• Title/Summary/Keyword: cubic number field

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$^{11}B$ Nuclear Magnetic Resonance Study of Calcium-hexaborides

  • Mean, B.J.;Lee, K.H.;Kang, K.H.;Lee, Moo-Hee;Lee, J.S.;Cho, B.K.
    • Journal of the Korean Magnetic Resonance Society
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    • v.7 no.2
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    • pp.80-88
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    • 2003
  • We have performed $^{11}$ B nuclear magnetic resonance (NMR) measurements to microscopically investigate an electronic structure of the ferromagnetic state in three different compositions of calcium-hexaboride single crystals. Although the crystal structure of Ca $B_{6}$ is cubic and three NMR lines may be expected for the nuclear spin 3/2 of $_{11}$ B, a larger number of NMR resonance peaks have been observed. The frequency and intensity of those peaks distinctively changes depending on the angle between crystalline axis and magnetic field. Analyzing this behavior, we find that the electric field gradient(EFG) tensor at the boron has its principal axis perpendicular to the six cubic faces with a quadrupole resonance frequency $v_{Q}$ 600 kHz. Even though the magnetization data highlight the ferromagnetic hysteresis, $^{11}$ B NMR linewidth data show no clear microscopic evidence of the ferromagnetic state in three different compositions of Ca $B_{6}$ single crystals.s.

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Study of Natural Convection of Magnetic Fluid in Cubic Cavity (정방형관 내에서 자성유체의 자연대류현상에 대한 수치적 연구)

  • Seo, Jae-Hyeong;Lee, Moo-Yeon;Seo, Lee-Soo
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.37 no.7
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    • pp.637-646
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    • 2013
  • This study aims to numerically investigate the natural convection characteristics of a magnetic fluid in a cubic cavity. The governing equations of the magnetic fluid are solved using the Generalized-Simplified Marker and Cell Method (GSMAC). The natural convection and heat transfer characteristics of the magnetic fluid were analyzed by varying the intensity and direction of the magnetic field. As a result, it was found that the natural convection characteristics were controlled by the intensity and direction of the magnetic field, and the mean Nusselt numbers were minimized at a vertical intensity of H=-4000 and horizontal intensity of H=12000 of the magnetic field. In addition, the mean Nusselt numbers increased with the intensities of the magnetic field, regardless of the direction of the magnetic field.

Dynamic analysis for delaminated composites based on finite element (다중 층간분리부가 내재된 복합재 평판의 유한요소 진동해석)

  • 오진호;조맹효;김준식
    • Proceedings of the Korean Society For Composite Materials Conference
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    • 2003.04a
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    • pp.143-146
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    • 2003
  • A finite element based on the efficient higher order zig-zag theory with multiple delaminations Is developed to refine the predictions of frequency and mode shapes. Displacement field through the thickness are constructed by superimposing linear zig-zag field to the smooth globally cubic varying field. The layer-dependent degrees of freedom of displacement fields are expressed in terms of reference primary degrees of freedom by applying interface continuity conditions including delaminated interfaces as well as free hounding surface conditions of transverse shear stresses. Thus the proposed theory is not only accurate but also efficient. This displacement field can systematically handle the number, shape, size, and locations of delaminations. Throught the dynamic version of variational approach, the dynamic equilibrium equations and variationally consistent boundary conditions are obtained. Through the natural frequency analysis and time response analysis of composite plate with multiple delaminations, the accuracy and efficiency of the present finite element are demonstrated. The present finite element is suitable in the predictions of the dynamic response of the thick composite plate with multiple delaminations.

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Higher Order Zig-Zag Theory for Composite Shell under Thermo-mechanical load (열, 기계 하중을 고려한 지그재그 고차 복합재 쉘 이론)

  • Oh Jin-Ho;Cho Maeng-Hyo
    • Proceedings of the Computational Structural Engineering Institute Conference
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    • 2005.04a
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    • pp.217-224
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    • 2005
  • A higher order zig-zag shell theory is developed to refine the predictions of the mechanical and thermal behaviors partially coupled. The in-plane displacement fields are constructed by superimposing linear zig-zag field to the smooth globally cubic varying field through the thickness. Smooth parabolic distribution through the thickness is assumed in the out-of-plane displacement in order to consider transverse normal deformation and stress. The layer-dependent degrees of freedom of displacement fields are expressed in terms of reference primary degrees of freedom by applying interface continuity conditions as well as bounding surface conditions of transverse shear stresses. Thus the proposed theory has only seven primary unknowns and they do not depend upon the number of layers. In the description of geometry and deformation of shell surface, all rigorous exact expressions are used. Through the numerical examples of partially coupled analysis, the accuracy and efficiency of the present theory are demonstrated. The present theory is suitable in the predictions of deformation and stresses of thick composite shell under mechanical and thermal loads combined.

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PIV measurement of step cavity with driven flow (구동류를 갖는 계단 캐비티의 PIV계측)

  • 조대환;김진구;이영호
    • Journal of Ocean Engineering and Technology
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    • v.12 no.1
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    • pp.113-119
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    • 1998
  • An experimental study was carried out in a three-dimensional cubic cavity driven by 2-dimensional plane Poiseuille flow for three kinds of Reynolds number, $10^4$, 3 $\times$ $10^4$ and 5 $\times$ $10^4$ based on the cavity width and cavity inlet mean flow velcoity. Instant simultaneous velocity vectors at whole field were measured by 2-D PIV system. Laser based illumination and two-frame grey-level cross correlation algorithm are adopted. Severe unsteady flow fluctuation within the cavity are remarkable at above Re = 3 $\times$ $10^4$ Reynolds numbers and sheared mixing layer phenomena are also found at the region where inlet driving Poiseuille flow is collided with the clock-wise rotating main primary vortex at upper center area. Instant velocity profiles reveal that deformed forced vortex formation is observed throughout the separate two areas.

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A Method for Distinguishing the Two Candidate Elliptic Curves in the Complex Multiplication Method

  • Nogami, Yasuyuki;Obara, Mayumi;Morikawa, Yoshitaka
    • ETRI Journal
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    • v.28 no.6
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    • pp.745-760
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    • 2006
  • In this paper, we particularly deal with no $F_p$-rational two-torsion elliptic curves, where $F_p$ is the prime field of the characteristic p. First we introduce a shift product-based polynomial transform. Then, we show that the parities of (#E - 1)/2 and (#E' - 1)/2 are reciprocal to each other, where #E and #E' are the orders of the two candidate curves obtained at the last step of complex multiplication (CM)-based algorithm. Based on this property, we propose a method to check the parity by using the shift product-based polynomial transform. For a 160 bits prime number as the characteristic, the proposed method carries out the parity check 25 or more times faster than the conventional checking method when 4 divides the characteristic minus 1. Finally, this paper shows that the proposed method can make CM-based algorithm that looks up a table of precomputed class polynomials more than 10 percent faster.

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Coupled electro-elastic analysis of functionally graded piezoelectric material plates

  • Wu, Chih-Ping;Ding, Shuang
    • Smart Structures and Systems
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    • v.16 no.5
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    • pp.781-806
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    • 2015
  • A unified formulation of finite layer methods (FLMs), based on the Reissner mixed variational theorem (RMVT), is developed for the three-dimensional (3D) coupled electro-elastic analysis of simply-supported, functionally graded piezoelectric material (FGPM) plates with open- and closed-circuit surface conditions and under electro-mechanical loads. In this formulation, the material properties of the plate are assumed to obey an exponent-law varying exponentially through the thickness coordinate, and the plate is divided into a number of finite rectangular layers, in which the trigonometric functions and Lagrange polynomials are used to interpolate the in- and out-of-plane variations of the primary field variables of each individual layer, respectively, such as the elastic displacement, transverse shear and normal stress, electric potential, and normal electric displacement components. The relevant orders used for expanding these variables in the thickness coordinate can be freely chosen as the linear, quadratic and cubic orders. Four different mechanical/electrical loading conditions applied on the top and bottom surfaces of the plate are considered, and the corresponding coupled electro-elastic analysis of the loaded FGPM plates is undertaken. The accuracy and convergence rate of the RMVT-based FLMs are assessed by comparing their solutions with the exact 3D piezoelectricity ones available in the literature.

Electronic and Magnetic Structure Calculations of Mn-dimer Molecular Magnet (Mn-dimer 분자자성체의 전자구조 및 자기구조 계산)

  • Park, Key Taeck
    • Journal of the Korean Magnetics Society
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    • v.24 no.4
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    • pp.97-100
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    • 2014
  • We have studied electronic and magnetic structure of Mn-dimer molecule using OpenMX method based on density functional method. The calculated density of states shows that the four O atoms split $e_g$ and $t_{2g}$ energy levels. The energy splitting by the crystal field is smaller than bulk MnO with cubic structure, because of small coordination number of atoms. Total energy with antiferromagnetic spin configuration is lower than that of ferromagnetic configurations. Calculated exchange interaction J between Mn atoms is one order larger than that of the other Mn-O magnetic molecules. That comes from the direct exchange interaction between Mn 3d orbitals and the super-exchange interactions caused by strong ${\sigma}$-bonding of Mn-O orbitals.

Development and validation of a non-linear k-ε model for flow over a full-scale building

  • Wright, N.G.;Easom, G.J.;Hoxey, R.J.
    • Wind and Structures
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    • v.4 no.3
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    • pp.177-196
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    • 2001
  • At present the most popular turbulence models used for engineering solutions to flow problems are the $k-{\varepsilon}$ and Reynolds stress models. The shortcoming of these models based on the isotropic eddy viscosity concept and Reynolds averaging in flow fields of the type found in the field of Wind Engineering are well documented. In view of these shortcomings this paper presents the implementation of a non-linear model and its evaluation for flow around a building. Tests were undertaken using the classical bluff body shape, a surface mounted cube, with orientations both normal and skewed at $45^{\circ}$ to the incident wind. Full-scale investigations have been undertaken at the Silsoe Research Institute with a 6 m surface mounted cube and a fetch of roughness height equal to 0.01 m. All tests were originally undertaken for a number of turbulence models including the standard, RNG and MMK $k-{\varepsilon}$ models and the differential stress model. The sensitivity of the CFD results to a number of solver parameters was tested. The accuracy of the turbulence model used was deduced by comparison to the full-scale predicted roof and wake recirculation zone lengths. Mean values of the predicted pressure coefficients were used to further validate the turbulence models. Preliminary comparisons have also been made with available published experimental and large eddy simulation data. Initial investigations suggested that a suitable turbulence model should be able to model the anisotropy of turbulent flow such as the Reynolds stress model whilst maintaining the ease of use and computational stability of the two equations models. Therefore development work concentrated on non-linear quadratic and cubic expansions of the Boussinesq eddy viscosity assumption. Comparisons of these with models based on an isotropic assumption are presented along with comparisons with measured data.

Structural and Electrical Properties of K(Ta0.70Nb0.30)O3/K(Ta0.55Nb0.45)O3 Heterolayer Thin Films for Electrocaloric Devices (전기 열량 소자로의 응용을 위한 K(Ta0.70Nb0.30)O3/K(Ta0.55Nb0.45)O3 이종층 박막의 구조적, 전기적 특성)

  • Byeong-Jun Park;Ji-Su Yuk;Sam-Haeng Yi;Myung-Gyu Lee;Joo-Seok Park;Sung-Gap Lee
    • Journal of the Korean Institute of Electrical and Electronic Material Engineers
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    • v.37 no.3
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    • pp.297-303
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    • 2024
  • In this study, KTN heterolayer thin films were fabricated by alternately stacking films of K(Ta0.70Nb0.30)O3 and K(Ta0.55Nb0.45)O3 synthesized using the sol-gel method. The sintering temperature and time were 750℃ and 1 hour, respectively. All specimens exhibited a polycrystalline pseudo-cubic crystal structure, with a lattice constant of approximately 0.398 nm. The average grain size was around 130~150 nm, indicating relatively uniform sizes regardless of the number of coatings. The average thickness of a single-coated film was approximately 70 nm. The phase transition temperature of the KTN heterolayer films was found to be approximately 8~12℃. Moreover, the 6-coated KTN heterolayer film displayed an excellent dielectric constant of about 11,000. As the number of coatings increased, and consequently the film thickness, the remanent polarization increased, while the coercive field decreased. The 6-coated KTN heterolayer film exhibited a remanent polarization and coercive field of 11.4 μC/cm2 and 69.3 kV/cm at room temperature, respectively. ΔT showed the highest value at a temperature slightly above the Curie temperature, and for the 6-coated KTN heterolayer film, the ΔT and ΔT/ΔE were approximately 1.93 K and 0.128×10-6 K·m/V around 40℃, respectively.