Calculation of linear stability boundaries for equilibria of Hamiltonian systems

1987 ◽  
Vol 122 (6-7) ◽  
pp. 331-334 ◽  
Author(s):  
J.E. Howard ◽  
R.S. Mackay
Keyword(s):  
Linear Stability ◽  
Hamiltonian Systems ◽  
Stability Boundaries

Viscosity effect on the longwave instability of a fluid interface subjected to horizontal vibrations

2017 ◽  
Vol 814 ◽  
pp. 24-41 ◽  
Author(s):  
D. V. Lyubimov ◽  
G. L. Khilko ◽  
A. O. Ivantsov ◽  
T. P. Lyubimova
Keyword(s):  
Linear Stability ◽  
High Frequency ◽  
Incompressible Fluids ◽  
Basic Flow ◽  
Fluid Interface ◽  
Helmholtz Instability ◽  
Stability Boundaries ◽  
Low Frequencies ◽  
Viscosity Effect ◽  
High Frequency Vibrations

The effect of viscosity on the longwave Kelvin–Helmholtz instability of two immiscible incompressible fluids under horizontal vibrations is considered. The linear stability boundaries are found analytically using series expansion in terms of small wavenumber. The values of parameters, at which a transition from the longwave to finite-wavelength instability takes place, are determined. It has been shown that for high-frequency vibrations a viscous dissipation has just a weak destabilizing effect. At vibrations of moderate frequencies, destabilization is more significant, especially in the systems with large viscosity contrast. In contrast to that, at low frequencies the viscosity stabilizes the basic flow by suppressing the longwave perturbations.

scholarly journals Linear instability of Vlasov-Maxwell systems revisited-A Hamiltonian approach

2022 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Zhiwu Lin
Keyword(s):  
Linear Stability ◽  
Hamiltonian Systems ◽  
Linear Instability ◽  
Steady States ◽  
Hamiltonian Approach ◽  
Collisionless Plasmas ◽  
Exponential Trichotomy

<p style='text-indent:20px;'>We consider linear stability of steady states of 1<inline-formula><tex-math id="M1">\begin{document}$ \frac{1}{2} $\end{document}</tex-math></inline-formula> and 3DVlasov-Maxwell systems for collisionless plasmas. The linearized systems canbe written as separable Hamiltonian systems with constraints. By using ageneral theory for separable Hamiltonian systems, we recover the sharp linearstability criteria obtained previously by different approaches. Moreover, weobtain the exponential trichotomy estimates for the linearized Vlasov-Maxwellsystems in both relativistic and nonrelativistic cases.</p>

Linear Stability Analysis of Journal Bearings Lubricated With a Non-Newtonian Rabinowitsch Fluid

2017 ◽  
Vol 35 (1) ◽  
pp. 107-112 ◽  
Author(s):  
J. R. Lin ◽  
T. C. Hung ◽  
C. H. Lin
Keyword(s):  
Linear Stability ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Fluid Model ◽  
Journal Bearings ◽  
Stable Region ◽  
Stability Boundaries ◽  
Linear Dynamic ◽  
Newtonian Dynamic ◽  
Plastic Lubricants

AbstractThe linear stability boundaries of journal bearings lubricated with a non-Newtonian fluid have been investigated in this paper. Based on the Rabinowitsch fluid model, a non-Newtonian dynamic Reynolds equation for journal bearings is derived and then applied to analyze the linear dynamic characteristics of short journal bearings. Comparing with the Newtonian-lubricant case, the non-Newtonian rheology of dilatant lubricants provides a larger area of linearly stable region. However, the non-Newtonian properties of pseudo-plastic lubricants results in a reverse trend for the short journal bearing.

Sign in / Sign up

Export Citation Format

Share Document