On the Stability of Plane Parallel Flow Between Differentially Heated, Tilted Planes

1974 ◽  
Vol 41 (3) ◽  
pp. 554-556 ◽  
Author(s):  
P. S. Ayyaswamy
Keyword(s):  
Stability Limit ◽  
Parallel Flow ◽  
Energy Stability ◽  
Interesting Application ◽  
Plane Parallel ◽  
The Stability

The linear and energy theories of stability of a plane parallel, antisymmetric flow between differentially heated, tilted planes are examined. The linear and energy results do not coincide indicating that subcritical motion may be possible. Also, it is seen that the energy stability limit corresponds to solutions independent of the coordinate in the direction of the flow. An interesting application of Busse’s theorem in this context is demonstrated.

The stability of parallel flow of a multi-component plasma

1980 ◽  
Vol 24 (2) ◽  
pp. 251-264 ◽  
Author(s):  
R. J. Lucas
Keyword(s):  
Gravitational Field ◽  
Sufficient Conditions ◽  
Parallel Flow ◽  
Liapunov Functional ◽  
Multicomponent Plasma ◽  
Plane Parallel ◽  
External Gravitational Field ◽  
Component Plasma ◽  
The Stability ◽  
System Variables

A Liapunov functional is constructed for the plane parallel flow of a multicomponent plasma in an external gravitational field. Sufficient conditions for stability to electrostatic perturbations are obtained. The L2-norms of certain system variables are shown to be bounded uniformly in time.

On the stability of homogeneous orientation in the plane-parallel cell of a liquid crystal doped with nanoparticles

2014 ◽  
Vol 49 (5) ◽  
pp. 196-201 ◽  
Author(s):  
M. R. Hakobyan ◽  
A. A. Ghandevosyan ◽  
R. S. Hakobyan ◽  
Yu. S. Chilingaryan
Keyword(s):  
Liquid Crystal ◽  
Plane Parallel ◽  
The Stability

Optimization of the Robust Stability Limit for Multi-Cutter Turning Processes

2015 ◽  
Author(s):  
Marta J. Reith ◽  
Daniel Bachrathy ◽  
Gabor Stepan
Keyword(s):  
Robust Stability ◽  
Optimal Parameter ◽  
Stability Limit ◽  
Boundary Function ◽  
Lower Envelope ◽  
Computation Method ◽  
Parameter Region ◽  
Dynamical Parameters ◽  
The Stability ◽  
Machining Parameter

Multi-cutter turning systems bear huge potential in increasing cutting performance. In this study we show that the stable parameter region can be extended by the optimal tuning of system parameters. The optimal parameter regions can be identified by means of stability charts. Since the stability boundaries are highly sensitive to the dynamical parameters of the machine tool, the reliable exploitation of the so-called stability pockets is limited. Still, the lower envelope of the stability lobes is an appropriate upper boundary function for optimization purposes with an objective function taken for maximal material removal rates. This lower envelope is computed by the Robust Stability Computation method presented in the paper. It is shown in this study, that according to theoretical results obtained for optimally tuned cutters, the safe stable machining parameter region can significantly be extended, which has also been validated by machining tests.

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