Frequency locking and devil's staircase for a two-dimensional ferrofluid droplet in an elliptically polarized rotating magnetic field

1997 ◽  
Vol 55 (3) ◽  
pp. 2640-2648 ◽  
Author(s):  
S. La-barcis ◽  
J. C. Bacri ◽  
A. Ce-barbers ◽  
R. Perzynski
Keyword(s):  
Magnetic Field ◽  
Rotating Magnetic Field ◽  
Two Dimensional ◽  
Devil's Staircase ◽  
Frequency Locking ◽  
Devil’S Staircase ◽  
Elliptically Polarized

scholarly journals Frequency locking in an injection-locked frequency divider equation

2008 ◽  
Vol 465 (2101) ◽  
pp. 283-306 ◽  
Author(s):  
Michele V Bartuccelli ◽  
Jonathan H.B Deane ◽  
Guido Gentile
Keyword(s):  
Output Signal ◽  
Numerical Results ◽  
Frequency Divider ◽  
Driving Frequency ◽  
Devil's Staircase ◽  
Frequency Locking ◽  
Devil’S Staircase ◽  
Explicit Formulae ◽  
Staircase Structure ◽  
Driving Signal

We consider a model for a resonant injection-locked frequency divider, and study analytically the locking onto rational multiples of the driving frequency. We provide explicit formulae for the width of the plateaux appearing in the devil's staircase structure of the lockings, and in particular show that the largest plateaux correspond to even integer values for the ratio of the frequency of the driving signal to the frequency of the output signal. Our results prove the experimental and numerical results available in the literature.

Interaction of a pair of ferrofluid drops in a rotating magnetic field

2018 ◽  
Vol 846 ◽  
pp. 121-142 ◽  
Author(s):  
Mingfeng Qiu ◽  
Shahriar Afkhami ◽  
Ching-Yao Chen ◽  
James J. Feng
Keyword(s):  
Magnetic Field ◽  
Uniform Magnetic Field ◽  
Hydrodynamic Interaction ◽  
Dipole Interaction ◽  
Rotating Magnetic Field ◽  
Viscous Drag ◽  
Planetary Motion ◽  
Two Dimensional ◽  
Initial Separation ◽  
Mutual Induction

We use two-dimensional numerical simulation to study the interaction between a pair of ferrofluid drops suspended in a rotating uniform magnetic field. Numerical results show four distinct regimes over the range of parameters tested: independent spin, planetary motion, drop locking and direct coalescence. These are in qualitative agreement with experiments, and the transition between them can be understood from the competition between magnetophoretic forces and viscous drag. We further analyse in detail the planetary motion, i.e. the revolution of the drops around each other while each spins in phase with the external magnetic field. For drops, as opposed to solid microspheres, the interaction is dominated by viscous sweeping, a form of hydrodynamic interaction. Magnetic dipole–dipole interaction via mutual induction only plays a secondary role. This insight helps us explain novel features of the planetary revolution of the ferrofluid drops that cannot be explained by a dipole model, including the increase of the angular velocity of planetary motion with the rotational rate of the external field, and the attainment of a limit separation between the drops that is independent of the initial separation.

Structural Organization in Magnetic Fluids with Magnetized Aggregates in Rotating Magnetic Field

2015 ◽  
Vol 233-234 ◽  
pp. 318-322 ◽  
Author(s):  
Dmitry V. Gladkikh ◽  
Yury I. Dikansky ◽  
Anastasia A. Kolesnikova
Keyword(s):  
Magnetic Field ◽  
Structural Organization ◽  
Magnetic Fluids ◽  
Rotating Magnetic Field ◽  
Polarization Ellipse ◽  
Field Polarization ◽  
Structural Lattice ◽  
Steady Magnetic Field ◽  
Magnetic Colloids ◽  
Elliptically Polarized

The results of the study of structures forming in magnetic colloids with magnetized aggregates under the action of an elliptically polarized rotating magnetic field are discussed. When a magnetic colloid layer with magnetized aggregates is affected by an elliptically polarized rotating magnetic field, some ordering of the structural lattice is observed, which is determined by the frequency and orientation of the rotating magnetic field polarization ellipse as well as by the value of an additionally imposed steady magnetic field.

Induced galvanomagnetic effects in copper

1970 ◽  
Vol 48 (15) ◽  
pp. 1806-1816 ◽  
Author(s):  
W. R. Datars
Keyword(s):  
Magnetic Field ◽  
Boundary Value Problem ◽  
Rotating Magnetic Field ◽  
Two Dimensional ◽  
Single Crystal Copper ◽  
One Dimensional ◽  
Open Orbit ◽  
Galvanomagnetic Properties ◽  
Resistivity Tensor ◽  
Galvanomagnetic Effects

The galvanomagnetic properties of copper were studied by observing the torque induced in single-crystal copper by a slowly rotating magnetic field at 1.4 °K. The induced torque varied linearly with the speed of magnet rotation and quadratically with magnetic field. There was large induced torque in high-purity samples from the open orbits in both one-dimensional and two-dimensional regions. In a sample with low ωcτ, there was also a background torque. The induced torque is described by Falicov's solution of the boundary value problem for a sample sphere with a resistivity tensor. The open-orbit torque in an uncompensated metal such as copper is approximately proportional to the transverse resistivity component ρ11. The anisotropy of the open-orbit torques for the (100) and (110) planes of copper is in agreement with that calculated for the magnetoresistance from the Fermi surface of copper. There is anisotropy in the background torque with minima in the region of symmetry directions and for a rotation in a (100) plane.

scholarly journals MATHEMATICAL MODEL TO CALCULATE THE TRAJECTORIES OF ELECTROMAGNETIC MILL OPERATING ELEMENTS

2021 ◽  
Vol 2021 (2) ◽  
pp. 26-34
Author(s):  
O. Makarchuk ◽  
◽  
D. Calus ◽  
V. Moroz ◽  
◽  
...  
Keyword(s):  
Magnetic Field ◽  
Mathematical Model ◽  
Driving Forces ◽  
Fem Analysis ◽  
Plane Motion ◽  
Rotating Magnetic Field ◽  
Hydrodynamic Resistance ◽  
Design Parameters ◽  
Two Dimensional ◽  
Working Chamber

The purpose of the research under consideration is to develop a mathematical model to calculate the trajectories of the ferromagnetic operating elements (millstones) of an electromagnetic mill, moving in a rotating magnetic field under electrodynamic and hydrodynamic resistance forces being limited by the space of the mill’s working chamber. The millstone motion is described through the equations of plane motion of arbitrary-shaped two-dimensional body. The driving forces of this motion are determined on the basis of the approximation of the tabulated functions connecting the module and the orientation of the equivalent force applied to the millstone, with its position in the working chamber and composite MMF phase of mill inductor winding. These tabulated functions are derived from the estimation of the magnetic field inside a working chamber with millstones, in two-dimensional quasi-stationary approximation, using FEM analysis. The publication contains the approximation algorithm for these tabulated vector functions of a vector argument, mathematical statement of millstones trajectories calculating, and analysis of mathematical experiments results that make it possible to evaluate the adequacy of the model. The developed tool enables conducting quantitative analysis of grinding/mixing process and will help to establish relationships between the electromagnetic mill design parameters and its performance. References 21, figures 6.

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