• Title/Summary/Keyword: Non-linear Equation

Search Result 591, Processing Time 0.029 seconds

Compensation of Peak Expiratory Air Flow Rate Considering Initial Slope in Velocity Type Air Flow Transducer (속도계측형 호흡기류센서에서 상승시간을 고려한 최고호기유량의 교정 기법)

  • Cha, Eun-Jong;Lee, In-Kwang;Kim, Seong-Sik;Kim, Wan-Suk;Park, Kyung-Soon;Kim, Wun-Jae;Kim, Kyung-Ah
    • The Transactions of The Korean Institute of Electrical Engineers
    • /
    • v.58 no.4
    • /
    • pp.867-872
    • /
    • 2009
  • Peak expiratory flow rate(PEF) is one of the most important diagnostic parameters in spirometry. PEF occurs in a very short duration during the forced expiratory maneuver, which could lead to measurement error due to non-ideal dynamic characteristic of the transducer. In such case the initial slope of the flow rate signal determines the accuracy of the measured PEF. The present study considered this initial slope as a parameter to compensate PEF. The 26 standard flow rate signals recommended by the American Thoracic Society(ATS) were flown through the air flow transducer followed by simultaneous measurements of PEF and maximum transducer output$(N_{PEF})$. $N_{PEF}$-PEF satisfied a quadratic equation in general, however, two signals (ATS #2 and #26) having large initial slopes deviated from the fitting equation to a significant degree. The relative error was found to be in a linear relationship with the initial slope, thus, $N_{PEF}$ was appropriately compensated to provide accurate PEF with mean relative error less than only 1%. The 99% confidence interval of the mean relative error was less than a half of the error limit of 5% recommended by ATS. Therefore, PEF can be very accurately determined by compensating the transducer output based on the initial slope, which should be a useful technique for air flow transducer calibration.

A Parabolic Approximation Model for Wave Deformation Combined Refraction, Diffraction, and Breaking (파랑(波浪)의 굴절(屈折), 회절(回折) 및 쇄파변형(碎波變形)에 관한 포물형근사모형(抛物形近似模型))

  • Lee, Dong Soo;Lee, Jong Sup;Park, II Heum
    • KSCE Journal of Civil and Environmental Engineering Research
    • /
    • v.14 no.3
    • /
    • pp.619-633
    • /
    • 1994
  • A wave deformation model for general purpose combined refraction, diffraction, and breaking is developed in the shallow water. A parabolic approximation equation considered a higher order diffraction term is derived from the previous mild slope equation. A wave energy dissipation term due to bottom friction and breaking is introduced from the turbulence model. The Crank-Nicoloson implicit scheme is used in the numerical calculation, then the solutions are compared with the various hydraulic experiment data in the circular, the elliptic shoal, and the surf zone. The wave height decay in the surf zone is sensitively affected by the incident wave steepness, and the wave height variation around the elliptic shoal is well explained by the non-linear dispersion relation and the wave energy dissipation term. The model is also applied to a field coastal area and reasonable results are obtained.

  • PDF

Finite Element Analysis of Unbalance Response of a High Speed Flexible Polygon Mirror Scanner Motor Considering the Flexibility of Supporting Structure (지지구조의 유연성을 고려한 고속 유연 폴리곤 미러 스캐너 모터의 유한 요소 불평형 응답 해석)

  • Jung, Kyung-Moon;Seo, Chan-Hee;Kim, Myung-Gyu;Jang, Gun-Hee
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
    • /
    • 2007.05a
    • /
    • pp.859-865
    • /
    • 2007
  • This paper presents a method to analyze the unbalance response of a high speed polygon mirror scanner motor supported by sintered bearing and flexible supporting structures by using the finite element method and the mode superposition method. The appropriate finite element equations for polygon mirror are described by rotating annular sector element using Kirchhoff plate theory and von Karman non-linear strain, and its rigid body motion is also considered. The rotating components except for the polygon mirror are modeled by Timoshenko beam element including the gyroscopic effect. The flexible supporting structures are modeled by using a 4-node tetrahedron element and 4-node shell element with rotational degrees of freedom. Finite element equations of each component of the polygon mirror scanner motor and the flexible supporting structures are consistently derived by satisfying the geometric compatibility in the internal boundary between each component. The rigid link constraints are also imposed at the interface area between sleeve and sintered bearing to describe the physical motion at this interface. A global matrix equation obtained by assembling the finite element equations of each substructure is transformed to a state-space matrix-vector equation, and both damped natural frequencies and modal damping ratios are calculated by solving the associated eigenvalue problem by using the restarted Arnoldi iteration method. Unbalance responses in time and frequency domain are performed by superposing the eigenvalues and eigenvectors from the free vibration analysis. The validity of the proposed method is verified by comparing the simulated unbalance response with the experimental results. This research also shows that the flexibility of supporting structures plays an important role in determining the unbalance response of the polygon mirror scanner motor.

  • PDF

Biodegradation Kinetics of Diesel in a Wind-driven Bioventing System

  • Liu, Min-Hsin;Tsai, Cyuan-Fu;Chen, Bo-Yan
    • Journal of Soil and Groundwater Environment
    • /
    • v.21 no.5
    • /
    • pp.8-15
    • /
    • 2016
  • Bioremediation, which uses microbes to degrade most organic pollutants in soil and groundwater, can be used in solving environmental issues in various polluted sites. In this research, a wind-driven bioventing system is built to degrade about 20,000 mg/kg of high concentration diesel pollutants in soil-pollution mode. The wind-driven bioventing test was proceeded by the bioaugmentation method, and the indigenous microbes used were Bacillus cereus, Achromobacter xylosoxidans, and Pseudomonas putida. The phenomenon of two-stage diesel degradation of different rates was noted in the test. In order to interpret the results of the mode test, three microbes were used to degrade diesel pollutants of same high concentration in separated aerated batch-mixing vessels. The data derived thereof was input into the Haldane equation and calculated by non-linear regression analysis and trial-and-error methods to establish the kinetic parameters of these three microbes in bioventing diesel degradation. The results show that in the derivation of μm (maximum specific growth rate) in biodegradation kinetics parameters, Ks (half-saturation constant) for diesel substance affinity, and Ki (inhibition coefficient) for the adaptability of high concentration diesel degradation. The Ks is the lowest in the trend of the first stage degradation of Bacillus cereus in a high diesel concentration, whereas Ki is the highest, denoting that Bacillus cereus has the best adaptability in a high diesel concentration and is the most efficient in diesel substance affinity. All three microbes have a degradation rate of over 50% with regards to Pristane and Phytane, which are branched alkanes and the most important biological markers.

Preliminary Survey of Age and Growth of the Short-necked Clam, Paphia undalate(Born), in Kwangyang Bay, Korea (광양만에 분포하는 농조개, Paphia undalata (Born)의 연령과 성장에 관한 기초연구)

  • 김영혜;장대수;박영철
    • The Korean Journal of Malacology
    • /
    • v.17 no.1
    • /
    • pp.7-12
    • /
    • 2001
  • The age and growth of the short-necked clam, Paphia undalata, was investigated from 546 samples randomly collected in December 2000 in Kwangyang Bay, Korea. Ages were determined from ring radius of shell and the maximum age was observed to be 2 years. The relationship between shell length (SL) and shell height (SH) of Paphia undalata was SL = 0.2105 + 1.7569 $\times$ SH ($R^2$= 0.98), and the shell length (SL)-total weight (TW) relationship was TW = 2.5824 $\times$ 10$^{-4}$ $\times$ S $L^{2.6769}$ ($R^2$= 0.92). The von Bertalanffy growth parameters were estimated by the non-linear method, with values as follows: $L_{\infty}$ = 81.46 mm, K : 0.20/year, $t_{0}$ = -1.19 year. The von Bertalnanffy growth equation was $L_{t}$ = 81.46(1- $e^{-0}$.20(t+1.19)/), $W_{t}$ = 33.68(1- $e^{-0}$.20(t+1.19)/)$^{2.6769}$.

  • PDF

Symbolic computation and differential quadrature method - A boon to engineering analysis

  • Rajasekaran, S.
    • Structural Engineering and Mechanics
    • /
    • v.27 no.6
    • /
    • pp.713-739
    • /
    • 2007
  • Nowadays computers can perform symbolic computations in addition to mere number crunching operations for which they were originally designed. Symbolic computation opens up exciting possibilities in Structural Mechanics and engineering. Classical areas have been increasingly neglected due to the advent of computers as well as general purpose finite element software. But now, classical analysis has reemerged as an attractive computer option due to the capabilities of symbolic computation. The repetitive cycles of simultaneous - equation sets required by the finite element technique can be eliminated by solving a single set in symbolic form, thus generating a truly closed-form solution. This consequently saves in data preparation, storage and execution time. The power of Symbolic computation is demonstrated by six examples by applying symbolic computation 1) to solve coupled shear wall 2) to generate beam element matrices 3) to find the natural frequency of a shear frame using transfer matrix method 4) to find the stresses of a plate subjected to in-plane loading using Levy's approach 5) to draw the influence surface for deflection of an isotropic plate simply supported on all sides 6) to get dynamic equilibrium equations from Lagrange equation. This paper also presents yet another computationally efficient and accurate numerical method which is based on the concept of derivative of a function expressed as a weighted linear sum of the function values at all the mesh points. Again this method is applied to solve the problems of 1) coupled shear wall 2) lateral buckling of thin-walled beams due to moment gradient 3) buckling of a column and 4) static and buckling analysis of circular plates of uniform or non-uniform thickness. The numerical results obtained are compared with those available in existing literature in order to verify their accuracy.

Development of Curve Fitted Equation about Dynamic Response Analysis of a Buried Concrete Pipelines (콘크리트 매설관의 동적응답해석에 대한 곡선적합식의 개발)

  • Jeong Jin-Ho;Kim Sung-Ban;Ahn Myung-Seok
    • Explosives and Blasting
    • /
    • v.24 no.1
    • /
    • pp.9-19
    • /
    • 2006
  • The objective of this study is to propose curve fitted equations that can facilitate calculations and improve a practical applicability when the seismic performance of buried pipelines needs to be evaluated. The curve fitted equations are derived based on the evaluation of the dynamic responses of concrete pipe with a boundary condition of fixed-free ends. To study the dynamic response of underground pipe, the numerical analysis program developed in the previous research has been used. The location of maximum strain has been determined through dynamic analyses for a boundary condition of fixed-free ends. Then $wavelength{\lambda}$ of 5-1000(m) and propagation velocity(Vs) of 100-2000(m/s) have been applied at the location of maximum strain and the unit srain curve with the changes of the $wavelength{\lambda}$ and propagation velocity(Vs) has been obtaind. Non-linear least-square regression has been used to develop highly applicable curve fitted equations and various types of exponential regression equations have been checked out. Thus curve fitted equations and necessary coefficients with best results are suggested.

Molting and Growth of the Snow Crab Chionoecetes opilio in the East Sea of Korea (한국 동해안 대게, Chionoecetes opilio의 탈피와 성장)

  • Chun, Young-Yull;Lee, Sung-Il;Yoon, Sang-Chul;Cha, Hyung-Kee;Kim, Jong-Bin
    • Korean Journal of Fisheries and Aquatic Sciences
    • /
    • v.42 no.4
    • /
    • pp.380-386
    • /
    • 2009
  • Molting and growth of the snow crab, Chionoecetes opilio was investigated using samples captured in the East Sea from July 2002 to June 2004. Individuals over 40 mm carapace width (CW) molted once a year from July to October. Annual molt stage of C. opilio can be divided into four stages; premolt stage, molting stage, postmolt stage and intennolt stage. The relationship between CW and chela height (CH) can be expressed as Y=-82lnCW+73.1129lnCH+166. They were separated into two groups based on the equation, that is, one group having a negative value (below 70 mm in CW) and other group having a positive value (over 130 mm in CW). Carapace width at 50% terminal molt ($CW_{50%}$) of males was estimated to be 105 mm. The Gompertz growth equation estimated from a non-linear method was $CW=118.99e^{-6.296e^{-0.3062t}}$ for females and $CW=156368e^{-6.6619e^{-0.2626t}}$ for males.

Iterative Cumulant Moment Method for solution of Boltzmann Equation and its Application to Shock Wave Structure (반복적 Cumulant 모멘트 방법에 의한 Boltzmann 방정식의 해법과 충격파구조에 관한 연구)

  • Ohr, Young Gie
    • Journal of the Korean Chemical Society
    • /
    • v.42 no.4
    • /
    • pp.398-410
    • /
    • 1998
  • For non-linear solution of the Boltzmann equation, the cumulant moment method has been studied. To apply the method to the normal shock wave problem, we restricted ourselves to the monatomic Maxwell molecular gases. The method is based on the iterative approach developed by Maxwell-Ikenberry-Truesdell (MIT). The original MIT approach employs the equilibrium distribution function for the initial values in beginning the iteration. In the present work, we use the Mott-Smith bimodal distribution function to calculate the initial values and follow the MIT iteration procedure. Calculations have been carried out up to the second iteration for the profiles of density, temperature, stress, heat flux, and shock thickness of strong shocks, including the weak shock thickness of Mach range less than 1.4. The first iteration gives a simple analytic expression for the shock profile, and the weak shock thickness limiting law which is in exact accord with the Navier-Stokes theory. The second iteration shows that the calculated strong shock profiles are consistent with the Monte Carlo values quantitatively.

  • PDF

Autoignition Characteristics of Limonene - Expanded Polystyrene Mixture (Limonene - Expanded Polystyrene 혼합물의 자연발화 특성)

  • 송영호;하동명;정국삼
    • Fire Science and Engineering
    • /
    • v.18 no.1
    • /
    • pp.1-6
    • /
    • 2004
  • In the reutilization process using limonene, the organic solvent to reduce volume of EPS, the AIT was measured with the variation of concentration and volume of mixture, in order to present the fund-mental data on the fire hazard assessment of limonene - EPS mixture at storage and handling. And ignition zone was compared with non-ignition zone. The equation related to AIT, activation energy and ignition delay time, used by the most scientific basis for predicting AIT values, was suggested using linear regression analysis as ln t = 0.704/T-5.819. And the equation related to concentration of mixture and AIT was also suggested to predict ignition hazard of combustible mixture using nonlinear regression analysis as $T_m/=248.32+69.27X+172.60X^2$. It enabled to predict ignition temperature according to variation of ignition delay time and concentration of mixture by the suggested equations.