• Structural Engineering and Mechanics
• /
• v.23 no.1
• /
• pp.63-74
• /
• 2006

In this paper, the scattering of harmonic elastic anti-plane shear waves by two collinear cracks in functionally graded materials is investigated by means of nonlocal theory. The traditional concepts of the non-local theory are extended to solve the fracture problem of functionally graded materials. To overcome the mathematical difficulties, a one-dimensional non-local kernel is used instead of a two-dimensional one for the anti-plane dynamic problem to obtain the stress field near the crack tips. To make the analysis tractable, it is assumed that the shear modulus and the material density vary exponentially with coordinate vertical to the crack. By use of the Fourier transform, the problem can be solved with the help of a pair of triple integral equations, in which the unknown variable is the displacement on the crack surfaces. To solve the triple integral equations, the displacement on the crack surfaces is expanded in a series of Jacobi polynomials. Unlike the classical elasticity solutions, it is found that no stress singularities are present at crack tips.

• Bulletin of the Korean Chemical Society
• /
• v.33 no.3
• /
• pp.971-974
• /
• 2012

The facilitated diffusion effect on protein-DNA binding is studied. A rigorous theoretical approach is presented to deal with the coupling between one-dimensional and three-dimensional diffusive motions. For a simplified model, the present approach can provide numerically exact results, which are confirmed by the lattice-based Monte Carlo simulations.

• Bulletin of the Korean Mathematical Society
• /
• v.33 no.2
• /
• pp.233-241
• /
• 1996

The study of non-self-adjoint operator algebras on Hilbert space was only beginned by W.B. Arveson[1] in 1974. Recently, such algebras have been found to be of use in physics, in electrical engineering, and in general systems theory. Of particular interest to mathematicians are reflexive algebras with commutative lattices of invariant subspaces.

• Bulletin of the Korean Mathematical Society
• /
• v.57 no.4
• /
• pp.909-919
• /
• 2020

The 4-dimensional solvable Lie group Sol₀⁴ does not admit a lattice. The purpose of this paper is two-fold. We study poly-crystallographic groups of Sol₀⁴, and then we study Nielsen fixed point theory on the spaces modeled on Sol₀⁴.

• Bulletin of the Korean Mathematical Society
• /
• v.43 no.3
• /
• pp.461-470
• /
• 2006

As a continuation of [4], characterizations of fuzzy implicative ideals are given. An extension property for fuzzy implicative ideals is established. We prove that the family of fuzzy implicative ideals is a completely distributive lattice. Using level subsets of a BCk-algebra X with respect to a fuzzy set $\={A}$ in X, we construct a fuzzy implicative ideal of X containing $\={A}$.

• Proceedings of the Korean Vacuum Society Conference
• /
• 2014.02a
• /
• pp.199.1-199.1
• /
• 2014

In nonlinear optics, the properties of nonlinear optical responses such as polarization and nonlinear analysis of the nonlinear surfaces were investigated using the jellium model by optical second harmonic generation. The nonlinear response of the Al metal surfaces were calculated using TDLDA. Band structure, lattice constant and bulk modulus of the Al metal were investigated. Effective potential and electron density were compared by changing different.

• Proceedings of the Korea Contents Association Conference
• /
• 2013.05a
• /
• pp.369-370
• /
• 2013

Orthomodular lattice is a mathematical description of quantum theory which is based on the family CS(H) of all closed subspaces of a Hilbert space H. A partial multiplier is a function F from a non-empty subset D of a commutative semigroup A into A such that F(x)y = xF(y) for every elements x, y in A. In this paper, we define the notion of multipliers on orthomodular lattices and give some properties of multipliers. Also, we characterize some properties of orthomodular lattices by multipliers.

• Proceeding of EDISON Challenge
• /
• 2015.03a
• /
• pp.392-395
• /
• 2015

Metal Mono Chalcogenides(MMC)는 각각의 III족 metal 원자당한개의 chalchogen 원자를 갖고 있는(MX, M=Ga and In, X=S, Se, and Te)층상구조 화합물이다. MMC가 주목받는 가장 큰 이유는 single tetralayer MMC(SL-MMC)라는 2차원 구조를 갖기 때문이다. 2차원 물질은 다양한 물리적 현상을 증명하기 용이하다는 특징을 갖는다. 이 논문에서 우리는 SL-MMC중 Ga-MMC에서 chalchogen 원자가 변화함에 따라 바뀌는 실험 lattice constant를 조사하여 band gap과 formation energy를 Density Function Theory(DFT)로 계산했다.

• Structural Engineering and Mechanics
• /
• v.59 no.3
• /
• pp.475-502
• /
• 2016

Nanobeams are widely used as a structural element for nanodevices and nanomachines. The development of nano-sized machines depends on proper understanding of mechanical behavior of these nano-sized beam elements. Small length scales such as lattice spacing between atoms, surface properties, grain size etc. are need to be considered when applying any classical continuum model. In this study, Eringen's nonlocal elasticity theory is incorporated into classical beam model considering the effects of axial extension and the shear deformation to capture unique static behavior of the nanobeams under continuum mechanics theory. The governing differential equations are obtained for curved beams and solved exactly by using the initial value method. Circular uniform beam with concentrated loads are considered. The displacements, slopes and the stress resultants are obtained analytically. A detailed parametric study is conducted to examine the effect of the nonlocal parameter, mechanical loadings, opening angle, boundary conditions, and slenderness ratio on the static behavior of the nanobeam.

• Bulletin of the Korean Chemical Society
• /
• v.17 no.2
• /
• pp.192-198
• /
• 1996

We present a theoretical formulation of diffusion process on solid surface based on multidimensional transition state theory (TST). Surface diffusion of single adatom results from hopping processes on corrugated potential surface and is affected by surface vibrations of surface atoms. The rate of rare events such as hopping between lattice sites can be calculated by transition state theory. In order to include the interactions of the adatom with surface vibrations, it is assumed that the coordinates of adatom are coupled to the bath of harmonic oscillators whose frequencies are those of surface phonon modes. When nearest neighbor surface atoms are considered, we can construct Hamiltonians which contain terms for interactions of adatom with surface vibrations for the well minimum and the saddle point configurations, respectively. The escape rate constants, thus the surface diffusion parameters, are obtained by normal mode analysis of the force constant matrix based on the Hamiltonian. The analysis is applied to the diffusion coefficients of W, Ir, Pt and Ta atoms on the bcc(110) plane of W in the zero-coverage limit. The results of the calculations are encouraging considering the limitations of the model considered in the study.