• Nuclear Engineering and Technology
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• v.5 no.2
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• pp.77-82
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• 1973

A method of obtaining the partition function for a system of electrons is developed by defining a new density matrix, in which the Fermi statistics is explicitly incorporated. The corresponding Bloch equation is formulated and a practical method of solving the equation is obtained for weak potential. This theory is applied to structurally disordered ststems which might be reasonable models for liquid metals.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2011.04a
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• pp.693-696
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• 2011

본 논문에서는 레벨셋 방법을 이용하여, 소음을 차단하기 위한 음향 구조물의 형상 최적 설계를 수행하였다. 음향 결정 구조에서는 음향이 흩어져 있는 결정 구조에 의해서 굴절되기 때문에 결정 모양을 조정함으로써, 음향 거동을 제어 할 수 있다. 형상 최적 설계의 목적은 특정한 각도와 각속도로 입사되는 입사파에 대해서 음향 투과율(acoustic transmittance)이 최소가 되도록 음향 결정의 형상(inclusion shape)을 결정하는 것이다. 음향 압력(acoustic pressure)은 주기성을 갖는 음향 결정에 대해서 헬몰츠(Helmoltz)형태의 지배 방정식을 풀어서 얻을 수 있다. 본 연구에서는 음향 구조물로 결정이 수평 방향으로는 주기적으로 무한히 분포하고 수직방향으로는 유한한 층간 구조를 가지고 있는 소음 방어벽 (Noise barrier)을 고려한다. 결정의 위치는 고정되어 있고, 결정의 형상을 설계 변수로서 음파의 거동을 제어할 수 있도록 하였다. 주기적 구조물을 고려하기 때문에 결정의 좌와 우에 Bloch 이론을 적용해 주기적 경계조건을 부과하였고, 소음 방어벽 위와 아래에는 임피던스 행렬(impedance matrix)를 이용하여, 무한 균질 영역과 소음 방어벽사이의 음파 투과를 모사하였다. 복잡한 형상 변화를 표현하기 위해 임시적 경계를 이용한 레벨셋 방법을 사용하였다. 설계 민감도 해석을 통해 목적함수가 감소하는 방향으로 경계에서의 수직 벡터를 계산하고, 이를 헤밀턴-자코비(Hamilton-Jacob) 방정식에 대입하여, 최적의 형상을 나타내는 레벨셋 함수를 구하였다.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.25 no.6
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• pp.549-558
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• 2012

A topology optimization method for phononic crystals is developed for the design of sound barriers, using the level set approach. Given a frequency and an incident wave to the phononic crystals, an optimal shape of periodic inclusions is found by minimizing the norm of transmittance. In a sound field including scattering bodies, an acoustic wave can be refracted on the obstacle boundaries, which enables to control acoustic performance by taking the shape of inclusions as the design variables. In this research, we consider a layered structure which is composed of inclusions arranged periodically in horizontal direction while finite inclusions are distributed in vertical direction. Due to the periodicity of inclusions, a unit cell can be considered to analyze the wave propagation together with proper boundary conditions which are imposed on the left and right edges of the unit cell using the Bloch theorem. The boundary conditions for the lower and the upper boundaries of unit cell are described by impedance matrices, which represent the transmission of waves between the layered structure and the semi-infinite external media. A level set method is employed to describe the topology and the shape of inclusions. In the level set method, the initial domain is kept fixed and its boundary is represented by an implicit moving boundary embedded in the level set function, which facilitates to handle complicated topological shape changes. Through several numerical examples, the applicability of the proposed method is demonstrated.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.32 no.4
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• pp.241-247
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• 2019

A band gap refers to a certain frequency range where the propagation of mechanical waves is prohibited. This work focuses on engineering three-dimensional Kelvin lattices having external band gaps at low audible frequency ranges using a gradient-based design optimization method. Elastic wave propagation in an infinite periodic lattice is investigated by employing the Bloch theorem. We model the ligaments using a shear-deformable beam model obtained by consistent linearization in a geometrically exact beam theory. For a given lattice topology, we enlarge band gap sizes by controlling the configuration of the beam neutral axis and cross-section thickness that are smoothly parameterized by B-spline basis functions within the isogeometric analysis framework.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.21 no.4
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• pp.143-148
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• 2021

A systematic study of Bloch surface wave (BSW), which is created by guided mode resonance (GMR) of dielectric multilayer structures with a grating profile, is presented to analyze the sensing performance of bio-sensors. The effect of structural parameters on optical behavior is evaluated by using Babinet's principle and modal transmission-line theory. The sensitivity of designed bio-sensors is proportional to the grating constant at wavelength spectrum, and inversely proportional to the normal wave vector of incident electromagnetic wave at angular spectrum. Numerical results for two devices with SiO/SiO₂ and TiO₂/SiO₂ multilayer dielectric stacks are presented, showing that BSW can be exploited for the realization of efficient diffraction-based bio-sensors from infrared to visible-band range.

• Archives of design research
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• v.15 no.4
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• pp.149-156
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• 2002

The success of a product is only possible on the basis of user preference for products and the user preference for products is greatly influenced by the design. Designers have to understand user preference and convert it into the combination of specified design attribute, and after that they should design products which have the image that they want to get. Then the product will be sure to be a hit. Therefore, on the point of view of design, it is necessary to find oui definitely the consumer preference frame : the relationship among design preference - design images - design attribute. This study will give you guidelines on which designers can select and design some more objective and reliable design factors, finding out the relation of cause and effect by which they can know what kind of product designs their consumers like and how the popular image which that products offer is composed of. Therefore, in this study, after we developed the consumer response framework which is proposed by Bloch(1995) : distinct relationship model among preference - design image adjective - design factors, we analyzed the relationship among preference-design image adjective - design factors through the empirical researches. And then we give the way of design.

• Applied Microscopy
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• v.40 no.1
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• pp.21-28
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• 2010

In a simulation study of atomic resolution transmission electron microscope images of single layer and bilayer graphene, it is demonstrated that the conventional Bloch wave formulations can be used when high-order Laue zone reflections are properly taken into account in the theory. The simulated images for bilayer graphene show 3-fold rotational lattice symmetry rather than the 6-fold one under certain conditions. This result can be understood as revealed the 3-fold rotational lattice symmetry of bilayer graphene in three dimensions along [0001]. For single layer graphene the observed phase images showing 3-fold rotational lattice symmetry were particularly noted. This phenomenon has been explained by an assumption of the re-configuration of electron density on the surface of graphene. And the matching images have been obtained as simulated with up to the second order Laue zone reflections only, reflecting the re-configuration of electrons on the surface.