• Title, Summary, Keyword: condition number

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A Study on the Air Foil Journal Bearing Analysis with Perturbed Rarefaction Coefficients

  • Lee, Yong-Bok;Park, Dong-Jin;Kim, Chang-Ho;Jang, Gun-Hee
    • KSTLE International Journal
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    • v.7 no.2
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    • pp.27-34
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    • 2006
  • Knudsen number is the ratio of molecular mean free path versus mm thickness and the criterion to determine the flow form. When its value is lower than 0.01, the flow can be assumed to has no slip boundary condition. And in the case that the value is between 0.01 and 10, then the flow has slip boundary condition at both the adjacent walls. The condition of the air flow between the rotating journal and top foil in the air foil bearing is determined by the rotating speed and load, and the Knudsen number is also varied by those values. Because the molecular mean free path is variable to the pressure and temperature, more exact formulation is necessary to understand and analyze the flow regime. In this study, the analysis considering Knudsen number formulated with those variables (pressure, temperature and mm thickness) was executed. The approximate value was examined using the equation to confirm whether the flow has the slip or no-slip boundary condition. From the analytic investigation, it was decided to range approximately 0.01 to 1.0 and the flow can be supposed to have the slip boundary condition. Under the condition of the slip flow, the static characteristics of the air foil bearing were examined using modified Reynolds equations. The results were compared with those considering no slip condition. It shows that the slip condition makes the flow decelerates and the load carrying capacity decreases compared with no slip condition. And as the bearing number and eccentricity ratio increase, the load carrying capacity also increased at both the cases. From this result, it can be supposed that the bearing torque also increases. In the analysis of the dynamic characteristics, the perturbed Knudsen number was taken into consideration. Because the Knudsen number is expressed as the terms of each variable, the perturbed equation can be simply derived. The results of both cases considering and not considering Knudsen number were compared each other. In the case of the direct terms of the stiffness and damping coefficients, the difference between both cases was little and increased as the bearing number and eccentricity ratio increased. And the cross terms have less or more differences.

Multicollinarity in Logistic Regression

  • Jong-Han lee;Myung-Hoe Huh
    • Communications for Statistical Applications and Methods
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    • v.2 no.2
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    • pp.303-309
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    • 1995
  • Many measures to detect multicollinearity in linear regression have been proposed in statistics and numerical analysis literature. Among them, condition number and variance inflation factor(VIF) are most popular. In this study, we give new interpretations of condition number and VIF in linear regression, using geometry on the explanatory space. In the same line, we derive natural measures of condition number and VIF for logistic regression. These computer intensive measures can be easily extended to evaluate multicollinearity in generalized linear models.

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Extended Graetz Problem Including Axial Conduction and Viscous Dissipation in Microtube

  • Jeong Ho-Eyoul;Jeong Jae-Tack
    • Journal of Mechanical Science and Technology
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    • v.20 no.1
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    • pp.158-166
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    • 2006
  • Extended Graetz problem in microtube is analyzed by using eigenfunction expansion to solve the energy equation. For the eigenvalue problem we applied the shooting method and Galerkin method. The hydrodynamically isothermal developed flow is assumed to enter the microtube with uniform temperature or uniform heat flux boundary condition. The effects of velocity and temperature jump boundary condition on the microtube wall, axial conduction and viscous dissipation are included. From the temperature field obtained, the local Nusselt number distributions on the tube wall are obtained as the dimensionless parameters (Peclet number, Knudsen number, Brinkman number) vary. The fully developed Nusselt number for each boundary condition is obtained also in terms of these parameters.

The Product Formula For Nielsen Root number

  • Yang, Ki-Yeol
    • Communications of the Korean Mathematical Society
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    • v.15 no.2
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    • pp.357-370
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    • 2000
  • In [6], Cheng-Ye You gave a condition equivalent to the Nielsen number product formula for fiber maps. And Jerzy Jezierski also gave a similar condition for coincidences of fiber maps. The main purpose of this paper is to find the condition for which holds the product formula for Nielsen root numbers N(f;a) = N(f;a) N(fb;a).

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Effects of Characteristic Condition Number on Convergence in Calculating Low Mach Number Flows, I : Euler Equations (저속 유동 계산의 수렴성에 미치는 특성 조건수의 영향 I : 오일러 방정식)

  • Lee, Sang-Hyeon
    • Journal of the Korean Society for Aeronautical & Space Sciences
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    • v.36 no.2
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    • pp.115-122
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    • 2008
  • The effects of characteristic condition number on the convergence of preconditioned Euler equations were investigated. The two-dimensional preconditioned Euler equations adopting Choi and Merkle's preconditioning and the temperature preconditioning are considered. Preconditioned Roe's FDS scheme was adopted for spatial discretization and preconditioned LU-SGS scheme was used for time integration. It is shown that the convergence characteristics of the Euler equations are strongly affected by the characteristic condition number, and there is an optimal characteristic condition number for a problem. The optimal characteristic condition numbers for the Choi and Merkle's preconditioning and temperature preconditioning are different.

The influence of joints on compressive strength and deformation behavior of rock with a circular hole. (원형공을 갖는 암석의 압축강도 및 변형거동에 미치는 절리의 영향)

  • 조의권;김일중;김기주;김영석
    • Tunnel and Underground Space
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    • v.7 no.2
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    • pp.108-115
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    • 1997
  • Uniaxial and biaxial compressive tests were conducted on limestone specimens containing artificial joints and a circular hole to investigate the influence of inclination and number of joints on compressive strength and deformation behavior of rock with a circular hole. Under uniaxial and biaxial compressive condition, the inclination of joints showing the maximum and minimum strength were 0$^{\circ}$ and 30$^{\circ}$ respectively, which was independent of the number of joints. Under uniaxial compressive condition, relative maximum strength of rock with n=1 and 3 to intact rock with a circular hole were 12.5%~82.8% and 11.4~62.5% respectively, and under biaxial compressive condition, 18.2~91.0% and 17.0~87.5% respectively. The influence of the number of joints on the decrease of compressive strength was greater under uniaxial than under biaxial compressive condition. Under uniaxial and biaxial compressive condition, axial and lateral deformations of rock showed the least values where $\alpha$=30$^{\circ}$. Under uniaxial compressive condition, axial and lateral deformation at maximum strength of rock have the increasing tendency with increase the number of joints. But they have the decreasing tendency under biaxial compressive condition. Under uniaxial and biaxial compressive conditions, axial deformation of circular hole was greater than lateral deformation without respect to the number of joints and the inclination of joints.

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Numerical simulation and experimental investigation of the shear mechanical behaviors of non-persistent joint in new shear test condition

  • Wang, Dandan;Zhang, Guang;Sarfarazi, Vahab;Haeri, Hadi;Naderi, A.A.
    • Computers and Concrete
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    • v.26 no.3
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    • pp.239-255
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    • 2020
  • Experimental and discrete element method were used to investigate the effects of joint number and its angularities on the shear behaviour of joint's bridge area. A new shear test condition was used to model the gypsum cracks under shear loading. Gypsum samples with dimension of 120 mm×100 mm×50 mm were prepared. the length of joints was 2cm. in experimental tests, the joint number is 1, 2 and 3 and its angularities change from 0° to 90° with increment of 45°. Assuming a plane strain condition, special rectangular models are prepared with dimension of 120 mm×100 mm. similar to joints configuration in experimental test, 9 models with different joint number and joint angularities were prepared. This testing show that the failure process is mostly governed by the joint number and joint angularities. The shear strengths of the specimens are related to the fracture pattern and failure mechanism of the discontinuities. The shear behaviour of discontinuities is related to the number of induced tensile cracks which are increased by increasing the rock bridge length. The strength of samples decreases by increasing the joint number and joint angularities. Failure pattern and failure strength are similar in both of the experimental test and numerical simulation.

A study on the effect of the condition number in the magnetic field mapping of the Air-Core solenoid

  • Huang, Li;Lee, Sangjin
    • Progress in Superconductivity and Cryogenics
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    • v.17 no.2
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    • pp.31-35
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    • 2015
  • Mapping is a useful tool in the magnetic field analysis and design. In some specific research area, such as the nuclear magnetic resonance (NMR) or the magnetic resonance imaging (MRI), it is important to map the magnetic field in the interesting space with high accuracy. In this paper, an indirect mapping method in the center volume of an air-core solenoid is presented, based on the solution of the Laplace's equation for the field. Through the mathematical analysis on the mapping calculation, we know that the condition number of the matrix, generated by the measurement points, can greatly affect the error of mapping result. Two different arrangement methods of the measurement points in field mapping are described in this paper: helical cylindrical line (HCL) method and parallel cylindrical line (PCL) method. According to the condition number, the HCL method is recommended to measure the field components using one probe. As a simple example, we mapped the magnetic fields in a MRI main magnet system. Comparing the results in the different methods, it is feasible and convenient to apply the condition number to reduce the error in the field mapping calculation. Finally, some guidelines were presented for the magnetic field mapping in the center volume of the air-core solenoid.

Effects of Characteristic Condition Number on Convergence in Calculating Low Mach Number Flows, II : Navier-Stokes Equations (저속 유동 계산의 수렴성에 미치는 특성 조건수의 영향 II : 나비어스톡스 방정식)

  • Lee, Sang-Hyeon
    • Journal of the Korean Society for Aeronautical & Space Sciences
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    • v.36 no.2
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    • pp.123-130
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    • 2008
  • The effects of characteristic condition number on the convergence of preconditioned Navier-Stokes equations were investigated. The two-dimensional preconditioned Navier-Stokes adopting Choi and Merkle's preconditioning and the temperature preconditioning are considered. Preconditioned Roe's FDS scheme was adopted for spatial discretization and preconditioned LU-SGS scheme was used for time integration. It is shown that the convergence characteristics of the Navier-Stokes equations are strongly affected by the characteristic condition number. Also it is shown that the optimal characteristic condition numbers for viscous flows are larger than that in inviscid flows.