mathematical Society
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• v.59 no.4
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• pp.961-977
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• 2022

In this paper, we consider the following Kirchhoff type equation on the whole space $$\{-(a+b{\displaystyle\smashmargin{2}{\int\nolimits_{{\mathbb{R}}^3}}}\;{\mid}{\nabla}u{\mid}^2dx){\Delta}u=u^5+{\lambda}k(x)g(u),\;x{\in}{\mathbb{R}}^3,\\u{\in}{\mathcal{D}}^{1,2}({\mathbb{R}}^3),$$ where λ > 0 is a real number and k, g satisfy some conditions. We mainly investigate the existence of ground state solution via variational method and concentration-compactness principle.

• Journal of Magnetics
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• v.16 no.3
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• pp.201-205
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• 2011

We performed total energy and electronic structure calculations for the basic ground state properties of Fe using the conventional generalized gradient approximation (GGA) and screened hybrid functionals as the form of the exchange-correlation functional. To that end, we calculated structural (equilibrium lattice constants, bulk moduli, and cohesive energies) and electronic (magnetic moments and densities of states) properties. Both functional calculations gave the correct ground state, the ferromagnetic bcc phase, in which the structural parameters agreed well with experimental results. However, the description of the cohesive energies and magnetic moments at the ground state exhibited different behavior from each other: the unusually small cohesive energy and large magnetic moment were observed in the screened hybrid functional calculations compared to the GGA calculations. The reason for the difference was examined by analyzing the calculated electronic structures.

• Bulletin of the Korean Chemical Society
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• v.34 no.7
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• pp.1961-1966
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• 2013

Theoretical investigations have been performed for the ground state ($S_0$) and the first excited state ($S_1$) of the hydrogen bonded green fluorescent protein (GFP) model. The potential energy surface (PESs) of $S_0$ was obtained by B3LYP method and that of $S_1$ was obtained by CIS method. Based on the relative stabilities of species and the energy barriers for the proton transfer, it was found that proton transfer could take place both under the ground state and the first excited state. As determined by the proton motions along the reaction coordinate, both the ground state proton transfer (GSPT) and the excited state proton transfer (ESPT) are considered as a concerted and asynchronous process.

• Journal of Photoscience
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• v.12 no.3
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• pp.119-122
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• 2005

The photophysical properties of coumarin 6 laser dye have been studied in two solvents; ethanol and acetonitrile using steady-state fluorescence depolarization technique. The experimentally measured reorientation time of coumarin 6 is more or less the same in given solvents at particular temperature. It is found that coumarin 6 rotates slower in acetonitrile than in ethanol especially at higher values of viscosity over temperature. We also measure the ground and excited state dipole moments of coumarin 6 by solvent perturbation method. The results found that excited state dipole moment is greater than ground state dipole moment, which indicates that excited state is more polar than the ground state.

• Proceedings of the Korean Geotechical Society Conference
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• 1993.06a
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• pp.73-82
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• 1993

Ground-borne vibration is one of the main causes of environmental impact from subway systems. The vibration resulting from track-train interaction is transuutted through the tunnel structure and the surrounding ground to adjacent buildings. This paper provides a summary of proposed noise and vibration criteria, a review of the ground vibration propagation mechanism and the theoretical isolation effectivenesss of each of the following underground transit systems : track, tunnel and vehicle itself.

• International Journal of Naval Architecture and Ocean Engineering
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• v.1 no.1
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• pp.1-12
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• 2009

Wing-in-Ground vehicles and aerodynamically assisted boats take advantage of increased lift and reduced drag of wing sections in the ground proximity. At relatively low speeds or heavy payloads of these craft, a flap at the wing trailing-edge can be applied to boost the aerodynamic lift. The influence of a flap on the two-dimensional NACA 4412 airfoil in viscous ground-effect flow is numerically investigated in this study. The computational method consists of a steady-state, incompressible, finite volume method utilizing the Spalart-Allmaras turbulence model. Grid generation and solution of the Navier-Stokes equations are completed using computer program Fluent. The code is validated against published experimental and numerical results of unbounded flow with a flap, as well as ground-effect motion without a flap. Aerodynamic forces are calculated, and the effects of angle of attack, Reynolds number, ground height, and flap deflection are presented for a split and plain flap. Changes in the flow introduced with the flap addition are also discussed. Overall, the use of a flap on wings with small attack angles is found to be beneficial for small flap deflections up to 5% of the chord, where the contribution of lift augmentation exceeds the drag increase, yielding an augmented lift-to-drag ratio.

• Bulletin of the Korean Chemical Society
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• v.22 no.6
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• pp.605-610
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• 2001

The molecular geometries and harmonic vibrational frequencies of dibenzofuran in the ground and lowest triplet state have been calculated using the Hartree-Fock and Becke-3-Lee-Yang-Parr(B3LYP)density functional methods with the 6-31G basis set. Upon the excitation to the lowest triplet state, the molecular structure retains the planar form but distorts from a benzene-like to a quinone-like form in skeleton. Scaled vibrational frequencies for the ground and lowest triplet state obtained from the B3LYP calculation show excellent agreement with the available experimental data. A few vibrational fundamentals for both states are newly assigned based on the B3LYP results.

• Bulletin of the Korean Chemical Society
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• v.31 no.10
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• pp.2806-2808
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• 2010

The structure of 3-aminophenol $(CO_2)_1$ cluster was computationally studied both in the ground and the lowest singlet excited electronic states. The ground state structure and binding energy of the cluster was investigated using the second-order M$\ddoot{o}$ller-Plesset perturbation theory (MP2) at the complete basis set (CBS) limit. The excited state geometry of the cluster was obtained at the second-order approximate coupled cluster (CC2) level with cc-pVDZ basis set, and the $S_0-S_1$ absorption spectrum was simulated by calculating Franck-Condon overlap integral. The ground state geometry of the global minimum with a very high binding energy of 4.3 kcal/mol was found for the cluster, due to the interaction between amino group and $CO_2$ in addition to the strong $\pi-\pi$ interaction between the aromatic ring and $CO_2$. The excited state geometry shows a very big shift in the position of $CO_2$ compared to the ground state geometry, which results in low intensity and broad envelope in the Franck-Condon simulation.