• Title, Summary, Keyword: analytic expression

Search Result 111, Processing Time 0.029 seconds

Validity of the Analytic Expression for the Temperature of Joule Heated Nano-wire

  • Ha, Seung-Seok;You, Chun-Yeol
    • Journal of Magnetics
    • /
    • v.12 no.1
    • /
    • pp.7-11
    • /
    • 2007
  • We confirm the validity of the analytic expression for the temperature of the Joule heated nano-wire [C.-Y. You et al. Appl. Phys. Lett. 89, 222513 (2006)] with finite element method. The temperature of the Joule heated nano-wire is essential information for the research of the current induced domain wall movement. The analytic expression includes an adjustable parameter which must be determined. Since the physical origin of the adjustable parameter is simplification of the heat source profile, the validity of the analytic expression must be examined for wide range of the nano-wire structure. By comparison with this analytic expression with the results of full numerical finite element method, the adjustable parameter has been determined. The numerically confirmed adjustable parameter values are in the range of 0.60$\sim$0.69, which is well matched with the theoretically expected one. Furthermore, it is found that the adjustable parameter is a slow varying function of the nano-wire geometry. Based on this numerical confirmation, we can apply the analytic expression for the wide range of the nano-wire geometry with proper adjustable parameters.

Analytic Expression of the Signal Distortion in Dispersion-Managed Optical Transmission (최적으로 색분산 보상된 광통신 시스템에서 신호 왜곡에 관한 근사적 수학식 연구)

  • Kim, Sung-Man
    • The Journal of the Korea institute of electronic communication sciences
    • /
    • v.8 no.8
    • /
    • pp.1235-1240
    • /
    • 2013
  • We investigate an approximate analytic expression of signal distortion caused by the interaction between self-phase modulation (SPM) and dispersion in the dispersion-managed optical transmission where the dispersion is optimally compensated. From the analytic study, we obtain the analytic expression of the signal distortion in dispersion-managed optical transmission system. To confirm the validity of the analytic expression, we show that the eye-opening penalties calculated by the analytic expression correspond with the simulation results. Using the analytic result, we can easily estimate the signal distortion without complex nonlinear simulations.

Theory of Diffusion-Influenced Bimolecular Reactions in Solution : Effects of a Stochastic Gating Mode

  • Kim Joohyun;Lee Sangyoub
    • Bulletin of the Korean Chemical Society
    • /
    • v.13 no.4
    • /
    • pp.398-404
    • /
    • 1992
  • We have investigated the kinetics of diffusion-influenced bimolecular reactions in which one reactant has an internal mode, called the gating mode, that activates or deactivates its reactivity intermittently. The rate law and an expression for the time-dependent rate coefficient have been obtained from the general formalism based on the hierarchy of kinetic equations involving reactant distribution functions. The analytic expression obtained for the steady-state reaction rate constant coincides with the one obtained by Szabo et al., who derived the expression by employing the conventional concentration-gradient approach. For the time-dependent reaction rate coefficient, we obtained for the first time an exact analytic expression in the Laplace domain which was then inverted numerically to give the time-domain results.

  • PDF

Molecular Reorientation of Oblate Symmetric Top Molecules with Internal Extended Rotational Diffusion

  • Shin, Kook-Joe Shin
    • Bulletin of the Korean Chemical Society
    • /
    • v.4 no.5
    • /
    • pp.228-230
    • /
    • 1983
  • Molecular reorientation of oblate symmetric top molecules with internal rotation is investigated theoretically and an analytic expression for the overall reorientational correlation time in terms of the internal angular momentum correlation time is derived. This expression is quite different from the expression for prolate symmetric top molecules but reduces to the same expression in the spherical top limit. Fast internal rotation is treated by a modified version of the extended rotational diffusion while the bulky symmetric top mainbody is treated by the rotational diffusion model.

  • PDF

A study on the analytic geometric characteristics of Archimedes' 《The Method》 and its educational implications (아르키메데스의 《The Method》의 해석기하학적 특성과 그 교육적 시사점에 대한 연구)

  • Park, Sun-Yong
    • Journal for History of Mathematics
    • /
    • v.27 no.4
    • /
    • pp.271-283
    • /
    • 2014
  • This study takes a look at Polya's analysis on Archimedes' "The Method" from a math-historical perspective. We, based on the elaboration of Polya's analysis, investigate the analytic geometric characteristics of Archimedes' "The Method" and discuss the way of using the characteristics in education of school calculus. So this study brings up the educational need of approach of teaching the definite integral by clearly disclosing the transition from length, area, volume etc into the length as an area function under a curve. And this study suggests the approach of teaching both merit and deficiency of the indivisibles method, and the educational necessity of making students realizing that the strength of analytic geometry lies in overcoming deficiency of the indivisibles method by dealing with the relation of variation and rate of change by means of algebraic expression and graph.

A Study on the Effectiveness of Dynamic Geometry Software in Solving High School Analytic Geometry Problems. (탐구형 소프트웨어를 활용한 고등학교 해석 기하 교육에 관한 사례 연구)

  • 황우형;차순규
    • The Mathematical Education
    • /
    • v.41 no.3
    • /
    • pp.341-360
    • /
    • 2002
  • The purpose of the study was to investigate the effectiveness of dynamic software in solving high school analytic geometry problems compared with traditional algebraic approach. Three high school students who have revealed high performance in mathematics were involved in this study. It was considered that they mastered the basic concepts of equations of plane figure and curves of secondary degree. The research questions for the study were the followings: 1) In what degree students understand relationship between geometric approach and algebraic approach in solving geometry problems? 2) What are the difficulties students encounter in the process of using the dynamic software? 3) In what degree the constructions of geometric figures help students to understand the mathematical concepts? 4) What are the effects of dynamic software in constructing analytic geometry concepts? 5) In what degree students have developed the images of algebraic concepts? According to the results of the study, it was revealed that mathematical connections between geometric approach and algebraic approach was complementary. And the students revealed more rely on the algebraic expression over geometric figures in the process of solving geometry problems. The conceptual images of algebraic expression were not developed fully, and they blamed it upon the current college entrance examination system.

  • PDF

A Model for AC Characteristics of GaAs MESFET's (GaAs MESFET의 AC특성 모델에 관한 연구)

  • 김창우;김홍배;곽계달
    • Journal of the Korean Institute of Telematics and Electronics
    • /
    • v.25 no.2
    • /
    • pp.196-203
    • /
    • 1988
  • A new analytic model for small-singnal circuit model of GaAs MESFET's is presented. This model is a charge model which considers the formation of a statioanary Gunn-domain and the transistion region that exists in the depletion region boundary. From this charge model the analytic expression of the equivalent circuit elements is derived, and the voltage dependences of each element are explained. The results of the calcualtion are in good agreement with experimental data.

  • PDF

ERROR BOUNDS FOR GAUSS-RADAU AND GAUSS-LOBATTO RULES OF ANALYTIC FUNCTIONS

  • Ko, Kwan-Pyo
    • Communications of the Korean Mathematical Society
    • /
    • v.12 no.3
    • /
    • pp.797-812
    • /
    • 1997
  • For analytic functions we give an expression for the kernel $K_n$ of the remainder terms for the Gauss-Radau and the Gauss-Lobatto rules with end points of multiplicity r and prove the convergence of the kernel we obtained. The error bound are obtained for the type $$\mid$R_n(f)$\mid$ \leq \frac{1}{\pi}l(\Gamma) max_{z \in \Gamma} $\mid$K_n(z)$\mid$ max_{z \in \Gamma} $\mid$f(z)$\mid$$, where $l(\Gamma)$ denotes the length of contour $\Gamma$.

  • PDF

Effect of surface bolt on the collapse mechanism of a shallow rectangular cavity

  • Huang, Fu;Zhao, Lian-heng;Zhang, Sheng
    • Geomechanics and Engineering
    • /
    • v.13 no.3
    • /
    • pp.505-515
    • /
    • 2017
  • Based on the collapse characteristics of a shallow rectangular cavity, a three-dimensional failure mechanism which can be used to study the collapsing region of the rock mass above a shallow cavity roof is constructed. Considering the effects of surcharge pressure and surface bolt on the collapsing block, the external rate of works produced by surcharge pressure and surface bolt are included in the energy dissipation calculation. Using variational approach, an analytic expression of surface equation for the collapsing block, which can be used to study the collapsing region of the rock mass above a shallow cavity roof, is derived in the framework of upper bound theorem. Based on the analytic expression of surface equation, the shape of the collapsing block for shallow cavity is drawn. Moreover, the changing law of the collapsing region for different parameters indicates that the collapsing region of rock mass decreases with the increase of the density of surface bolt. This conclusion can provide reference for practicing geotechnical engineers to achieve an optimal design of supporting structure for a shallow cavity.

The solar cell modeling using Lambert W-function (Lambert W 함수를 이용한 태양전지 모델링)

  • Bae, Jong-Guk;Kang, Gi-Hwan;Kim, Kyung-Soo;Yu, Gwon-Jong;Ahn, Hyung-Geun;Han, Deuk-Young
    • 한국태양에너지학회:학술대회논문집
    • /
    • /
    • pp.278-281
    • /
    • 2011
  • This system can predict the maximum output about all illumination levels so that the PV system designer can design the system having the best efficiency. For the output prediction exact about the solar cell, that is the device the basis most in the PV system, the basis has to be in order to try this way. The solution based on Lambert W-function are presented to express the transcendental current-voltage characteristic containing parasitic power consuming parameters like series and shunt resistances. A simple and efficient method for the extraction of a single current-voltage (I-V) curve under the constant illumination level is proposed. With the help of the Lambert W function, the explicit analytic expression for I is obtained. And the explicit analytic expression for V is obtained. This analytic expression is directly used to fit the experimental data and extract the device parameters. The I-V curve of the solar cell was expressed through the modeling using Lambert W-function and the numerical formula where there is the difficulty could be logarithmically expressed This method expresses with the I-V curve through the modeling using Lambert W-function which adds other loss ingredients to the equation2 as to the research afterward. And the solar cell goes as small and this I-V curve can predict the power penalty in the system unit.

  • PDF