Stability of gravitating fluid layer of infinite extent but finite thickness including Hall effect

1968 ◽  
Vol 46 (19) ◽  
pp. 2201-2205 ◽  
Author(s):  
K. P. Das
Keyword(s):  
Hall Effect ◽  
Hall Current ◽  
Fluid Layer ◽  
Finite Thickness ◽  
Perturbation Parameter ◽  
Displacement Current ◽  
Plane Symmetric ◽  
Infinite Extent ◽  
Mode Method ◽  
The Stability

The stability of a gravitating, homogeneous, incompressible fluid layer of infinite extent but finite thickness is considered, including Hall effect, by the use of the normal mode method. A uniform magnetic field is assumed to be present throughout parallel to its boundary. The displacement current is neglected. An asymptotic analysis for small nonzero Hall current shows a destabilizing effect of order ε where ε is the perturbation parameter. The stability analysis is restricted to plane-symmetric modes.

Thermal Stability of Two Fluid Layers Separated by a Solid Interlayer of Finite Thickness and Thermal Conductivity

1984 ◽  
Vol 106 (3) ◽  
pp. 605-612 ◽  
Author(s):  
I. Catton ◽  
J. H. Lienhard
Keyword(s):  
Thermal Conductivity ◽  
Fluid Layer ◽  
Heated Surface ◽  
Finite Thickness ◽  
Fluid Layers ◽  
The Stability ◽  
Stability Limits ◽  
Range Of Values ◽  
Two Fluid ◽  
Thermal Stability Of

Stability limits of two horizontal fluid layers separated by an interlayer of finite thermal conductivity are determined. The upper cooled surface and the lower heated surface are taken to be perfectly conducting. The stability limits are found to depend on the ratio of fluid layer thicknesses, the ratio of interlayer thickness to total fluid layer thickness, and the ratio of fluid thermal conductivity to interlayer thermal conductivity. Results are given for a range of values of each of the governing parameters.

Chaotic mode competition in parametrically forced surface waves

1985 ◽  
Vol 158 ◽  
pp. 381-398 ◽  
Author(s):  
S. Ciliberto ◽  
J. P. Gollub
Keyword(s):  
Fluid Layer ◽  
Chaotic Regime ◽  
Mode Competition ◽  
Sampling Techniques ◽  
Onset Of Chaos ◽  
Chaotic Mode ◽  
The Stability ◽  
Degenerate Modes ◽  
Local Sampling ◽  
Slow Timescale

Vertical forcing of a fluid layer leads to standing waves by means of a subharmonic instability. When the driving amplitude and frequency are chosen to be near the intersection of the stability boundaries of two nearly degenerate modes, we find that they can compete with each other to produce either periodic or chaotic motion on a slow timescale. We utilize digital image-processing methods to determine the time-dependent amplitudes of the competing modes, and local-sampling techniques to study the onset of chaos in some detail. Reconstruction of the attractors in phase space shows that in the chaotic regime the dimension of the attractor is fractional and at least one Lyapunov exponent is positive. The evidence suggests that a theory incorporating four coupled slow variables will be sufficient to account for the mode competition.

The Stability of Natural Convection in an Inclined Fluid Layer in the Presence of AC Electric Field

1996 ◽  
Vol 65 (8) ◽  
pp. 2479-2484 ◽  
Author(s):  
Mohamed A. K. El Adawi ◽  
El Sayed F. El Shehawey ◽  
Safaa A. Shalaby ◽  
Mohamed I. A. Othman
Keyword(s):  
Natural Convection ◽  
Electric Field ◽  
Fluid Layer ◽  
Ac Electric Field ◽  
Inclined Fluid Layer ◽  
The Stability

Quantum Hall effects

Quantum 20/20 ◽  
2019 ◽  
pp. 303-322
Author(s):  
Ian R. Kenyon
Keyword(s):  
Magnetic Field ◽  
Hall Effect ◽  
Energy Gap ◽  
Quantum Hall ◽  
Free Electrons ◽  
Electron Gases ◽  
Hall Conductance ◽  
Hall Effects ◽  
The Stability ◽  
The Magnetic Field

It is explained how plateaux are seen in the Hall conductance of two dimensional electron gases, at cryogenic temperatures, when the magnetic field is scanned from zero to ~10T. On a Hall plateau σ‎xy = ne 2/h, where n is integral, while the longitudinal conductance vanishes. This is the integral quantum Hall effect. Free electrons in such devices are shown to occupy quantized Landau levels, analogous to classical cyclotron orbits. The stability of the IQHE is shown to be associated with a mobility gap rather than an energy gap. The analysis showing the topological origin of the IQHE is reproduced. Next the fractional QHE is described: Laughlin’s explanation in terms of an IQHE of quasiparticles is presented. In the absence of any magnetic field, the quantum spin Hall effect is observed, and described here. Time reversal invariance and Kramer pairs are seen to be underlying requirements. It’s topological origin is outlined.

scholarly journals Spiral-arm instability – III. Fragmentation of primordial protostellar discs

2019 ◽  
Vol 491 (1) ◽  
pp. L24-L28 ◽  
Author(s):  
Shigeki Inoue ◽  
Naoki Yoshida
Keyword(s):  
Gravitational Instability ◽  
Finite Thickness ◽  
Linear Perturbation ◽  
Gas Cooling ◽  
Formation And Evolution ◽  
Linear Perturbation Theory ◽  
The Stability ◽  
Protostellar Discs ◽  
Self Gravity ◽  
Spiral Arm

ABSTRACT We study the gravitational instability and fragmentation of primordial protostellar discs by using high-resolution cosmological hydrodynamics simulations. We follow the formation and evolution of spiral arms in protostellar discs, examine the dynamical stability, and identify a physical mechanism of secondary protostar formation. We use linear perturbation theory based on the spiral-arm instability (SAI) analysis in our previous studies. We improve the analysis by incorporating the effects of finite thickness and shearing motion of arms, and derive the physical conditions for SAI in protostellar discs. Our analysis predicts accurately the stability and the onset of arm fragmentation that is determined by the balance between self-gravity and gas pressure plus the Coriolis force. Formation of secondary and multiple protostars in the discs is explained by the SAI, which is driven by self-gravity and thus can operate without rapid gas cooling. We can also predict the typical mass of the fragments, which is found to be in good agreement with the actual masses of secondary protostars formed in the simulation.

scholarly journals Creep Instability of Ice Sheets

1976 ◽  
Vol 16 (74) ◽  
pp. 278-279
Author(s):  
Garry K.C. Clarke
Keyword(s):  
Melting Point ◽  
Ambient Temperature ◽  
Finite Thickness ◽  
Wave Number ◽  
Slab Thickness ◽  
Perturbation Equation ◽  
Rate Of Increase ◽  
The Stability ◽  
Image Position ◽  
Advection Velocity

Abstract The equation governing the growth or decay of a temperature perturbation T’ in an ice slab under shear stress σ xy is where K and k are respectively the thermal conductivity and diffusivity of ice, KB-v is the advection velocity normal to the bed and is the rate of increase of strain heating with temperature assuming a power law for flow. For a slab of infinite thickness under constant stress and at constant ambient temperature, T Fourier analysis gives -k2+a/k < o as the condition for stability where k is the wave number of a sinusoidal perturbation. When the slab has finite thickness the stability depends on the sign of the eigenvalues λm of the perturbation equation and on the boundary condition at the ice-rock interface. In general the eigenfunctions and eigenvalues must be found by approximate methods such as the Rayleigh-Ritz procedure but in the case where the stress and ambient temperature are constant over the slab thickness and there is no advection the eigenfunctions are either sines or cosines depending on the boundary conditions. In this special case the stability condition is if the bed is frozen and if it is at the melting point. The eigenvalue associated with the smallest value of m is the least stable so the maximum stable thickness is thus h = ½ π(a/K)1/2 if the bed is frozen or h = π (a/K)1/2 if it is at the melting point. For typical flow-law parameters these depths are around 250 m and 500 m respectively. The eigenvalues are related in a simple way to the growth or decay rates of the eigenfunctions: (K λm)–1 is the time constant for the mth eigenfunction. Depth-dependent stress, temperature, and advection have a marked effect on stability. A slab in which stress and temperature increase to values B and T B at the bed is considerably more stable than a slab held at constant stressσB and a constant temperature T B. Advection normal to the bed also has a major influence on stability. If the advection velocity is taken to vary linearly with depth and the bed is frozen, the effect of upward advection is to decrease stability and of downward advection to increase it. When the bed is temperate the effect of advection is more complex: downward advection increases stability but upward advection may increase or decrease it depending on the magnitude of the advection velocity.

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