Theoretical Analysis of Pneumatic Instability of Externally Pressurized Porous Gas Journal Bearings Considering Velocity Slip

1988 ◽  
Vol 110 (4) ◽  
pp. 730-733 ◽  
Author(s):  
M. C. Majumder ◽  
B. C. Majumdar
Keyword(s):  
Perturbation Theory ◽  
Theoretical Analysis ◽  
Mass Parameter ◽  
Velocity Slip ◽  
Journal Bearings ◽  
Order Perturbation ◽  
Rigid Rotor ◽  
First Order ◽  
First Order Perturbation

An analysis based on first-order perturbation theory is presented for the determination of pneumatic instability of a rigid rotor supported on externally pressurized porous gas journal bearings considering velocity slip. The variation of threshold mass parameter with feeding parameter for various supply pressures and L/D ratios under slip and no slip conditions is shown. It has been observed that there is a little decrease in stability when slip is taken in the analysis.

Analysis of Pneumatic Instability of Externally Pressurized Porous Gas Journal Bearings

1979 ◽  
Vol 101 (1) ◽  
pp. 48-53 ◽  
Author(s):  
N. S. Rao ◽  
B. C. Majumdar
Keyword(s):  
Theoretical Analysis ◽  
Mass Parameter ◽  
Journal Bearings ◽  
Order Perturbation ◽  
Rigid Rotor ◽  
Eccentricity Ratio ◽  
Dynamic Displacement ◽  
First Order ◽  
Supply Pressure ◽  
First Order Perturbation

A theoretical analysis is presented for the study of pneumatic instability for a rigid rotor supported in externally pressurized porous gas journal bearings. The analysis is based on a first-order perturbation with respect to the amplitude of dynamic displacement of rotor. The variation of threshold mass parameter with feeding parameter is shown. In addition, the effects of supply pressure, eccentricity ratio, L/D ratio, and porosity parameter are investigated and presented in the form of graphs.

Note on Interference Effects in Two-Step Reaction Processes

1975 ◽  
Vol 53 (23) ◽  
pp. 2590-2592
Author(s):  
J. Cejpek ◽  
J. Dobeš
Keyword(s):  
Perturbation Theory ◽  
Point Of View ◽  
Order Perturbation ◽  
Interference Effects ◽  
Qualitative Explanation ◽  
First Order ◽  
One Step ◽  
Step Transition ◽  
Reaction Processes ◽  
First Order Perturbation

The reaction processes in which a one-step transition is forbidden are analyzed from the point of view of the first order perturbation theory. The interference between two competing two-step reaction paths is found to be always constructive. A qualitative explanation of the experimentally observed reaction intensities is presented.

scholarly journals Low-degree mixed modes in red giant stars with moderate core magnetic fields

2019 ◽  
Author(s):  
Shyeh Tjing Loi ◽  
John C B Papaloizou
Keyword(s):  
Magnetic Field ◽  
Perturbation Theory ◽  
Magnetic Fields ◽  
Differential Equations ◽  
Order Perturbation ◽  
First Order ◽  
Low Degree ◽  
Mixed Modes ◽  
The Magnetic Field ◽  
First Order Perturbation

Abstract Observations of pressure-gravity mixed modes, combined with a theoretical framework for understanding mode formation, can yield a wealth of information about deep stellar interiors. In this paper, we seek to develop a formalism for treating the effects of deeply buried core magnetic fields on mixed modes in evolved stars, where the fields are moderate, i.e. not strong enough to disrupt wave propagation, but where they may be too strong for non-degenerate first-order perturbation theory to be applied. The magnetic field is incorporated in a way that avoids having to use this. Inclusion of the Lorentz force term is shown to yield a system of differential equations that allows for the magnetically-affected eigenfunctions to be computed from scratch, rather than following the approach of first-order perturbation theory. For sufficiently weak fields, coupling between different spherical harmonics can be neglected, allowing for reduction to a second-order system of ordinary differential equations akin to the usual oscillation equations that can be solved analogously. We derive expressions for (i) the mixed-mode quantisation condition in the presence of a field and (ii) the frequency shift associated with the magnetic field. In addition, for modes of low degree we uncover an extra offset term in the quantisation condition that is sensitive to properties of the evanescent zone. These expressions may be inverted to extract information about the stellar structure and magnetic field from observational data.

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