• Title/Summary/Keyword: analytical series solution

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Simulation of non-Gaussian stochastic processes by amplitude modulation and phase reconstruction

  • Jiang, Yu;Tao, Junyong;Wang, Dezhi
    • Wind and Structures
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    • v.18 no.6
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    • pp.693-715
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    • 2014
  • Stochastic processes are used to represent phenomena in many diverse fields. Numerical simulation method is widely applied for the solution to stochastic problems of complex structures when alternative analytical methods are not applicable. In some practical applications the stochastic processes show non-Gaussian properties. When the stochastic processes deviate significantly from Gaussian, techniques for their accurate simulation must be available. The various existing simulation methods of non-Gaussian stochastic processes generally can only simulate super-Gaussian stochastic processes with the high-peak characteristics. And these methodologies are usually complicated and time consuming, not sufficiently intuitive. By revealing the inherent coupling effect of the phase and amplitude part of discrete Fourier representation of random time series on the non-Gaussian features (such as skewness and kurtosis) through theoretical analysis and simulation experiments, this paper presents a novel approach for the simulation of non-Gaussian stochastic processes with the prescribed amplitude probability density function (PDF) and power spectral density (PSD) by amplitude modulation and phase reconstruction. As compared to previous spectral representation method using phase modulation to obtain a non-Gaussian amplitude distribution, this non-Gaussian phase reconstruction strategy is more straightforward and efficient, capable of simulating both super-Gaussian and sub-Gaussian stochastic processes. Another attractive feature of the method is that the whole process can be implemented efficiently using the Fast Fourier Transform. Cases studies demonstrate the efficiency and accuracy of the proposed algorithm.

Analysis for Potentail Distribution of Asymmetric Double Gate MOSFET Using Series Function (급수함수를 이용한 비대칭 이중게이트 MOSFET의 전위분포 분석)

  • Jung, Hakkee
    • Journal of the Korea Institute of Information and Communication Engineering
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    • v.17 no.11
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    • pp.2621-2626
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    • 2013
  • This paper has presented the potential distribution for asymmetric double gate(DG) MOSFET, and sloved Poisson equation to obtain the analytical solution of potential distribution. The symmetric DGMOSFET where both the front and the back gates are tied together is three terminal device and has the same current controllability for front and back gates. Meanwhile the asymmetric DGMOSFET is four terminal device and can separately determine current controllability for front and back gates. To approximate with experimental values, we have used the Gaussian function as doping distribution in Poisson equation. The potential distribution has been observed for gate bias voltage and gate oxide thickness and channel doping concentration of the asymmetric DGMOSFET. As a results, we know potential distribution is greatly changed for gate bias voltage and gate oxide thickness, especially for gate to increase gate oxide thickness. Also the potential distribution for source is changed greater than one of drain with increasing of channel doping concentration.

Theoretical Investigations and measuring Techniques of Geometrical Factor influencing Sensitive Electronic Devices (감도전자장치에 영향을 주는 기하학적 인수의 이론적 연구와 측정)

  • S. K. Lee
    • 전기의세계
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    • v.14 no.1
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    • pp.5-12
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    • 1965
  • In the designs of the sensitive electronic devices such as phase sensitive detector, X-ray diffractometer, and neutron diffractometers, we must take into account the geometrical factors in a coil systems and extraneous stray fields. Input wave forms in such a sensitive electronic devices are often altered by the influence of these factors. Since the magnitude of the stray fields is generally very small, this affection may be removed by applying a good shielding but it is not ease to remove the affection from a geometrical factor. This affection must be however calculated by the theoretical methods and analytical solution in the equation of these factors. The fundamental purpose of this paper lie in the theoretical calculations and practical measurements of the geometrical factor in the coil systems, finite solenoid, and four point prove. In the heoretical calculations, the geometrical factors in the coil systems were calculated by applying the elliptic functions and in the contact points were calculated by applying the elliptic functions and in the contact points were calculated by applying the eigen functions and the infinite series. The measurements were carried out by using the sensitive electronic device made from author's design, as shown in the Fig. 9. The result of this work has verified the essential correctness of theoretical investigations and measuring techniques of geometrical factors on the design of sensitive electronic devices. It also has several advantages such that: (1) all the data obtained may give effective data to designer to work on the field of sensitive electronic devices or microelectronic devices, (2) it has evidently explained the characteristics of electrical investigations and physical definition, and has removed the conventional error of geometrical factors in the coil systems and contact points.

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Dynamical Predictions of the Structural Connection by the Reduced Approach (축약법에 의한 구조물 결합부의 동적 거동 예측)

  • Yun, Seong-Ho
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.27 no.6
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    • pp.589-596
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    • 2014
  • Joints, fasteners or connected parts frequently have a significant effect on the dynamical behavior of assembled mechanical structures. Therefore, the analytical prediction of structural responses depends on the accuracy of joint modeling. This paper deals with the formulation and analysis of dynamic mechanism for joint flexibilities whose relevant magnitudes of stiffnesses are investigated by using linear and torsional springs. The equation of motion is derived by using a generic joint in the middle of clamped-clamped beam. A reanalysis due to changes in magnitudes of joint stiffnesses is based on the reduced analysis where the binomial series terms are used as basis vectors. The solution procedures are straightforward and the method can be readily used with a general finite element method. The computational effort needed by this approach is usually much smaller than the effort needed for complete vibration analysis. Two numerical examples show that accurate results are obtained efficiently by reducing the number of degree in the reduced model.

Nonlocal elasticity approach for free longitudinal vibration of circular truncated nanocones and method of determining the range of nonlocal small scale

  • Li, C.;Sui, S.H.;Chen, L.;Yao, L.Q.
    • Smart Structures and Systems
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    • v.21 no.3
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    • pp.279-286
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    • 2018
  • The free longitudinal vibration of a circular truncated nanocone is investigated based on the nonlocal elasticity theory. Exact analytical formulations for tapered nanostructures are derived and the nonlinear differential governing equation of motion is developed. The nonlocal small scale effect unavailable in classical continuum theory is addressed to reveal the long-range interaction of atoms implicated in nonlocal constitutive relation. Unlike most previous studies applying the truncation method to the infinite higher-order differential equation, this paper aims to consider all higher-order terms to show the overall nonlocality. The explicit solution of nonlocal stress for longitudinal deformation is determined and it is an infinite series incorporating the classical stress derived in classical mechanics of materials and the infinite higher-order derivative of longitudinal displacement. Subsequently, the first three modes natural frequencies are calculated numerically and the significant effects of nonlocal small scale and vertex angle on natural frequencies are examined. The coupling phenomenon of natural frequency is observed and it is induced by the combined effects of nonlocal small scale and vertex angle. The critical value of nonlocal small scale is defined, and after that a new proposal for determining the range of nonlocal small scale is put forward since the principle of choosing the nonlocal small scale is still unclear at present. Additionally, two different types of nonlocal effects, namely the nonlocal stiffness weakening and strengthening, reversed phenomena existing in nanostructures are observed and verified. Hence the opposite nonlocal effects are resolved again clearly. The nano-engineers dealing with a circular truncated nanocone-based sensors and oscillators may benefit from the present work.

A Study on the Genesis of Fluorite Deposits of South Korea (남한(南韓)의 형석광상(螢石鑛床)의 성인(成因)에 관(關)한 연구(硏究))

  • Chi, Jeong Mahn
    • Economic and Environmental Geology
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    • v.8 no.1
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    • pp.25-56
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    • 1975
  • Most fluorite deposits of South Korea are distributed in three metallogenic zones namly as: Hwacheon, Hwangangni and Geumsan metallogenic zones. Fluorite deposits of each zone show The characteristic features owing to the geological setting, the structural patterns and their forming processes. deposits of the Hwacheon metallogenic zone are wholly fissure filling hydrothermal veins emThe bedded in shear fractures of the granite gneiss or schists of Precambrian age or in the cooling fractures of the granite and acidic hypabyssal rocks which are assumed to be a differentiated sister rock of the granite. Localization of most fluorite veins of the region is structurally controlled by NW and EW fracture systems and genetically related to the granite intrusion which ascertained as motivating rock of the fluorite mineralization. Fluorites are in most cases accompanied by quartz, chalcedony mainly and rarely agate, calcite, barite and sulphide base metals in some localities. The deposits of the Hwangangni metallogenic zone were formed at the last stage of hydrothermal polymineralization of W, Mo, Cu, Pb, Zn. The majority of the fluorite ore bodies were originated from replacement in limestone beds of Great Limestone Series or in calcareous interbeds of metasediments, whereas some cavity-filling ore bodies were embedded in phyllites and schists of the Ockcheon system and along the fissures in the replaced beds which were originated by volume decrease. The localization of fluorite deposits in this region is genetically related to the Moongyong granite which has been dated as middle Cretaceous, and controlled structurally by the $N20^{\circ}{\sim}50^{\circ}W$ extension fracture system or axial planes of folds, and by faults of NE direction that acted as paths of ore solution. The deposits of the Geumsan metallogenic zone are seemed to be formed through the similar process as that of Hwangangni metallogenic zone, but characteristic distinctions are in that they are more prevailing fracture filling veins and large number of the deposits are localized in roof-pendants or xenolithes of limestone in granites and porphyries. Igneous rocks that presumably motivated the mineraltzation are middle Cretaceous Geumsan granite and porphyries. Metallogenic epoch of the fluorite mineralization of South Korea are puesumably limited in early-middle Cretaceous. Studies of the fluid inclusions in fluorites of the region reveal that the homogenization temperature of the fluorite deposits are as follows: Hwacheon metallogenic zone : $95^{\circ}C{\sim}165^{\circ}C$; Hwangangni metallogenic zone : $97^{\circ}C{\sim}235^{\circ}C$; Geumsan metallogenic zone : $93^{\circ}C{\sim}236^{\circ}C$. Judging from the above results, the deposits of the Hwancheon region were formed at the epithermal stage, and those in the Hwangangni and Geumsan regions, were deposited at epithermal stage preceded by mesothermal mineralization of small scale in which some sulphide minerals were deposited. The analytical data of minor elements in the fluorites reveal that ore solutions of Hwangangni metallogenic zone seemed to be emanated in more acidic stage of magma differentiation than Hwacheon metallogenic zone did.

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Suitability evaluation of magnesium substituted biphasic calcium phosphates prepared by coprecipitation method (공침법을 이용한 마그네슘이 첨가된 biphasic calcium phosphate의 적합성 평가)

  • Lee, Hyoung-Sin;Kim, Tae-Wan;Kim, Dong-Hyun;Park, Hong-Chae;Yoon, Seog-Young
    • Journal of the Korean Crystal Growth and Crystal Technology
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    • v.20 no.5
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    • pp.237-242
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    • 2010
  • Magnesium-substituted BCP (biphasic calcium phosphate) powders were prepared by incorporating small amounts of magnesium into the structure of different hydroxyapatite (HAp)/${\beta}$-tricalcium phosphate (${\beta}$-TCP) ratios through coprecipitation method. A series of magnesium substitutions ranging from 0, 0.5, and 1.0 wt%, which are comparable to the measured magnesium contents, were performed. The obtained powders were characterized by the following analytical techniques: X-ray diffraction analysis (XRD), Thermo Gravimetric Analyzer (TGA) and Fourier transform infrared spectroscopy (FT-IR). The results have shown that substitution of magnesium in the calcium-deficient apatites resulted in the formation of biphasic mixtures of different HAP/${\beta}$-TCP ratios after heating above $1000^{\circ}C$. The 1.0 wt% magnesiumsubstituted-BCP were soaked in Hank's solutions after 2 weeks to observe the morphology of the biocement, especially needle-like hydroxyapatite crystals and to estimate the length and diameter of nanoneedle crystals.

Analysis Method for Non-Linear Finite Strain Consolidation for Soft Dredged Soil Deposit - Part II: Analysis Method and Craney Island Case Study (초연약 준설 매립지반의 비선형 유한변형 압밀해석기법 - Part II: 해석기법과 Craney Island 사례분석)

  • Choi, Hang-Seok;Kwak, Tae-Hoon;Lee, Chul-Ho;Lee, Dong-Seop;Stark, T.D.
    • Journal of the Korean Geotechnical Society
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    • v.27 no.11
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    • pp.5-15
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    • 2011
  • This paper presents two analysis methods for characterizing the non-linear finite strain consolidation behavior of highly deformable dredged soil deposits along with the fundamental parameters obtained in the companion paper; that is, the zero effective stress void ratio, the non-linear relationships of void ratio-effective stress and void ratio-hydraulic conductivity. The simplified Morris's analytical solution (2002) and the widely recognized numerical program, PSDDF (primary Consolidation, Secondary Compression, and Desiccation of Dredged Fill) for both single and double drainage conditions are adopted in this paper to verify a series of laboratory experiments for self-weight consolidation of the Incheon clay and Kaolinite. The comparisons show that the analysis methods proposed herein can properly simulate the long-term non-linear finite strain consolidation behavior for dredged soils in the field. In addition, a case study for the artificial Craney Island has been conducted to illustrate the importance of obtaining appropriate non-linear finite strain consolidation parameters and the applicability of PSDDF in promoting dredged soil disposal.

Parallel Computation on the Three-dimensional Electromagnetic Field by the Graph Partitioning and Multi-frontal Method (그래프 분할 및 다중 프론탈 기법에 의거한 3차원 전자기장의 병렬 해석)

  • Kang, Seung-Hoon;Song, Dong-Hyeon;Choi, JaeWon;Shin, SangJoon
    • Journal of the Korean Society for Aeronautical & Space Sciences
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    • v.50 no.12
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    • pp.889-898
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    • 2022
  • In this paper, parallel computing method on the three-dimensional electromagnetic field is proposed. The present electromagnetic scattering analysis is conducted based on the time-harmonic vector wave equation and the finite element method. The edge-based element and 2nd -order absorbing boundary condition are used. Parallelization of the elemental numerical integration and the matrix assemblage is accomplished by allocating the partitioned finite element subdomain for each processor. The graph partitioning library, METIS, is employed for the subdomain generation. The large sparse matrix computation is conducted by MUMPS, which is the parallel computing library based on the multi-frontal method. The accuracy of the present program is validated by the comparison against the Mie-series analytical solution and the results by ANSYS HFSS. In addition, the scalability is verified by measuring the speed-up in terms of the number of processors used. The present electromagnetic scattering analysis is performed for a perfect electric conductor sphere, isotropic/anisotropic dielectric sphere, and the missile configuration. The algorithm of the present program will be applied to the finite element and tearing method, aiming for the further extended parallel computing performance.

Numerical simulations on electrical resistivity survey to predict mixed ground ahead of a TBM tunnel (TBM 터널 전방 복합지반 예측을 위한 전기 비저항 탐사의 수치해석적 연구)

  • Seunghun Yang;Hangseok Choi;Kibeom Kwon;Chaemin Hwang;Minkyu Kang
    • Journal of Korean Tunnelling and Underground Space Association
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    • v.25 no.6
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    • pp.403-421
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    • 2023
  • As the number of underground structures has increased in recent decades, it has become crucial to predict geological hazards ahead of a tunnel face during tunnel construction. Consequently, this study developed a finite element (FE) numerical model to simulate electrical resistivity surveys in tunnel boring machine (TBM) operations for predicting mixed ground conditions in front of tunnel faces. The accuracy of the developed model was verified by comparing the numerical results not only with an analytical solution but also with experimental results. Using the developed model, a series of parametric studies were carried out to estimate the effect of geological conditions and sensor geometric configurations on electrical resistivity measurements. The results of these studies showed that both the interface slope and the difference in electrical resistivity between two different ground formations affect the patterns and variations in electrical resistivity observed during TBM excavation. Furthermore, it was revealed that selecting appropriate sensor spacing and optimizing the location of the electrode array were essential for enhancing the efficiency and accuracy of predictions related to mixed ground conditions. In conclusion, the developed model can serve as a powerful and reliable tool for predicting mixed ground conditions during TBM tunneling.