Small disturbances in a conducting fluid in the presence of a current-carrying conductor

1964 ◽  
Vol 60 (2) ◽  
pp. 325-339
Author(s):  
A. M. J. Davis
Keyword(s):  
Uniform Magnetic Field ◽  
Equations Of Motion ◽  
Conducting Fluid ◽  
Alfven Wave ◽  
Displacement Current ◽  
Wave Fronts ◽  
Acoustic Disturbance ◽  
Linear Partial Differential Equations ◽  
A Current ◽  
Small Disturbances

1. Introduction. The problem considered here derives its motivation from a paper by Friedlander (8) on the propagation of small disturbances in a compressible, conducting fluid in the presence of a uniform magnetic field (see also Courant and Hilbert (3), VI, §3a). In this the displacement current and energy dissipation by viscosity, heat conduction and Joule heat are neglected and a system of linear partial differential equations is obtained, which generalizes the equations of motion of the theory of sound. Their solution is in general the superposition of an arbitrary incompressible Alfven wave and a magneto-acoustic disturbance. This latter was considered by constructing a Green's function by means of suitable combinations of plane wave solutions and it was found that there are fast and slow wave fronts diverging from a point disturbance. The latter are conoidal in shape and have a singularity at their vertices which propagate along the field line in either direction from the source.

On the spin-up of an electrically conducting fluid Part 2. Hydromagnetic spin-up between infinite flat insulating plates

1970 ◽  
Vol 43 (4) ◽  
pp. 785-799 ◽  
Author(s):  
David E. Loper ◽  
Edward R. Benton
Keyword(s):  
Magnetic Field ◽  
Time Scale ◽  
Uniform Magnetic Field ◽  
Conducting Fluid ◽  
Flow Structures ◽  
Magnetic Diffusion ◽  
Electrically Conducting ◽  
Physical Mechanisms ◽  
Electrically Conducting Fluid ◽  
A Current

The linear spin-up of a homogeneous electrically conducting fluid confined between infinite flat insulating plates is analyzed for the case in which a uniform magnetic field is applied normal to the boundaries. As in part 1 (Benton & Loper 1969), complete hydromagnetic interaction is embraced even within linearized equations. Approximate inversion of the exact Laplace transform solution reveals the presence of several flow structures: two thin Ekman–Hartmann boundary layers (one on each plate), which are quasi-steady on the time scale of spin-up, two thicker continuously growing magnetic diffusion regions, and an essentially inviscid, current-free core, which may or may not be present on the spin-up time scale, depending upon the growth rate of the magnetic diffusion regions. When a current-free core exists, it is found to spin-up at the same rate as the fluid within magnetic diffusion regions, although different physical mechanisms are at play. As a result, a single hydromagnetic spin-up time is derived, independently of the thickness of magnetic diffusion regions; this time is shorter than in the non-magnetic problem.

Sound pulses in a conducting medium

1959 ◽  
Vol 55 (4) ◽  
pp. 341-367 ◽  
Author(s):  
F. G. Friedlander
Keyword(s):  
Acoustic Waves ◽  
Equations Of Motion ◽  
Displacement Current ◽  
Hydrodynamic Waves ◽  
Sound Waves ◽  
First Order ◽  
The Subject ◽  
Sound Pulses ◽  
Considerable Complexity ◽  
Small Disturbances

1. Introduction. The subject of this paper is the propagation of small disturbances in a compressible fluid which is also a conductor of electricity, in the presence of a magnetic field. The characteristic feature of the problem is that it combines sound waves and magneto-hydrodynamic waves. The theory is based on linearized equations which generalize the equations of motion of the theory of sound. The disturbances with which it deals might therefore be called magneto-acoustic waves. Energy dissipation by viscosity, heat conduction and Joule heat is neglected, and so is the displacement current. Even so, a hyperbolic system of seven partial differential equations of the first order is obtained, whose solution requires analysis of considerable complexity.

Basin of Attraction of the Simplest Walking Model

2001 ◽  
Author(s):  
A. L. Schwab ◽  
M. Wisse
Keyword(s):  
Equations Of Motion ◽  
Basin Of Attraction ◽  
Mapping Method ◽  
Walking Robots ◽  
Natural Energy ◽  
Walking Motion ◽  
The Stability ◽  
The Basin Of Attraction ◽  
General Method ◽  
Small Disturbances

Abstract Passive dynamic walking is an important development for walking robots, supplying natural, energy-efficient motions. In practice, the cyclic gait of passive dynamic prototypes appears to be stable, only for small disturbances. Therefore, in this paper we research the basin of attraction of the cyclic walking motion for the simplest walking model. Furthermore, we present a general method for deriving the equations of motion and impact equations for the analysis of multibody systems, as in walking models. Application of the cell mapping method shows the basin of attraction to be a small, thin area. It is shown that the basin of attraction is not directly related to the stability of the cyclic motion.

On some similarity solutions in magnetohydrodynamics

1971 ◽  
Vol 6 (2) ◽  
pp. 331-341 ◽  
Author(s):  
C. Sozou
Keyword(s):  
Electrical Conductivity ◽  
Flow Field ◽  
Boundary Conditions ◽  
Electric Discharge ◽  
Current Source ◽  
Similarity Solutions ◽  
Conducting Fluid ◽  
Axisymmetric Configuration ◽  
A Current ◽  
Conducting Fluids

In this paper we employ similarity considerations to investigate the flow field produced by an electric discharge (mathematically a current source) and a jet of momentum emerging from the same hole of a plane wall bounding a viscous, incompressible conducting fluid, which extends to infinity. We also use similarity solutions in considering the axisymmetric configuration of a problem that has recently received some attention in connexion with field line reconnexion in conducting fluids. We derive the similarity equations for an incompressible, viscous conducting fluid, and discuss the solutions for the case when the fluid is perfectly conducting. When the electrical conductivity of the fluid is finite, we could not construct solutions, satisfying the appropriate boundary conditions.

Construction of a Cost Effective Current Balance for Physics Teaching

2013 ◽  
Vol 770 ◽  
pp. 374-377
Author(s):  
Apichart Sankote ◽  
Kheamrutai Thamaphat ◽  
Supanee Limsuwan
Keyword(s):  
Magnetic Field ◽  
Uniform Magnetic Field ◽  
Magnetic Force ◽  
Magnetic Field Direction ◽  
Horizontal Segment ◽  
Applied Current ◽  
Copper Sheet ◽  
Physics Teaching ◽  
The Magnetic Field ◽  
A Current

In this work, a method to measuring the magnitude of a uniform magnetic field in space using current balance was described. A simple experimental set was designed and constructed using low-cost materials. This constructed current balance consists of copper sheet, weight pan, and acrylic sheet. A copper sheet was cut into a U-shape and attached at the end of acrylic balance arm. A weight pan was hanged in the opposite side of the balance arm with high sensitivity to a small torque. The horizontal segment of the U-shaped copper sheet, which the length l was 3 cm, was located inside the influence of an uniform magnetic field produced by two parallel bar magnets with opposite poles facing each other. The magnetic field direction was perpendicular to the horizontal segment. When a current was supplied to the copper sheet, the magnetic force acting on a horizontal segment of length l carrying a current I in a magnetic field B was given by. In the experiment, the current was varied from 0 1 A. For each value of applied current, the magnetic force on a thin straight sheet of length l was measured by adding masses to the pan until the balance arm moved to the equilibrium between opposing gravitational and magnetic forces. The results showed that the magnetic force increased linearly with increasing applied current. By plotting a linear graph of magnetic force versus applied current, the magnetic field B can be calculated from . The calculated and actual values of B were 100.32 and 100.13 mT, respectively. This constructed current balance is an excellent tool for high school and undergraduate fundamental physics courses. Students will be excited when they see the balance arm rising or going down due to magnitude and direction of current flowing in a conductor wire.

On the Dynamic Stability of Self-Aligning Journal Gas Bearings

1977 ◽  
Vol 99 (4) ◽  
pp. 434-440 ◽  
Author(s):  
M. J. Cohen
Keyword(s):  
Dynamic Stability ◽  
Journal Bearing ◽  
Equations Of Motion ◽  
Stability Boundary ◽  
Initial Condition ◽  
Small Motion ◽  
Gas Bearings ◽  
Loading Case ◽  
The Stability ◽  
Small Disturbances

The report presents an investigation of the dynamic stability behaviour of self-aligning journal gas bearings when subjected to arbitrary small disturbances from an initial condition of operational equilibrium. The method is based on an approach similar to the nonlinear-ph solution of the author for the quasi-static loading case but the equations of motion of the journal are the linearized forms for small motion in the two degrees (translational) of freedom of the journal center. The stability domains for the infinite journal bearing are presented for the whole of the eccentricity (ε) and rotational speed (Λ) ranges for any given bearing geometry, in the shape of stability boundaries in that domain. It is shown that a given bearing will be stable within a corridor in the (ε, Λ) parametral domain having as its lower bound the so called “half-speed” whirl stability boundary and as its upper bound another whirling instability at a higher characteristic (relative) frequency, the instability occurs generally at the higher eccentricities and lower rotational speeds.

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