A note on the first order perturbation solution of a straight crack with slightly branched and curved extension under a general geometric and loading condition

1986 ◽  
Vol 24 (3) ◽  
pp. 479-481 ◽  
Author(s):  
Y. Sumi
Keyword(s):  
Loading Condition ◽  
Perturbation Solution ◽  
Order Perturbation ◽  
Straight Crack ◽  
First Order ◽  
First Order Perturbation

An Improved Analytical Solution for Self-Acting, Gas-Lubricated Journal Bearings of Finite Length

1961 ◽  
Vol 83 (2) ◽  
pp. 188-192 ◽  
Author(s):  
J. S. Ausman
Keyword(s):  
Analytical Solution ◽  
Finite Length ◽  
Load Capacity ◽  
Journal Bearings ◽  
Perturbation Solution ◽  
Order Perturbation ◽  
Small Eccentricity ◽  
First Order ◽  
Bearing Load ◽  
First Order Perturbation

An improved analytical solution designated the “linearized ph” solution is obtained for gas-lubricated journal bearings of finite length. Whereas the older first-order perturbation solution is useful for small eccentricity ratios (ε < 1/2), the linearized ph solution may be used for high eccentricity ratios. As such it permits estimation of ultimate bearing load capacity. The linearized ph solution is expressed in the form of simple corrections to the first-order perturbation solution, and as such can be computed quickly and easily.

scholarly journals Perturbation Solution for Four-Stream Infrared Radiative Transfer

2020 ◽  
Vol 77 (4) ◽  
pp. 1497-1507
Author(s):  
Jiangnan Li ◽  
Howard W. Barker
Keyword(s):  
Radiative Transfer ◽  
Perturbation Method ◽  
Zero Order ◽  
Perturbation Solution ◽  
Order Perturbation ◽  
Dual Wavelength ◽  
Perturbation Equation ◽  
First Order ◽  
Using Data ◽  
First Order Perturbation

Abstract A four-stream solution of the longwave radiative transfer is proposed. It is based on the exact perturbation method utilizing the absorption approximation equation as the zero-order solution. Scattering is handled by the first-order perturbation equation. The two- and four-stream approximations are compared both offline and using data from CALIPSO’s dual-wavelength lidar.

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