Regular and chaotic dynamics of a chain of magnetic dipoles with moments of inertia

Шутый, А. М.

doi:10.1134/s1063776109050173

Cited by 20 publications

(4 citation statements)

References 4 publications

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“…The bodies with dipole moments are considered to be homogeneous and spherical [7]. The dynamic equa tions for the system of dipoles have the following form [8][9][10]: (1) where and are the dipole moment and the angular velocity of the ith dipole ( is the angle of rotation of the ith dipole about the axis j = x, y, z of the Cartesian system of coordinates); J i is the moment of inertia; and α i is the dissipation parameter. In the absence of an external field, the field that is created at…”

Section: Initial Equationsmentioning

confidence: 99%

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Orientational transitions in four-row magnetic-dipole lattices

Шутый

2014

Phys. Metals Metallogr.

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Square lattices with four rows of dipoles have been considered. It has been shown that, if there are several stable equilibrium configurations, an external field excites transitions that change the direction of the dipole moments of one of the lattice rows. Orientational transitions in the structure that consists of intersect ing perpendicular lattices have been studied. It has been found that the front of the orientational transition that results in a configuration with rows having alternating directions passes through the region of the inter section of the lattices into the other part of the lattice. The front of the other orientational transitions stops in the region of the intersection. The effect of an external field on certain dipoles located in the region of the intersection makes it possible to control the movement of the orientational transition front; i.e., the front can be forced to pass through the region of the intersection in the initial direction; its direction can be changed, the configuration of the orientational transition can be changed or the front can be stopped in the region of the intersection.

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Section: Initial Equationsmentioning

confidence: 99%

“…If an external field f is applied, it is added to the field (2). The dipoles that make up the lattice are assumed to be identical, i.e., and Let us now pass to the following dimensionless parameters [8,9]:…”

Section: A M Shutyimentioning

confidence: 99%

Orientational transitions in four-row magnetic-dipole lattices

Шутый

2014

Phys. Metals Metallogr.

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“…In biological environments, magnetic particles in bacteria can affect the movements of these bacteria in a changing external magnetic field [5]. Theoretical calculations have already shown that the rotation of linearly connected magnetic dipoles (magnetic chains) can show chaotic behaviour in sinusoid alternating external fields [6], while other results have suggested a phenomenon of synchronization [7].…”

Section: Introductionmentioning

confidence: 99%

A simple magnetic oscillator-rotator model made of magnetic balls, and its examination by video-analysis

Egri

Bihari

2021

Eur. J. Phys.

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We built a simple structure of seven dipole neodymium magnetic balls, a magnetic spinner that easily rotates around its central ball. This proved to be a very simple magnetic oscillator-rotator with a dipole-like field. After capturing videos of its rotating movements in different magnetic fields, video analysis has provided us with the rotation angle-time function of the motion, either in the case of a stationary magnetic field (damped oscillation) or an alternating magnetic field (forced oscillations). We were able to obtain a numerical solution for the differential equation describing the motion, a solution which was in tune with the special phenomena observed. It was especially interesting—and can be utilised in physics education—that the oscillation of the system was very strongly dependent on the initial conditions and seemed to be quite chaotic. The rotation angle, angular speed functions and their representation in phase space have shown the characteristics of chaotic behaviour, especially in the case of coupled oscillations. Thus, this kind of chaotic movement can be demonstrated very simply, even in classroom conditions by the use of such magnetic systems. At the same time, such models might help in the scientific understanding of magnetic nanostructures—their self-assembly and motions in alternating magnetic fields—which is the basis of practical applications such as magnetic hyperthermia.

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“…Each nanoparticle can rotate about the center of masses. The dynamic equations for this system of magnetic dipoles can be represented as follows [9][10][11]: (1) where and are the dipole magnetic moment and the angular velocity of the ith dipole (ϕ ij is the angle of rotation of the dipole about the axis ), is the moment of inertia, and is the dissipation parameter. The effective field produced at the site of the location of the ith dipole by the other dipoles and by an external magnetic field h is deter mined as follows:…”

Section: Introductionmentioning

confidence: 99%

Equilibrium states of planar arrays of magnetic dipoles with allowance for exchange interaction

Шутый

Семенцов

2015

Phys. Metals Metallogr.

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Equilibrium states of planar square arrays of magnetic dipoles have been studied. It has been shown that, in the presence of exchange interaction, the main equilibrium states are configurations with the orientation of dipoles along the diagonal of the system, along its side, and vortex configurations with different location of the center of the vortex and different magnitudes of the magnetic moment of the system. Condi tions for transitions between equilibrium configurations caused by the planar field that acts on the entire array and by the local normal field acting on part of dipoles entering into the system have been considered. The possibility of transitions between the configurations has been shown and the changes in the total magnetic moment due to the action of the field on separate dipoles of the system has been discussed.

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Regular and chaotic dynamics of a chain of magnetic dipoles with moments of inertia

Cited by 20 publications

References 4 publications

Orientational transitions in four-row magnetic-dipole lattices

Orientational transitions in four-row magnetic-dipole lattices

A simple magnetic oscillator-rotator model made of magnetic balls, and its examination by video-analysis

Equilibrium states of planar arrays of magnetic dipoles with allowance for exchange interaction

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