Elementary model of internal electromagnetic pinch-type instability

We analyse numerically a pinch-type instability in a semi-infinite planar layer of inviscid conducting liquid bounded by solid walls and carrying a uniform electric current. Our model is as simple as possible but still captures the salient features of the instability which otherwise may be obscured by the technical details of more comprehensive numerical models and laboratory experiments. Firstly, we show the instability in liquid metals, which are relatively poor conductors, differs significantly from the astrophysically relevant Tayler instability. In liquid metals, the instability develops on the magnetic response time scale, which depends on the conductivity and is much longer than the Alfvén time scale, on which the Tayler instability develops in well conducting fluids. Secondly, we show that this instability is an edge effect caused by the curvature of the magnetic field, and its growth rate is determined by the linear current density and independent of the system size. Our results suggest that this instability may affect future liquid-metal batteries when their size reaches a few metres.

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Flux expulsion with dynamics

Journal of Fluid Mechanics ◽

10.1017/jfm.2016.60 ◽

2016 ◽

Vol 791 ◽

pp. 568-588 ◽

Cited By ~ 5

Author(s):

Andrew D. Gilbert ◽

Joanne Mason ◽

Steven M. Tobias

Keyword(s):

Magnetic Field ◽

Magnetic Fields ◽

Lorentz Force ◽

Differential Rotation ◽

Time Scale ◽

Scaling Laws ◽

Dynamical Regime ◽

Kinematic Evolution ◽

Flux Expulsion ◽

The Magnetic Field

In the process of flux expulsion, a magnetic field is expelled from a region of closed streamlines on a $TR_{m}^{1/3}$ time scale, for magnetic Reynolds number $R_{m}\gg 1$ ($T$ being the turnover time of the flow). This classic result applies in the kinematic regime where the flow field is specified independently of the magnetic field. A weak magnetic ‘core’ is left at the centre of a closed region of streamlines, and this decays exponentially on the $TR_{m}^{1/2}$ time scale. The present paper extends these results to the dynamical regime, where there is competition between the process of flux expulsion and the Lorentz force, which suppresses the differential rotation. This competition is studied using a quasi-linear model in which the flow is constrained to be axisymmetric. The magnetic Prandtl number $R_{m}/R_{e}$ is taken to be small, with $R_{m}$ large, and a range of initial field strengths $b_{0}$ is considered. Two scaling laws are proposed and confirmed numerically. For initial magnetic fields below the threshold $b_{core}=O(UR_{m}^{-1/3})$, flux expulsion operates despite the Lorentz force, cutting through field lines to result in the formation of a central core of magnetic field. Here $U$ is a velocity scale of the flow and magnetic fields are measured in Alfvén units. For larger initial fields the Lorentz force is dominant and the flow creates Alfvén waves that propagate away. The second threshold is $b_{dynam}=O(UR_{m}^{-3/4})$, below which the field follows the kinematic evolution and decays rapidly. Between these two thresholds the magnetic field is strong enough to suppress differential rotation, leaving a magnetically controlled core spinning in solid body motion, which then decays slowly on a time scale of order $TR_{m}$.

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Effect of magnetic field on parametrically driven surface waves

Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rspa.2006.1789 ◽

2006 ◽

Vol 463 (2079) ◽

pp. 711-722 ◽

Cited By ~ 6

Author(s):

Supriyo Paul ◽

Krishna Kumar

Keyword(s):

Magnetic Field ◽

Surface Waves ◽

Liquid Metals ◽

Tricritical Point ◽

Thin Layers ◽

Vertical Magnetic Field ◽

Harmonic Solution ◽

Chandrasekhar Number ◽

The Magnetic Field ◽

Primary Instability

Stability analysis of parametrically driven surface waves in liquid metals in the presence of a uniform vertical magnetic field is presented. Floquet analysis gives various subharmonic and harmonic instability zones. The magnetic field stabilizes the onset of parametrically excited surface waves. The minima of all the instability zones are raised by a different amount as the Chandrasekhar number is raised. The increase in the magnetic field leads to a series of bicritical points at a primary instability in thin layers of a liquid metal. The bicritical points involve one subharmonic and another harmonic solution of different wavenumbers. A tricritical point may also be triggered as a primary instability by tuning the magnetic field.

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Soft Robot Based on Hyperelastic Buckling Controlled by Discontinuous Magnetic Field

Journal of Mechanisms and Robotics ◽

10.1115/1.4051241 ◽

2021 ◽

pp. 1-35

Author(s):

Yingdong Xu ◽

Dongze Yan ◽

Kai Zhang ◽

Xuequan Li ◽

Y.F. Xing ◽

...

Keyword(s):

Magnetic Field ◽

Flexible Electronics ◽

Nonlinear Deformation ◽

Numerical Models ◽

Optical Path ◽

Magnetic Composite ◽

Soft Robot ◽

New Ideas ◽

Cargo Transportation ◽

The Magnetic Field

Abstract Most untethered magnetic soft robots are controlled by a continuously applied magnetic field. The accuracy of their motion depends completely on the accuracy of external magnetic field, consequently any slight disturbance may cause a dramatic change. Here, we report a new structure and driven method design to achieve a novel magnetic soft robot, which can achieve accurate and stable locomotion with weakly dependence on the magnetic field. The robot consists of functional magnetic composite materials with one central transportation platform and four crawling arms, whose motion is mainly based on hyperelastic buckling and recovering of the arms. The robot is capable of cargo transportation with multimodal locomotion, such as crawling, climbing and turning with high adaptability to various surfaces. The robot consumes much less driven energy compared to conventional magnetic robots. Moreover, we develop theoretical and numerical models to rationally design the precisely controlled robot. Our study shows applications in terms of transportation functions, such as for optical path adjustments and photographic tasks in complex circumstances. This work also provides new ideas on how to utilize nonlinear deformation more efficiently, one could combine the benefits for both the flexible electronics and actuation applications.

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HALL AND MAGNETORESISTANCE EFFECTS OBTAINED FROM SIMULTANEOUS MEASUREMENTS OF LIQUID METALS AND SEMICONDUCTORS

International Journal of Modern Physics B ◽

10.1142/s0217979204027153 ◽

2004 ◽

Vol 18 (27n29) ◽

pp. 3625-3628

Author(s):

M. OGITA ◽

T. ITO ◽

M. ISAI ◽

I. MOGI ◽

S. AWAJI ◽

...

Keyword(s):

Magnetic Field ◽

Liquid Metals ◽

Simultaneous Methods ◽

Hall Measurements ◽

Hall Effects ◽

Galvanomagnetic Effects ◽

Liquid States ◽

Low Magnetic Field ◽

The Magnetic Field ◽

Solid And Liquid States

Hall measurements of liquid metals, using two-frequency, ac-dc and simultaneous methods are described. The Hall effect has been measured in Hg and Ga metals, in both solid and liquid states. The magnetoresistance and Hall effects have also been measured in an InSb single crystal, which exhibited magnetoresistance even in low magnetic field, and in Si , which did not exhibit magnetoresistance in low magnetic field. In order to investigate the magnetic field dependence of the observed galvanomagnetic effects for solid and liquid state metals, and for semiconductors, Hall measurements in high magnetic field, up to ±9 T, were also performed.

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Transformation of beams of dia-, para-, and ferromagnetic particles by the magnetic field of a linear current

Technical Physics ◽

10.1134/1.1258766 ◽

1997 ◽

Vol 42 (8) ◽

pp. 980-983

Author(s):

N. I. Shtepa

Keyword(s):

Magnetic Field ◽

Linear Current ◽

The Magnetic Field ◽

Ferromagnetic Particles

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A mathematical model for the movement of a conducting liquid through a conducting porous medium: I. Excitation of oscillations of the magnetic field by the surface Rayleigh wave

Mathematical and Computer Modelling ◽

10.1016/0895-7177(96)00082-9 ◽

1996 ◽

Vol 24 (1) ◽

pp. 79-84 ◽

Cited By ~ 2

Author(s):

Kh.Kh. Imomnazarov

Keyword(s):

Magnetic Field ◽

Mathematical Model ◽

Porous Medium ◽

Rayleigh Wave ◽

Conducting Liquid ◽

The Magnetic Field ◽

Surface Rayleigh Wave

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Galactic Dynamics and Magnetic Field Amplification

Symposium - International Astronomical Union ◽

10.1017/s0074180900174492 ◽

1993 ◽

Vol 157 ◽

pp. 395-401 ◽

Cited By ~ 1

Author(s):

Harald Lesch

Keyword(s):

Magnetic Field ◽

Angular Momentum ◽

Magnetic Fields ◽

Time Scale ◽

Numerical Models ◽

Momentum Transport ◽

Angular Momentum Transport ◽

Field Amplification ◽

Gravitational Instabilities ◽

Magnetic Diffusivity

Stimulated by recent high frequency radio polarization measurements of M83 and M51, we consider the influence of non-axisymmetric features (bars, spiral arms, etc…) on galactic magnetic fields. The time scale for the field amplification due to the non-axisymmetric velocity field is related to the time scale of angular momentum transport in the disk by the non-axisymmetric features. Due to its dissipational character (cooling and angular momentum transport) the gas plays a major role for the excitation of non-axisymmetric instabilities. Since it is the gaseous component of the interstellar gas in which magnetic field amplification takes place we consider the interplay of gasdynamical processes triggered by gravitational instabilities and magnetic fields. A comparison with the time scale for dynamo action in a disk from numerical models for disk dynamos gives the result that field amplification by non-axisymmetric features is faster in galaxies like M83 (strong bar) and M51 (compagnion and very distinct spiral structure), than amplification by an axisymmetric dynamo. Furthermore, we propose that axisymmetric gravitational instabilities may provide the turbulent magnetic diffusivity ηT. Based on standard galaxy models we obtain a radially dependent diffusivity whose numerical value rises from 1025cm2s−1 to 1027cm2s−1, declining for large radii.

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Numerical Modelling of the Ultrasonic Treatment of Aluminium Melts: An Overview of Recent Advances

Materials ◽

10.3390/ma12193262 ◽

2019 ◽

Vol 12 (19) ◽

pp. 3262 ◽

Cited By ~ 1

Author(s):

Bruno Lebon ◽

Iakovos Tzanakis ◽

Koulis Pericleous ◽

Dmitry Eskin

Keyword(s):

Best Practice ◽

Acoustic Pressure ◽

Pressure Field ◽

State Of The Art ◽

Liquid Metals ◽

Numerical Models ◽

Acoustic Cavitation ◽

Velocity Fields ◽

Melt Processing ◽

Best Practice Guidelines

The prediction of the acoustic pressure field and associated streaming is of paramount importance to ultrasonic melt processing. Hence, the last decade has witnessed the emergence of various numerical models for predicting acoustic pressures and velocity fields in liquid metals subject to ultrasonic excitation at large amplitudes. This paper summarizes recent research, arguably the state of the art, and suggests best practice guidelines in acoustic cavitation modelling as applied to aluminium melts. We also present the remaining challenges that are to be addressed to pave the way for a reliable and complete working numerical package that can assist in scaling up this promising technology.

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A Transient Temperature Solution for Bore-Hole Model Testing

Journal of Glaciology ◽

10.1017/s0022143000008613 ◽

1987 ◽

Vol 33 (114) ◽

pp. 140-148 ◽

Cited By ~ 5

Author(s):

Brian Hanson ◽

Robert E. Dickinson

Keyword(s):

Response Time ◽

Time Scale ◽

Numerical Models ◽

Ice Sheet ◽

Energy Balance Equation ◽

Finite Difference Approximation ◽

Difference Approximation ◽

Small Scale ◽

Transient Temperature ◽

Vertical Column

AbstractTransient temperature variations in a vertical column of ice with horizontally uniform conditions, constant vertical strain-rate and specified surface temperature, and basal heat flux can be calculated analytically. The solution consists of eigenfunctions which are forms of the confluent hypergeometric function. This solution shows that advection and diffusion have clearly separated areas of dominance, with diffusion being a sufficient approximation for small-scale perturbations in the temperature profile and advection placing an upper limit on the response time of the ice sheet as a whole. This solution is useful for analysis and testing of numerical models, for evaluation of the response time of an ice sheet and for exploratory analysis of real bore-hole data. The lowest eigenvalue of the solution determines the time-scale for transient decay of temperature anomalies. The time-scale can be determined for more general strain-rates using a finite-difference approximation to the linearized energy-balance equation.

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