• The Journal of the Acoustical Society of Korea
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• 제17권1E호
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• pp.70-75
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• 1998

The analysis of dynamic responses are carried out on several anisotropic systems due to buried pulsating line sources. These include infinite, semi-infinite spaces. The media possess orthotropic or higher symmetry. The load is in the from of a normal stress acting with parallel to symmetry axis on the plane of symmetry within the materials. The results are first derived for infinite media. Subsequently the results for semi-infinite are derived by using superposition of the solution in the infinite medium together with a scattered solution from the boundaries. The sum of both solutions has to satisfy stress free boundary conditions, thereby leading to the complete solutions. The solutions are simplified to the systems possessing of higher symmetry, such as orthotropic, transversely isotropic, cubic, and isotropic symmetry.

• Coupled systems mechanics
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• 제7권1호
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• pp.61-77
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• 2018

This paper establish a high concentration ratio approximation of linear elastic properties of materials with periodic microstructure with cubic inclusions. The approximation is derived using first few terms of power series expansion of the solution of the equivalent eigenstrain problem with a homogeneous eigenstrain approximation. Viability of the approximation at high concentration ratios is proved by comparison with a numerical solution of the homogenization problem. To this end some theoretical result of symmetry properties of the homogenization problem are given. Using these results efficient numerical computation on a reduced computational domain is presented.

• Bulletin of the Korean Chemical Society
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• 제12권5호
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• pp.544-554
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• 1991

Using the Huckel method, we obtain the analytical expressions for eigenvalues and eigenvectors of s.c., f.c.c. and b.c.c. clusters of rectangular parallelepiped shape, and of an arbitrary size. Our formula converage to those derived from the Bloch sum, in the limit of infinite extension. DOS and LDOS reveal that the major contribution of the states near Fermi level originates from the surface atoms, also symmetry of DOS curves disappears by the introduction of 2nd nearest neighbor interactions, in all the cubic lattices. An accumulation of the negative charges on surface of cluster is observed.

• 대한기계학회논문집A
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• 제31권1호
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• pp.97-104
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• 2007

Vibration analysis of a rigid body supported by in-parallel linear springs can be greatly simplified by utilizing the conditions for a plane of symmetry. The vibration modes of an oscillatory system having plane of symmetry are classified into the in-plane and out-of-plane modes. From the viewpoint of screw theory, they represent respectively the vibration axes perpendicular to the plane of symmetry and lying in the plane of symmetry. In this paper, the sets of orthogonal and mutually intersecting three springs are used as resilient support of a rigid body. The geometrical conditions for the system to have a plane of symmetry and diagonalized stiffness matrix are presented. From the orthogonality of the vibration modes with respect to the inertia matrix, the geometrical relation between the reaction wrenches and the vibration modes are derived. This geometrical relation is then used to get the cubic design equation for the design of out-of-plane modes. The numerical design example of engine mounts is presented in order to explain the suggested design technique.

• 공업화학
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• 제4권2호
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• pp.342-348
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• 1993

1473 K, 대기압하에서 $Sm_{1-x}Sr_xFe^{3+}{_{1-t}}Fe^{4+}{_t}O_{3-y}$ ($0.00{\leq}x{\leq}1.00$) 페라이트계에 대하여 균일상의 시료를 제조하였다. x값의 증가에 따라 $Fe^{4+}$ 이온의 양이 증가하였으며 결정학적 구조는 orthorhombic에서 cubic으로 변화함을 알 수 있었다. $Fe^{4+}$ 이온의 증가에따라 일정온도에서의 전기전도도는 급격히 증가하며, 활성화에너지는 감소한다. x=0.00 시료의$M{\ddot{o}}ssbauer$ spectrum은 six-line 형태를 보이며 팔면체 자리에 $Fe^{3+}$ 이온이 존재함을 확인시켜 주었다.

• 열처리공학회지
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• 제31권5호
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• pp.237-243
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• 2018

In-rich InGaN epilayers were grown on (0001) sapphire substrates by radio-frequency plasma-assisted molecular beam epitaxy (RF-MBE). InGaN epilayers grown at various growth condition were observed by SEM, XRD, and RHEED. When plasma power of nitrogen increased from 290 to 350 W, surface morphology and crystal quality became worse according to more active nitrogen on the surface of InGaN at N-rich growth condition. As In composition was reduced from 89 to 71% by changing the incoming flux of In and Ga, surface morphology and crystal quality became worse. In addition, weak peaks of cubic InGaN phase was observed from InGaN layer with 71% In composition by XRD ${\Phi}$ scan measurement. When growth temperature decreased from 500 to $400^{\circ}C$, RHEED diffraction pattern was changed to be from streaky to spotty which means atomically rough surface, and spotty pattern showed cubic symmetry of InGaN clearly. XRD ${\Phi}$ scan measurement gave clear evidence that more cubic InGaN phase was formed at low growth temperature. All these results indicates that extremely low surface mobility of Ga adatom caused inferior crystal quality and cubic InGaN phase.

• 복합신소재구조학회 논문집
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• 제2권3호
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• pp.1-11
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• 2011

본 연구에서는 하위 요소로(sub-element) 구성된 3차원 대칭 단위 요소들로 조합된 트러스 격자 구조물의 연속적인 물성치를 제안하였다. 개별적인 트러스 격자 물성치는 균질화 작업을 통하여 유효한 응력과 변형률 관계로 이루어진 연속적인 물성치 모델로 나타낼 수 있다. 미시적인 규모(micro scale) 스트럿의 인장이나 압축 응답에 의한 축강성은 전체 격자재료의 대부분의 강도를 차지하고, 이러한 스트럿의 부피 분율(fraction)은 효과적인 강도뿐만 아니라 복제 가능한 단위 요소로 이루어진 격자판의 상대밀도에 큰 영향을 주었다. 그러므로 균질한 강성부재로 구성된 연속적인 구성모델은 미시적인 규모로 간주되는 스트럿의 강도, 내부응력 상태 및 부피 분율과 관련된 역학적인 특성들을 포함하고 있다는 것을 확인할 수 있었다. 미시적인 규모의 응력에서 소성흐름은 균질한 구성식에서 파생된 거시적인 규모에서의 (macro-scale)응력 표면에 있는 연속적인 응력함수의 영역을 확장한다. 따라서 본 연구를 통하여 3차원 대칭 단위요소 구조물의 기본 기하학을 조사하고 압력에 의존적인 마크로 규모에서의 (macro-scale) 응력함수를 예측하는 연속적인 소성모델을 공식화하였다.

• 한국수학사학회지
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• 제32권4호
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• pp.159-173
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• 2019

In this paper, we examine the brief history of the ring of four almonds regarding Mesopotamian mathematics, and present reasons why the Omar Khayyam's triangle, a special right triangle in a ring of four almonds, was essential for artisans due to its unique pattern. We presume that the ring of four almonds originated from a point symmetry figure given two concentric squares used in the proto-Sumerian Jemdet Nasr period (approximately 3000 B.C.) and a square halfway between two given concentric squares used during the time of the Old Akkadian period (2340-2200 B.C.) and the Old Babylonian age (2000-1600 B.C.). Artisans tried to create a new intricate pattern as almonds and 6-pointed stars by subdividing right triangles in the pattern of the popular altered Old Akkadian square band at the time. Therefore, artisans needed the Omar Khayyam's triangle, whose hypotenuse equals the sum of the short side and the perpendicular to the hypotenuse. We presume that artisans asked mathematicians how to construct the Omar Khayyam's triangle at a meeting between artisans and mathematicians in Isfahan. The construction of Omar Khayyam's triangle requires solving an irreducible cubic polynomial. Omar Khayyam was the first to classify equations of integer polynomials of degree up to three and then proceeded to solve all types of cubic equations by means of intersections of conic sections. Omar Khayyam's triangle gave practical meaning to the type of cubic equation $x^3+bx=cx^2+a$. The work of Omar Khayyam was completed by Descartes in the 17th century.

• 한국자기공명학회논문지
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• 제16권2호
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• pp.111-121
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• 2012

The spin-lattice relaxation times, $T_1$, and spin-spin relaxation times, $T_2$, of the $^{27}Al$ and $^{87}Rb$ nuclei in $RbAl(CrO_4)_2{\cdot}2H_2O$ crystals were investigated. The presence of only one resonance line for the $^{27}Al$ nuclei indicates that the results in a dynamical averaging of the crystal electric field that produces a cubic symmetry field. The changes in the temperature dependence of $T_1$ are related to variations in the symmetry of the octahedra of water molecules surrounding $Al^+$ and $Rb^+$. The $T_1$ values for the $^{27}Al$ and $^{87}Rb$ nuclei are different due to differences in the local environments of these ions. We also compared these $^{27}Al$ and $^{87}Rb$ NMR results with those obtained for $RbAl(CrO_4)_2{\cdot}2H_2O$ crystals. The relaxation mechanisms of $RbAl(XO_4)_2{\cdot}nH_2O$ (X=Cr and S) crystals are characterized by completely different NMR behaviors.

• 대한화학회지
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• 제34권5호
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• pp.413-417
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• 1990

Sol-gel법을 통하여 만들어진 비정질 SiO$_2$ gel들의 구조가 열처리 온도, 80$^{\circ}C$, 250$^{\circ}C$, 450$^{\circ}C$ 그리고 1000$^{\circ}C$에 따라 변화하는 과정을 X-선 회절 강도 측정으로부터 구한 동경분포곡선을 이용하여 알아보았다. 그리고 이를 6개의 결정들과 비교하여 예상되는 구조를 밝혔다. 각 시편들은 용융법으로 구한 SiO$_2$의 구조와 O-O결합쌍을 제외하고는 가장 유사한 구조를 가지며 cubic형으로 나타났다.