scholarly journals Convection and its Stability in the Equatorial Regions of the Convection Zone

1990 ◽  
Vol 138 ◽  
pp. 325-328
Author(s):  
A.V. Klyachkin
Keyword(s):  
Convection Zone ◽  
Time Derivative ◽  
Equilibrium Temperature ◽  
Boussinesq Approximation ◽  
Gravitational Acceleration ◽  
Basic Equilibrium ◽  
Geophysical Hydrodynamics ◽  
Image Position ◽  
Total Time Derivative ◽  
Adiabatic Temperature Gradient

The problem of the existence, evolution, and stability of spatial structures in convection is of considerable importance to astrophysics as well as to geophysical hydrodynamics. The Boussinesq approximation will be used because the considered motions in stars are sufficiently slow. The system of hydrodynamic equations describing convection in a rotating inhomogeneous medium has the form: Here Dt is the total time derivative, U the velocity, P, T, and C the deviations of the pressure, temperature, and helium abundance (by mass) from the basic equilibrium values, ρm, νm, χm, and Dm the values averaged over the considered layer of the density, viscosity, thermal and helium diffusivities, βT and βc the averaged coefficients of the thermal and helium expansions, g and Ω the gravitational acceleration and angular velocity, ∇Tb, and ∇Cb the values of the basic equilibrium temperature and helium gradients, and ñTad the adiabatic temperature gradient.

scholarly journals 19. Convection Zones and Coronae of White Dwarfs

1971 ◽  
Vol 42 ◽  
pp. 130-135 ◽  
Author(s):  
K. H. Böhm ◽  
J. Cassinelli
Keyword(s):  
Chemical Composition ◽  
Temperature Gradient ◽  
White Dwarf ◽  
White Dwarfs ◽  
Convection Zone ◽  
Adiabatic Temperature ◽  
Turbulent Convection ◽  
Cool White Dwarfs ◽  
Adiabatic Temperature Gradient

Outer convection zones of white dwarfs in the range 5800 K ≤ Teff ≤ 30000 K have been studied assuming that they have the same chemical composition as determined by Weidemann (1960) for van Maanen 2. Convection is important in all these stars. In white dwarfs Teff < 8000 K the adiabatic temperature gradient is strongly influenced by the pressure ionization of H, HeI and HeII which occurs within the convection zone. Partial degeneracy is also important.Convective velocities are very small for cool white dwarfs but they reach considerable values for hotter objects. For a white dwarf of Teff = 30000 K a velocity of 6.05 km/sec and an acoustic flux (generated by the turbulent convection) of 1.5 × 1011 erg cm−2 sec−1 is reached. The formation of white dwarf coronae is briefly discussed.

scholarly journals Boussinesq convection in a gaseous spherical shell

2019 ◽  
Vol 82 ◽  
pp. 373-382
Author(s):  
L. Korre ◽  
N. Brummell ◽  
P. Garaud
Keyword(s):  
Temperature Gradient ◽  
Boundary Conditions ◽  
Spherical Shell ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Boussinesq Approximation ◽  
Fixed Temperature ◽  
Planetary Interiors ◽  
Adiabatic Temperature Gradient ◽  
Relevant Quantity

In this paper, we investigate the dynamics of convection in a spherical shell under the Boussinesq approximation but considering the compressibility which arises from a non zero adiabatic temperature gradient, a relevant quantity for gaseous objects such as stellar or planetary interiors. We find that depth-dependent superiadiabaticity, combined with the use of mixed boundary conditions (fixed flux/fixed temperature), gives rise to unexpected dynamics that were not previously reported.

scholarly journals An Analysis of the Relation Between the Surface and Bedrock Profiles of Ice Caps

1971 ◽  
Vol 10 (59) ◽  
pp. 197-209 ◽  
Author(s):  
W.F. Budd ◽  
D.B. Carter
Keyword(s):  
Flow Line ◽  
Smooth Curve ◽  
Small Scale ◽  
Ice Thickness ◽  
Damping Factor ◽  
Gravitational Acceleration ◽  
Ice Caps ◽  
Ice Cap ◽  
The Mean ◽  
Image Position

AbstractResults art, presented of spectral analyses of the surface and bedrock profiles along a flow line of the Wilkes ice cap and the surface along the Greenland E.G.I.G. profile. Although the bedrock appears irregular over all was velengths studied, the ice-cap surface is typically characterized by a smooth curve with small-scale surface undulations superimposed on it. The following relations of Budd (1969, 19701 are confirmed. The “damping factor" or ratio of the bedrock amplitude to the surface amplitude is a minimum for wavelengths λ about 3.3 times the ice thickness. The surface lags the bed in the direction of motion by λ/4. The magnitude of the minimum damping factor φmis typically least near the coast, and increases inland depending on the ice thicknessZ, the velocityV, and the mean ice viscosityη(which is a function of stress and temperature) according towherepis the mean ice density andgis the gravitational acceleration. Thus the determination of the damping factors provides a valuable means of estimating the ice flow parameterη.

On matrix methods for the solution of partial differential equations

1965 ◽  
Vol 61 (1) ◽  
pp. 129-132 ◽  
Author(s):  
M. Wadsworth ◽  
A. Wragg
Keyword(s):  
Partial Differential Equations ◽  
Finite Difference ◽  
Differential Equations ◽  
Laplace Transformation ◽  
Time Derivative ◽  
Partial Differential ◽  
Matrix Methods ◽  
Finite Difference Equations ◽  
Difference Form ◽  
Image Position

Bickley and McNamee (1) describe techniques for obtaining the solution of finite difference equations, arising from partial differential equations, making extensive use of matrix methods. In all cases solutions are obtained by solving algebraic equations as distinct from differential equations. For example, in order to solvethe second space derivative is replaced by finite differences and the time derivative is replaced either by substituting the backward finite difference form or by using the Laplace transformation.

scholarly journals Non-Radial Oscillations in Red Giants

1980 ◽  
Vol 5 ◽  
pp. 497-500
Author(s):  
Douglas Keeley
Keyword(s):  
Convection Zone ◽  
Normal Modes ◽  
Wave Number ◽  
Red Giants ◽  
Radial Wave ◽  
Giant Stars ◽  
Oscillation Modes ◽  
Red Giant ◽  
Image Position ◽  
Very High

The structure of red giant stars allows non-radial oscillation modes which propagate as p-modes near the surface, to propagate below the convection zone as g-modes with very high radial wave number [Dziembowski (1971, 1977), Shibahashi and Osaki (1976)]. Under some conditions the oscillations in these two propagation regions can be treated as virtually independent normal modes [Shibahashi and Osaki (1976)]. This paper examines the situation in which this approximation is not good, and discusses possible observational consequences of the interaction of the two propagation regions.The linearized differential equations describing non-radial adiabatic oscillations in stars can be written in the form, 1a1b

Supersymmetric Quantum Mechanics and the Equivalent Classical Transformation

1997 ◽  
Vol 12 (13) ◽  
pp. 899-903 ◽  
Author(s):  
A. Agostinho Neto ◽  
E. Drigo Filho
Keyword(s):  
Quantum Mechanics ◽  
Time Derivative ◽  
Lagrangian Function ◽  
Supersymmetric Quantum Mechanics ◽  
Fermionic Sector ◽  
Classical Transformation ◽  
Total Time Derivative

In the usual supersymmetric quantum mechanics, the supercharges change the eigenfunction from the bosonic to fermionic sector and conversely. The classical correspondent of this transformation is shown to be the addition of a total time derivative of a purely imaginary function to the Lagrangian function of the system.

scholarly journals New methods for quantifying rapidity of action potential onset differentiate neuron types

PLoS ONE ◽  
2021 ◽  
Vol 16 (4) ◽  
pp. e0247242
Author(s):  
Ahmed A. Aldohbeyb ◽  
Jozsef Vigh ◽  
Kevin L. Lear
Keyword(s):  
Action Potential ◽  
Time Derivative ◽  
Ratio Method ◽  
Half Maximum ◽  
Peak Width ◽  
Phase Plot ◽  
New Methods ◽  
Relative Standard ◽  
Image Position ◽  
Potential Onset

Two new methods for quantifying the rapidity of action potential onset have lower relative standard deviations and better distinguish neuron cell types than current methods. Action potentials (APs) in most central mammalian neurons exhibit sharp onset dynamics. The main views explaining such an abrupt onset differ. Some studies suggest sharp onsets reflect cooperative sodium channels activation, while others suggest they reflect AP backpropagation from the axon initial segment. However, AP onset rapidity is defined subjectively in these studies, often using the slope at an arbitrary value on the phase plot. Thus, we proposed more systematic methods using the membrane potential’s second-time derivative (V¨m) peak width. Here, the AP rapidity was measured for four different cortical and hippocampal neuron types using four quantification methods: the inverse of full-width at the half maximum of the V¨m peak (IFWd2), the inverse of half-width at the half maximum of the V¨m peak (IHWd2), the phase plot slope, and the error ratio method. The IFWd2 and IHWd2 methods show the smallest variation among neurons of the same type. Furthermore, the AP rapidity, using the V¨m peak width methods, significantly differentiates between different types of neurons, indicating that AP rapidity can be used to classify neuron types. The AP rapidity measured using the IFWd2 method was able to differentiate between all four neuron types analyzed. Therefore, the V¨m peak width methods provide another sensitive tool to investigate the mechanisms impacting the AP onset dynamics.

scholarly journals An Analysis of the Relation Between the Surface and Bedrock Profiles of Ice Caps

1971 ◽  
Vol 10 (59) ◽  
pp. 197-209 ◽  
Author(s):  
W.F. Budd ◽  
D.B. Carter
Keyword(s):  
Flow Line ◽  
Smooth Curve ◽  
Small Scale ◽  
Ice Thickness ◽  
Damping Factor ◽  
Gravitational Acceleration ◽  
Ice Caps ◽  
Ice Cap ◽  
The Mean ◽  
Image Position

AbstractResults art, presented of spectral analyses of the surface and bedrock profiles along a flow line of the Wilkes ice cap and the surface along the Greenland E.G.I.G. profile. Although the bedrock appears irregular over all was velengths studied, the ice-cap surface is typically characterized by a smooth curve with small-scale surface undulations superimposed on it. The following relations of Budd (1969, 19701 are confirmed. The “damping factor" or ratio of the bedrock amplitude to the surface amplitude is a minimum for wavelengths λ about 3.3 times the ice thickness. The surface lags the bed in the direction of motion by λ/4. The magnitude of the minimum damping factor φm is typically least near the coast, and increases inland depending on the ice thickness Z, the velocity V, and the mean ice viscosity η (which is a function of stress and temperature) according to where p is the mean ice density and g is the gravitational acceleration. Thus the determination of the damping factors provides a valuable means of estimating the ice flow parameter η.

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