STATISTICAL EVALUATION OF ELECTRICAL SOUNDlNG METHODS. PART I: EXPERIMENT DESIGN

Geophysics ◽  
1976 ◽  
Vol 41 (6) ◽  
pp. 1207-1221 ◽  
Author(s):  
W. E. Glenn ◽  
S. H. Ward
Keyword(s):  
Magnetic Field ◽  
Tilt Angle ◽  
Experiment Design ◽  
Eigenvalue Decomposition ◽  
Earth Model ◽  
Model Parameters ◽  
Design Technique ◽  
Horizontal Magnetic Field ◽  
Geophysical Surveys ◽  
The Magnetic Field

Traditional experiment design techniques, widely applied to both linear and nonlinear problems in many scientific fields, is applicable to the design of exploration geophysical surveys. The design technique is formulated using the mathematics of the generalized inverse and its construction via eigenvalue decomposition. The design technique is demonstrated by the designing of electromagnetic sounding surveys for a horizontal loop source. The experiment is designed whereby it is determined (1) which one of the electromagnetic field quantities, vertical and horizontal magnetic field amplitudes or phases, and polarization ellipse quantities, tilt angle, and ellipticity, and (2) which set of transmitter and receiver separations and transmitter frequencies, best resolve the conductivities and thicknesses of a given layered earth model. Model resolution is sensitive to the data error. As an example, for different assumed data errors, a model is best resolved in one instance by the phase of the two components of the magnetic field, while in another instance it is best resolved by tilt angle and ellipticity measurements. The best designs are obtained using field measurements made at several transmitter frequencies and at two or more transmitter and receiver separations. The functional relationship between the earth model parameters and the magnetic field quantities is nonlinear. The effect of this nonlinearity on the statistics applied in the method of experiment design has been reported in the literature and is reexamined here. Based on Beale's measure of nonlinearity, the models studied here exhibit adequate linearity to permit use of the linear statistics for experiment design. A study of the eigenvectors and information density matrix provide insight to model parameter correlations and measurement correlations which can be exploited for improving the design of an experiment.

The Magnetic Anisotropy of Stretched Rubber as a Function of the Tension to Which It Is Subjected

1945 ◽  
Vol 18 (1) ◽  
pp. 8-9 ◽  
Author(s):  
Eugénie Cotton-Feytis
Keyword(s):  
Magnetic Field ◽  
Magnetic Anisotropy ◽  
Uniaxial Crystal ◽  
Horizontal Magnetic Field ◽  
First Approximation ◽  
The Difference ◽  
The Times ◽  
Angular Displacements ◽  
The Magnetic Field ◽  
Oscillation Method

Abstract From the standpoint of its magnetic anisotropy, stretched rubber is comparable in a first approximation to a uniaxial crystal, in which the direction of the axis is the same as the direction of elongation. It is possible to measure this anisotropy by means of the oscillation method used by Krishnan, Guha and Banerjee in studying crystals. The sample to be examined is suspended in a uniform horizontal magnetic field in such a manner that its axis is horizontal. It is then so arranged that the torsion of the suspension wire is zero when the rubber sample is in a position of equilibrium in the field. The times of oscillation T′ and T for very small angular displacements around this position, in the presence and then in the absence of the magnetic field, are then recorded. In this way the difference between the specific susceptibilities in the direction of the axis and in the horizontal direction perpendicular to the axis is calculated by application of the equation:

Magnetohydrodynamic convection in a vertical slot with horizontal magnetic field

2003 ◽  
Vol 475 ◽  
pp. 21-40 ◽  
Author(s):  
ULRICH BURR ◽  
LEOPOLD BARLEON ◽  
PAUL JOCHMANN ◽  
ARKADY TSINOBER
Keyword(s):  
Magnetic Field ◽  
Heat Transport ◽  
Convective Heat ◽  
Convective Motion ◽  
Vortex Structures ◽  
Test Fluid ◽  
Local Anisotropy ◽  
Horizontal Magnetic Field ◽  
Vertical Slot ◽  
The Magnetic Field

This article presents an experimental study of magnetohydrodynamic convection in a tall vertical slot under the influence of a horizontal magnetic field. The test fluid is an eutectic sodium potassium Na22K78 alloy with a small Prandtl number of Pr ≈ 0:02. The experimental setup covers Rayleigh numbers in the range 103 [lsim ] Ra [lsim ] 8×104 and Hartmann numbers 0 < M < 1600. The effect of the magnetic field on the convective heat transport is determined not only by damping as expected from Joule dissipation but also, for magnetic fields not too strong, the convective heat transfer may be considerably enhanced compared to ordinary hydrodynamic (OHD) flow. Estimates of the isotropy properties of the flow by a four-element temperature probe demonstrate that the increase in convective heat transport accompanies the formation of strong local anisotropy of the turbulent eddies in the sense of an alignment of the main direction of vorticity with the magnetic field. The reduced three-dimensional nonlinearities in non-isotropic flow favour the formation of largescale vortex structures compared to OHD flow, which are more effective for convective heat transport. Along with the formation of quasi-two-dimensional vortex structures, temperature fluctuations may be considerably enhanced in a magnetic field that is not too strong. However, above Hartmann numbers M [gsim ] 400 the formerly strongly time-dependent flow suddenly becomes stationary with an extended region of high convective heat transport at stationary flow. Finally, for very high Hartmann numbers the convective motion is strongly suppressed and the heat transport is reduced to a state close to pure heat conduction.

scholarly journals Comparative Study on Planetary Magnetosphere in the Solar System

Sensors ◽  
2020 ◽  
Vol 20 (6) ◽  
pp. 1673
Author(s):  
Ching-Ming Lai ◽  
Jean-Fu Kiang
Keyword(s):  
Magnetic Field ◽  
Solar Wind ◽  
Solar System ◽  
Comparative Study ◽  
Magnetic Reconnection ◽  
Tilt Angle ◽  
Planetary Magnetosphere ◽  
Field Distributions ◽  
Mhd Simulations ◽  
The Magnetic Field

The magnetospheric responses to solar wind of Mercury, Earth, Jupiter and Uranus are compared via magnetohydrodynamic (MHD) simulations. The tilt angle of each planetary field and the polarity of solar wind are also considered. Magnetic reconnection is illustrated and explicated with the interaction between the magnetic field distributions of the solar wind and the magnetosphere.

scholarly journals Large-scale dynamos in rapidly rotating plane layer convection

2018 ◽  
Vol 612 ◽  
pp. A97 ◽  
Author(s):  
P. J. Bushby ◽  
P. J. Käpylä ◽  
Y. Masada ◽  
A. Brandenburg ◽  
B. Favier ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Large Scale ◽  
Plane Layer ◽  
Cycle Period ◽  
Dynamo Action ◽  
Horizontal Magnetic Field ◽  
Vortex Instability ◽  
Large Scale Vortex ◽  
The Mean ◽  
The Magnetic Field

Context.Convectively driven flows play a crucial role in the dynamo processes that are responsible for producing magnetic activity in stars and planets. It is still not fully understood why many astrophysical magnetic fields have a significant large-scale component.Aims.Our aim is to investigate the dynamo properties of compressible convection in a rapidly rotating Cartesian domain, focusing upon a parameter regime in which the underlying hydrodynamic flow is known to be unstable to a large-scale vortex instability.Methods.The governing equations of three-dimensional non-linear magnetohydrodynamics (MHD) are solved numerically. Different numerical schemes are compared and we propose a possible benchmark case for other similar codes.Results.In keeping with previous related studies, we find that convection in this parameter regime can drive a large-scale dynamo. The components of the mean horizontal magnetic field oscillate, leading to a continuous overall rotation of the mean field. Whilst the large-scale vortex instability dominates the early evolution of the system, the large-scale vortex is suppressed by the magnetic field and makes a negligible contribution to the mean electromotive force that is responsible for driving the large-scale dynamo. The cycle period of the dynamo is comparable to the ohmic decay time, with longer cycles for dynamos in convective systems that are closer to onset. In these particular simulations, large-scale dynamo action is found only when vertical magnetic field boundary conditions are adopted at the upper and lower boundaries. Strongly modulated large-scale dynamos are found at higher Rayleigh numbers, with periods of reduced activity (grand minima-like events) occurring during transient phases in which the large-scale vortex temporarily re-establishes itself, before being suppressed again by the magnetic field.

Hydromagnetic Stability of Two Rivlin-Ericksen Elastico-Viscous Superposed Conducting Fluids

1997 ◽  
Vol 52 (6-7) ◽  
pp. 528-532
Author(s):  
R. C. Sharma ◽  
P. Kumar
Keyword(s):  
Magnetic Field ◽  
Wave Number ◽  
Horizontal Magnetic Field ◽  
Number Range ◽  
Wave Number Range ◽  
Unstable Configuration ◽  
The Stability ◽  
Superposed Fluids ◽  
The Magnetic Field ◽  
Conducting Fluids

Abstract The stability of the plane interface separating two Rivlin-Ericksen elastico-viscous superposed fluids of uniform densities when the whole system is immersed in a uniform horizontal magnetic field has been studied. The stability analysis has been carried out, for mathematical simplicity, for two highly viscous fluids of equal kinematic viscosities and equal kinematic viscoelasticities. It is found that the stability criterion is independent of the effects of viscosity and viscoelasticity and is dependent on the orientation and magnitude of the magnetic field. The magnetic field is found to stabilize a certain wave-number range of the unstable configuration. The behaviour of growth rates with respect to kinematic viscosity and kinematic viscoelasticity parameters are examined numerically.

Magnetohydrodynamic Stability of Two Streaming Superposed Viscoelastic Conducting Fluids

2001 ◽  
Vol 56 (6-7) ◽  
pp. 416-439
Author(s):  
Mohamed Fahmy El
Keyword(s):  
Magnetic Field ◽  
Stable Configuration ◽  
Retardation Time ◽  
Horizontal Magnetic Field ◽  
Fluid Velocities ◽  
Unstable Configuration ◽  
The Stability ◽  
The Magnetic Field ◽  
Conducting Fluids ◽  
Alfven Velocity

Abstract The stability of the plane interface separating two Oldroydian viscoelastic superposed moving fluids of uniform densities when immersed in a uniform horizontal magnetic field has been in­ vestigated. The stability analysis has been carried out, for mathematical simplicity, for two highly viscous fluids of equal kinematic viscosities. It is found that the potentially stable configuration remains stable if the fluids are at rest, while it becomes unstable if the fluids move. The stability criterion is found to be independent of the viscosity and viscoelasticity, and to be dependent on the orientation of the magnetic field and the magnitudes of the fluids and Alfven velocities. It is also found that the potentially unstable configuration remains unstable in the absence of average fluid velocities, or in the presence of fluid velocities and absence of a magnetic field. The magnetic field is found to stabilize a certain wavenumbers range of the unstable configuration even in the presence of the effects of viscoelasticity. The behaviour of growth rates with respect to the stress relaxation time, strain retardation time, fluid and Alfven velocity parameters is examined analytically, and the stability conditions are obtained and discussed. -Pacs: 47.20.-k; 47.50.+d; 47.65.+a.

Nonlinear compressible magnetoconvection. Part 3. Travelling waves in a horizontal field

1995 ◽  
Vol 300 ◽  
pp. 287-309 ◽  
Author(s):  
D. P. Brownjohn ◽  
N. E. Hurlburt ◽  
M. R. E. Proctor ◽  
N. O. Weiss
Keyword(s):  
Magnetic Field ◽  
Numerical Experiments ◽  
Strong Field ◽  
Travelling Waves ◽  
Standing Waves ◽  
Weak Field ◽  
Horizontal Magnetic Field ◽  
Weakly Nonlinear ◽  
Physical Mechanisms ◽  
The Magnetic Field

We present results of numerical experiments on two-dimensional compressible convection in a polytropic layer with an imposed horizontal magnetic field. Our aim is to determine how far this geometry favours the occurrence of travelling waves. We therefore delineate the region of parameter space where travelling waves are stable, explore the ways in which they lose stability and investigate the physical mechanisms that are involved. In the magnetically dominated regime (with the plasma beta, $\hat{\beta}$ = 8), convection sets in at an oscillatory bifurcation and travelling waves are preferred to standing waves. Standing waves are stable in the strong-field regime ($\hat{\beta}$ = 32) but travelling waves are again preferred in the intermediate region ($\hat{\beta}$ = 128), as suggested by weakly nonlinear Boussinesq results. In the weak-field regime ($\hat{\beta}$ ≥ 512) the steady nonlinear solution undergoes symmetry-breaking bifurcations that lead to travelling waves and to pulsating waves as the Rayleigh number, $\circ{R}$, is increased. The numerical experiments are interpreted by reference to the bifurcation structure in the ($\hat{\beta}$, $\circ{R}$)-plane, which is dominated by the presence of two multiple (Takens-Bogdanov) bifurcations. Physically, the travelling waves correspond to slow magnetoacoustic modes, which travel along the magnetic field and are convectively excited. We conclude that they are indeed more prevalent when the field is horizontal than when it is vertical.

scholarly journals On the coronal heating mechanism by the resonant absorption of Alfven waves

1993 ◽  
Vol 16 (4) ◽  
pp. 811-816 ◽  
Author(s):  
H. Y. Alkahby
Keyword(s):  
Magnetic Field ◽  
Resonant Absorption ◽  
Alfven Waves ◽  
Alfvén Waves ◽  
Heating Process ◽  
Oscillatory Process ◽  
Horizontal Magnetic Field ◽  
Resonance Frequencies ◽  
Isothermal Atmosphere ◽  
The Magnetic Field

In this paper, we will investigate the heating of the solar corona by the resonant absorption of Alfven waves in a viscous and isothermal atmosphere permeated by a horizontal magnetic field. It is shown that if the viscosity dominates the motion in a high (low)-βplasma, it creates an absorbing and reflecting layer and the heating process is acoustic (magnetoacoustic). When the magnetic field dominates the oscillatory process it creates a non-absorbing reflecting layer. Consequently, the heating process is magnetohydrodynamic. An equation for resonance is derived. It shows that resonances may occur for many values of the frequency and of the magnetic field if the wavelength is matched with the strength of the magnetic field. At the resonance frequencies, magnetic and kinetic energies will increase to very large values which may account for the heating process. When the motion is dominated by the combined effects of the viscosity and the magnetic field, the nature of the reflecting layer and the magnitude of the reflection coefficient depend on the relative strengths of the magnetic field and the viscosity.

scholarly journals Research on a novel magnetic tilt sensor designed using Hall elements and ferrofluid

2019 ◽  
Vol 70 (5) ◽  
pp. 406-411
Author(s):  
Yavuz Öztürk ◽  
Ismail Yariçi
Keyword(s):  
Magnetic Field ◽  
Hall Effect ◽  
Tilt Angle ◽  
Face To Face ◽  
Restoring Forces ◽  
Working Principle ◽  
Tilt Sensor ◽  
Hall Effect Sensors ◽  
Two Sides ◽  
The Magnetic Field

Abstract In this study, a simple, adjustable, bidirectional tilt sensor was designed using a pair of linear Hall effect sensors and magnets. Theoretical analysis and experimental results of the sensor system were presented. The working principle of the designed sensor is based on sensing the magnetic field of a mobile magnet which displaces with respect to the tilt angle. Two magnet sets were placed at the two ends of the system to apply repulsive restoring forces on the mobile magnet. The mobile magnet was coated with a light hydrocarbon based ferrofluid as a lubricant to reduce friction. Fixed Hall effect sensors were placed face to face at the two sides of the mobile magnet to monitor the magnetic field of the mobile magnet. It was shown that both experimentally and theoretically, it is possible to measure the approximate tilt angle linearly and quadratically by calculating the sum and difference of the Hall sensor voltages for the relatively small movements of the mobile magnet. Moreover, the system was also examined for the different sets of side magnets. For three different side magnet configurations, approximately 0.7, 1.1 and 1.68 V/rad sensitivity values were observed in the linear range.

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