• Title/Summary/Keyword: linear approximation

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Envelope-Function Equation and Motion of Wave Packet in a Semiconductor Superlattice Structure

  • Kim, Byoung-Whi;Jun, Young-Il;Jung, Hee-Bum
    • ETRI Journal
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    • v.21 no.1
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    • pp.1-27
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    • 1999
  • We present a new description of envelope-function equation of the superlattice (SL). The SL wave function and corresponding effective-mass equation are formulated in terms of a linear combination of Bloch states of the constituent material with smaller band gap. In this envelope-function formalism, we review the fundamental concept on the motion of a wave packet in the SL structure subjected to steady and uniform electric fields F. The review confirms that the average of SL crystal momentums K = ($k_x,k_y,q$), where ($K_x,k_y$) are bulk inplane wave vectors and q SL wave vector, included in a wave packet satisfies the equation of motion = $_0+Ft/h$; and that the velocity and acceleration theorems provide the same type of group velocity and definition of the effective mass tensor, respectively, as in the Bulk. Finally, Schlosser and Marcus's method for the band theory of metals has been by Altarelli to include the interface-matching condition in the variational calculation for the SL structure in the multi-band envelope-function approximation. We re-examine this procedure more thoroughly and present variational equations in both general and reduced forms for SLs, which agrees in form with the proposed envelope-function formalism. As an illustration of the application of the present work and also for a brief investigation of effects of band-parameter difference on the subband energy structure, we calculate by the proposed variational method energies of non-strained $GaAs/Al_{0.32}Ga_{0.68}As$ and strained $In_{0.63}Ga_{0.37}As/In_{0.73}Ga_{0.27}As_{0.58}P_{0.42}SLs$ with well/barrier widths of $60{\AA}/500{\AA}$ and 30${\AA}/30{\AA}$, respectively.

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A Method for Thresholding and Correction of Skew in Camera Document Images (카메라 문서 영상의 이진화 및 기울어짐 보정 방법)

  • Jang Dae-Geun;Chun Byung-Tae
    • Journal of the Korea Society of Computer and Information
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    • v.10 no.3 s.35
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    • pp.143-150
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    • 2005
  • Camera image is very sensitive to illumination that result in difficulties for recognizing character. Also Camera captured document images have not only skew but also vignetting effect and geometric distortion. Vignetting effect make it difficult to separate characters from the document images. Geometric distortion, occurred by the mismatch of angle and center position between the document image and the camera, make the shape of characters to be distorted, so that the character recognition is more difficult than the case of using scanner. In this paper, we propose a method that can increase the performance of character recognition by correcting the geometric distortion of document images using a linear approximation which changes the quadrilateral region to the rectangle one. The proposed method also determine the quadrilateral transform region automatically, using the alignment of character lines and the skewed angles of characters located in the edges of each character line. Proposed method, therefore, can correct the geometric distortion without getting positional information from camera.

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Stability Analysis of Limit Cycles on Continuous-time Cyclic Connection Neural Networks (연속시간 모델 순환결합형 신경회로망에서의 리미트사이클의 안정성 해석)

  • Park, Cheol-Young
    • Journal of the Korean Institute of Intelligent Systems
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    • v.16 no.2
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    • pp.179-184
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    • 2006
  • An intuitive understanding of the dynamic pattern generation in asymmetric networks may be considered an essential component in developing models for the dynamic information processing. It has been reported that the neural network with cyclic connections generates multiple limit cycles. The dynamics of discrete time network with cyclic connections has been investigated intensively. However, the dynamics of a cyclic connection neural network in continuous-time has not been well-known due to the considerable complexity involved in its calculation. In this paper, the dynamic behavior of a continuous-time cyclic connection neural network, in which each neuron is connected only to its nearest neurons with binary synaptic weights of ${\pm}1$, has been investigated. Furthermore, the dynamics and stability of the network have been analyzed using a piece-wise linear approximation.

Numerical Integration based on Harmonic Oscillation and Jacobi Iteration for Efficient Simulation of Soft Objects with GPU (GPU를 활용한 고성능 연체 객체 시뮬레이션을 위한 조화진동 모델과 야코비 반복법 기반 수치 적분 기술)

  • Kang, Young-Min
    • Journal of Korea Game Society
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    • v.18 no.5
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    • pp.123-132
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    • 2018
  • Various methods have been proposed to efficiently animate the motion of soft objects in realtime. In order to maintain the topology between the elements of the objects, it is required to employ constraint forces, which limit the size of the time steps for the numerical integration and reduce the efficiency. To tackle this, an implicit method with larger steps was proposed. However, the method is, in essence, a linear system with a large matrix, of which solution requires heavy computations. Several approximate methods have been proposed, but the approximation is obtained with an increased damping and the loss of accuracy. In this paper, new integration method based on harmonic oscillation with better stability was proposed, and it was further stabilized with the hybridization with approximate implicit method. GPU parallelism can be easily implemented for the method, and large-scale soft objects can be simulated in realtime.

A Study on Calculation of RCS Using MUSIC Algorithm (MUSIC 알고리즘에 의한 레이더 반사단면적 계산법에 관한 연구)

  • Pang Tian Ting;Jeong Jung-Sik;Park Sung-Hyeon;Nam Taek-Kun;Yim Jeong-Bin;Aim Young-sup
    • Proceedings of the Korean Institute of Navigation and Port Research Conference
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    • 2005.10a
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    • pp.43-46
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    • 2005
  • The detectability of radar depends on RCS(radar cross section). The RCS for complex radar targets may be only approximately calculated by using low-frequency or high-frequency scattering methods, while the RCS for simple rob targets can be exactly obtained by applying an eigen-function method. However, the conventional methods for calculation of RCS are computationally complex. We propose an approximation method for RCS calculation by MUSIC algorithm In this research, it is assumed toot the radar target is considered as a ring of scatterers. The amplitudes of scatterers may be statistically distributed. As the result, the radar signal model is proposed to use MUSIC, and the RCS is calculated by a simple linear algebraic method.

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Fuzzy Modeling and Fuzzy Rule Generation in Global Approximate Response Surfaces (전역근사화 반응표면의 생성을 위한 퍼지모델링 및 퍼지규칙의 생성)

  • Lee, Jong-Soo;Hwang, Jeong-Su
    • Journal of the Korean Institute of Intelligent Systems
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    • v.12 no.3
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    • pp.231-238
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    • 2002
  • As a modeling method where the merits of fuzzy inference system and evolutionary computation are put together, evolutionary fuzzy modeling performs global approximate optimization. The paper proposes fuzzy clustering as fuzzy rule generation process which is one of the most important steps in evolutionary fuzzy modeling. With application of fuzzy clustering into the experiment or simulation results, fuzzy rules which properly describe non-linear and complex design problem can be obtained. The efficiency of evolutionary fuzzy modeling can be improved utilizing the membership degrees of data to clusters from the results of fuzzy clustering. To ensure the validity of the proposed method, the real design problem of an automotive inner trim is applied and the global approximation is achieved. Evolutionary fuzzy modeling is performed for several cases which differ in the number of clusters and the criterion of rule selection and their results are compared to prove that the proposed method can provide proper fuzzy rules for a given system and reduce computation time while maintaining the errors of modeling as a satisfactory level.

Pedagogical Implications for Teaching and Learning Normal Distribution Curves with CAS Calculator in High School Mathematics (CAS 계산기를 활용한 고등학교 정규분포곡선의 교수-학습을 위한 시사점 탐구)

  • Cho, Cheong-Soo
    • Communications of Mathematical Education
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    • v.24 no.1
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    • pp.177-193
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    • 2010
  • The purpose of this study is to explore normal distribution in probability distributions of the area of statistics in high school mathematics. To do this these contents such as approximation of normal distribution from binomial distribution, investigation of normal distribution curve and the area under its curve through the method of Monte Carlo, linear transformations of normal distribution curve, and various types of normal distribution curves are explored with CAS calculator. It will not be ablt to be attained for the objectives suggested the area of probability distribution in a paper-and-pencil classroom environment from the perspectives of tools of CAS calculator such as trivialization, experimentation, visualization, and concentration. Thus, this study is to explore various properties of normal distribution curve with CAS calculator and derive from pedagogical implications of teaching and learning normal distribution curve.

An analytic solution for the stirling engines with saw-toothed piston motions in adiabatic cylinders (단열실린더내에서 톱날파형 피스톤운동을 하는 스터링기관에 대한 해석적인 해)

  • 유호선
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.12 no.5
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    • pp.1197-1205
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    • 1988
  • An analytical method to predict qualitative performance characteristics of the Stirling Engines in the preliminary design stages is investigated. Both the expansion and the compression cylinder are treated as adiabatic and piston motions are approximated as saw-toothed waves. Basic equations which were originally proposed by Finkelstein consist of mass conservation and energy balances for each adiabatic cylinder. The approximation on piston motions and physical conditions make it possible to divide an engine cycle into four fundamental processes. In each process, first, pressure can be expressed as a function of the crank angle by solving a nonlinear first order ordinary differential equation and other thermodynamic variables are determined in turn. Application of the cyclic steady condition to the whole processes can complete a cycle. Also, further analysis results in analytic expressions for cyclic work and heat transfer in terms of the engine parameters and thermodynamic variables at boundary points. The results are expected useful as a quick reference for the engine performances. Finally, the present method can be applied to the other adiabatic analyses on the Stirling Engines with piece wise linear piston motions, if mass variations are predictable.

A Terrain Surface Approximation Using the Hermite Function (Hermite함수를 이용한 지형곡면근사)

  • 문두열;정범석;이용희
    • Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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    • v.20 no.3
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    • pp.265-272
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    • 2002
  • By this time, many methods have been developed for computing the pit excavation volumes, ranging from a simple formula to more complicated numerical methods. Earlier the standard methods for pit excavation volume computation requires that the considered area be divided the boundary ranges of x and y directions into a rectangular grid. whereas these methods may not calculate the estimation of pit excavation volume that is often required in many surveying situation exactly. In Easa methods(1998), the rectangular grid is divided into the same linear in the range x and y directions respectively. This method employs a cubic Hermite polynomial for individual intervals in both directions of the grid. Because the height data over the same boundary of x and y interval ranges have to be exist, it is not possible to choose the governing points of the terrain boundary such as points of maximum and minimum height. In this study, a method of volume computation, that combines the advantages of Easa methods(1998) and avoids the drawbacks of it, is presented. The proposed method employs a cubic Hermite polynomial for individual intervals in both directions of the non-grid, the all over intervals of it may be unequal grid x in width and y in length y, partially. The new proposed method should produce better accuracy than the other conventional methods.

Mesh Simplification Algorithm Using Differential Error Metric (미분 오차 척도를 이용한 메쉬 간략화 알고리즘)

  • 김수균;김선정;김창헌
    • Journal of KIISE:Computer Systems and Theory
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    • v.31 no.5_6
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    • pp.288-296
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    • 2004
  • This paper proposes a new mesh simplification algorithm using differential error metric. Many simplification algorithms make use of a distance error metric, but it is hard to measure an accurate geometric error for the high-curvature region even though it has a small distance error measured in distance error metric. This paper proposes a new differential error metric that results in unifying a distance metric and its first and second order differentials, which become tangent vector and curvature metric. Since discrete surfaces may be considered as piecewise linear approximation of unknown smooth surfaces, theses differentials can be estimated and we can construct new concept of differential error metric for discrete surfaces with them. For our simplification algorithm based on iterative edge collapses, this differential error metric can assign the new vertex position maintaining the geometry of an original appearance. In this paper, we clearly show that our simplified results have better quality and smaller geometry error than others.