Magnetized Sphere Research Articles

The larmor frequency shift in magnetically heterogeneous media depends on their mesoscopic structure.

Recent studies have addressed the determination of the NMR precession frequency in biological tissues containing magnetic susceptibility differences between cell types. The purpose of this study is to investigate the dependence of the precession frequency on medium microstructure using a simple physical model. This dependence is governed by diffusion of NMR-visible molecules in magnetically heterogeneous microenvironments. In the limit of fast diffusion, the precession frequency is determined by the average susceptibility-induced magnetic field, whereas in the limit of slow diffusion it is determined by the average local phase factor of precessing spins. The main method used is Monte Carlo simulation of isotropic suspensions of impermeable magnetized spheres. In addition, NMR spectroscopy was performed in aqueous suspensions of polystyrene microbeads. The precession frequency depends on the structural organization of magnetized objects in the medium. Monte Carlo simulations demonstrated a nonmonotonic transition between the regimes of fast and slow diffusion. NMR experiments confirmed the transition, but were unable to confirm its precise form. Results for a given pattern of structural organization obey a scaling law. The NMR precession frequency exhibits a complex dependence on medium structure. Our results suggest that the commonly assumed limit of fast water diffusion holds for biological tissues with small cells. Magn Reson Med 79:1101-1110, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

Periodic nonlinear sliding modes for two uniformly magnetized spheres

A uniformly magnetized sphere slides without friction along the surface of a second, identical sphere that is held fixed in space, subject to the magnetic force and torque of the fixed sphere and the normal force. The free sphere has two stable equilibrium positions and two unstable equilibrium positions. Two small-amplitude oscillatory modes describe the sliding motion of the free sphere near each stable equilibrium, and an unstable oscillatory mode describes the motion near each unstable equilibrium. The three oscillatory modes remain periodic at finite amplitudes, one bifurcating into mixed modes and circumnavigating the free sphere at large energies. For small energies, the free sphere is confined to one of the two discontiguous domains, each surrounding a stable equilibrium position. At large energies, these domains merge and the free sphere may visit both positions. The critical energy at which these domains merge coincides with the cumulation point of an infinite cascade of mixed-mode bifurcations. These findings exploit the equivalence of the force and torque between two uniformly magnetized spheres and the force and torque between two equivalent point dipoles, and offer clues to the rich nonlinear dynamics of this system. Online MagPhyx visualizations illustrate the dynamics.

Interactions between uniformly magnetized spheres

We use simple symmetry arguments suitable for undergraduate students to demonstrate that the magnetic energy, forces, and torques between two uniformly magnetized spheres are identical to those between two point magnetic dipoles. These arguments exploit the equivalence of the field outside of a uniformly magnetized sphere with that of a point magnetic dipole, and pertain to spheres of arbitrary sizes, positions, and magnetizations. The point dipole/sphere equivalence for magnetic interactions may be useful in teaching and research, where dipolar approximations for uniformly magnetized spheres can now be considered to be exact. The work was originally motivated by interest in the interactions between collections of small neodymium magnetic spheres used as desk toys.

A Model for the Braking Indices of Pulsars

Stars known as pulsars are generally modeled as magnetized spheres made of neutrons with high rotation frequency. It is known that such stars are spinning down and this braking is measured by a parameter, n, known as braking index. For the canonical model such parameter should have a single value for all pulsars: n = 3. However, from observations it is known that n diverges from 3. In this work, differently from the canonical model, we have hypothesized the existence of a variation of the moment of inertia of the star through a time-varying radius. Using energy conservation we find the values for the variation of the radius of our pulsar sample. Our results indicate that it may be reasonable to consider that the radius of pulsars can be changing with time.

Magnon Kerr effect in a strongly coupled cavity-magnon system

We experimentally demonstrate magnon Kerr effect in a cavity-magnon system, where magnons in a small yttrium iron garnet (YIG) sphere are strongly but dispersively coupled to the photons in a three-dimensional cavity. When the YIG sphere is pumped to generate considerable magnons, the Kerr effect yields a perceptible shift of the cavity's central frequency and more appreciable shifts of the magnon modes. We derive an analytical relation between the magnon frequency shift and the drive power for the uniformly magnetized YIG sphere and find that it agrees very well with the experimental results of the Kittel mode. Our study paves the way to explore nonlinear effects in the cavity-magnon system.

Dynamical interactions between two uniformly magnetized spheres

Studies of the two-dimensional motion of a magnet sphere in the presence of a second, fixed sphere provide a convenient venue for exploring magnet–magnet interactions, inertia, friction, and rich nonlinear dynamical behavior. These studies exploit the equivalence of these magnetic interactions to the interactions between two equivalent point dipoles. We show that magnet–magnet friction plays a role when magnet spheres are in contact, table friction plays a role at large sphere separations, and eddy currents are always negligible. Web-based simulation and visualization software, called MagPhyx, is provided for education, exploration, and discovery.

Electromagnetic braking revisited with a magnetic point dipole model

A theoretical model is developed to predict the trajectory of magnetized spheres falling through a copper pipe. The derive magnetic point dipole model agrees well with the experimental trajectories for NdFeB spherical magnets of varying diameter, which are embedded inside 3D printed shells with fixed outer dimensions. This demonstration of electrodynamic phenomena and Lenz's law serves as a good laboratory exercise for physics, electromagnetics, and dynamics classes at the undergraduate level.

Study on the properties of photonic band gap and flatbands in the three-dimensional magnetized plasma photonic crystals with a general case

In this paper, the properties of photonic band gap (PBG) and flatbands in the three-dimensional (3D) magnetized plasma photonic crystals (MPPCs) with a general case in face-centered-cubic lattices are theoretically investigated based on the modified plane wave expansion method, in which the homogeneous magnetized plasma spheres are immersed in the homogeneous and isotropic dielectric background, as the magneto-optical Faraday effects are considered. The more general situation has been considered, and the PBG of such MPPCs is for all of the electromagnetic waves. The derivation of the formulas for calculating also is given. Theoretical computing results show that a PBG and two flatbands regions can be obtained. Compared to the conventional dielectric-air photonic crystals with similar structure, the larger PBG can be obtained in such 3D MPPCs. However, the narrower PBG can be achieved compared to that for the right circular polarized (RCP) wave, and the larger upper edge frequency of second flatbands region can be achieved. For the flatbands region, the upper edge only can be tuned by the plasma frequency and plasma cyclotron frequency. The effects of plasma frequency and plasma cyclotron frequency (the external magnetic field) on the properties of PBG also are investigated theoretically in detail. Theoretical simulations show that the PBG can be manipulated by those two parameters. The results show that the properties of PBG are obviously different with those for RCP wave in the similar 3D MPPCs. Those results can hold promise for opening a new scope to design the filters, planar reflectors, omnidirectional mirrors, absorber or waveguides based on the 3D MPPCs.

Magnetooperated Polydisperse Granulated Magnetized Structures

The problem of influence of an external magnetic field on the torsional deformation of magnetic elastomers is considered. The magnetic elastomer is modeled by a structure consisting of polydisperse spherical two-phase cells of the same kind, each of which is a magnetized hard sphere with a shell of an easily deformable elastomer. Such сells continuously fill the volume of a hollow cylindrical rod, with smaller cells located in domains among larger ones. The problem is solved in a linear formulation for the micro- and macrolevels of magnetic and elastic strain fields which appear in the magnetic elastomer under the action of an external magnetic field. The volume fractions of magnetized spherical inclusions corresponding to the maximum torsional deformation of the composite rod are found.

Dynamic interaction of a magnetized solid body with a rarefied plasma flow

Dependences of the drag and lift coefficients of a magnetized sphere in a hypersonic rarefied plasma flow on the angle between the plasma flow velocity and the self-magnetic field induction vector of the body are obtained in a wide range of the ratio of the magnetic pressure to the plasma flow pressure. It is shown that changing the orientation of the magnetic field vector of the body and the incoming flow velocity can be used to control the dynamic interaction in the plasma–body system, namely, to decelerate and accelerate the magnetized sphere in a rarefied hypersonic plasma flow.

Fragmentation as an aggregation process: the role of defects.

A cohesive object will eventually break into fragment when experiencing a strong deformation, during an impact for instance. Using necklaces of cohesive magnetized spheres suddenly expanded, we have shown that the fragmentation of this one-dimensional material results from an inverse aggregation cascade (Vledouts et al. 2015 Proc. R. Soc. A 471, 20150678. (doi:10.1098/rspa.2015.0678)). Here, we explore a variant of this process by changing the force law between the attracting spheres, using hydrogel beads linked by capillary bridges. We also investigate the role of (weak) defects in the cohesion strength and the consequences of a distribution of forces between the beads. It is found that fragment do form by a cascade of aggregations, which is interrupted earlier when the force disorder is stronger.

Numerical Simulation of Radiative Natural Convection Flow Around a Magnetized Sphere

The natural convection flow from a magnetized sphere in the presence of thermal radiation is considered. The characteristics of boundary-layer flow in the form of skin friction, rate of heat transfer, and current density at different positions of the sphere are evaluated. The numerical solutions of velocity profile, temperature distribution, and transverse component of the magnetic field are also presented. In the present study, the finite-difference method is used to find the numerical solutions of the flow model.

Effect of a superconducting coating on the equilibrium state of a system of two concentric ferromagnetic spheres placed in a magnetic field

In the framework of the London theory, the free energy of a system consisting of two concentric uniformly magnetized spheres and a spherical superconducting shell coating them in an external magnetic field parallel to the magnetization of the outer sphere is determined for an arbitrary angle between the vectors of magnetic moments of the spheres. The field of switching from the magnetization of the inner sphere antiparallel to the magnetic moment of the outer sphere to the parallel magnetization is calculated, and the condition in which such a switching does not induce the transition of the shell to the normal state are determined.

On the ``Force-free Surface'' of the Magnetized Celestial Bodies

The field of a uniformly magnetized rotating sphere is studied with special attention to the surface where the electric and magnetic fields are orthogonal to each other. The equation of this surface, valid at arbitrary distances from the rotating magnetized sphere, is obtained. Inside the light cylinder this surface can be considered as a force-free surface, i.e. as a place where the particles with strong radiation damping can be trapped due to their energy loss. Outside the light cylinder this surface makes just a geometric locus which moves with a superlight velocity around the axis of rotation. The 2- and 3-dimensional plots of the force-free surface are constructed. Estimation of influence of the centrifugal force on the particle dynamics is made. It is shown, that in case of strong magnetic field the centrifugal force is negligible small everywhere except a narrow neighbourhood of the light cylinder.

The properties of photonic band gap and surface plasmon modes in the three-dimensional magnetized photonic crystals as the mixed polarized modes considered

In this paper, the properties of photonic band gap (PBG) and surface plasmon modes in the three-dimensional (3D) magnetized plasma photonic crystals (MPPCs) with face-centered-cubic (fcc) lattices are theoretically investigated based on the plane wave expansion (PWE) method, in which the homogeneous magnetized plasma spheres are immersed in the homogeneous dielectric background, as the Voigt effects of magnetized plasma are considered (the incidence electromagnetic wave vector is perpendicular to the external magnetic field at any time). The dispersive properties of all of the EM modes are studied because the PBG is not only for the extraordinary and ordinary modes but also for the mixed polarized modes. The equations for PBGs also are theoretically deduced. The numerical results show that the PBG and a flatbands region can be observed. The effects of the dielectric constant of dielectric background, filling factor, plasma frequency and plasma cyclotron frequency (the external magnetic field) on the dispersive properties of all of the EM modes in such 3D MPPCs are investigated in detail, respectively. Theoretical simulations show that the PBG can be manipulated by the parameters as mentioned above. Compared to the conventional dielectric-air PCs with similar structure, the larger PBG can be obtained in such 3D MPPCs. It is also shown that the upper edge of flatbands region cannot be tuned by the filling factor and dielectric constant of dielectric background, but it can be manipulated by the plasma frequency and plasma cyclotron frequency.

Effective potential energy for relativistic particles in the field of inclined rotating magnetized sphere

The dynamics of a charged relativistic particle in electromagnetic field of a rotating magnetized celestial body with the magnetic axis inclined to the axis of rotation is studied. The covariant Lagrangian function in the rotating reference frame is found. Effective potential energy is defined on the base of the first integral of motion. The structure of the equipotential surfaces for a relativistic charged particle is studied and depicted for different values of the dipole moment. It is shown that there are trapping regions for the particles of definite energies.

The Properties of Surface Plasmon Modes and Switching Gap for Extraordinary Mode in the 3-D Magnetized Plasma Photonic Crystals Based on the Voigt Effects

The properties of surface plasmon modes and switching gaps for extraordinary mode in the 3-D magnetized plasma photonic crystals (MPPCs) with body-centered-cubic lattices, that are composed of the core tellurium (Te) spheres with surrounded by the magnetized plasma shells inserted in the air, are theoretically investigated in detail by the plane wave expansion method, as the magneto-optical Voigt effects of magnetized plasma are considered (the incidence electromagnetic wave vector is perpendicular to the external magnetic field at any time). Our computing results show that the complete photonic bandgaps for extraordinary mode and two flatbands regions can be observed. The optical switching can be realized by such MPPCs, which can be tuned by the radius of core Te sphere, the plasma density and the external magnetic field, respectively. The flatbands regions are determined by the existence of surface plasmon modes. The numerical simulations also demonstrate that the interesting properties of surface plasmon modes can be found. If the thickness of magnetized plasma shell is larger than a threshold value, the band structures for extraordinary mode will be similar to those obtained from the same structure containing the pure magnetized plasma spheres. In this condition, the inserted core sphere also has no effect on the band structures. It is worth to be noticed that the upper edge frequencies of two flatbands regions will not depend on the topology of lattice. However, to the different topologies of lattices, if the thickness of magnetized plasma shell is close to zero, the frequencies of lower edges will be convergence to two different constants.

The properties of the extraordinary mode and surface plasmon modes in the three-dimensional magnetized plasma photonic crystals based on the magneto-optical Voigt effects

In this paper, the properties of the extraordinary mode and surface plasmon modes in the three-dimensional (3D) magnetized plasma photonic crystals (MPPCs) with face-centered-cubic lattices that are composed of the core tellurium (Te) spheres with surrounded by the homogeneous magnetized plasma shells inserted in the air, are theoretically investigated in detail by the plane wave expansion method, as the magneto-optical Voigt effects of magnetized plasma are considered (the incidence electromagnetic wave vector is perpendicular to the external magnetic field at any time). The optical switching or wavelength division multiplexer can be realized by the proposed 3D MPPCs. Our analyses demonstrate that the complete photonic band gaps (PBGs) and two flatbands regions for the extraordinary mode can be observed obviously. PBGs can be tuned by the radius of core Te sphere, the plasma density and the external magnetic field. The flatbands regions are determined by the existence of surface plasmon modes. Numerical simulations also show that if the thickness of magnetized plasma shell is larger than a threshold value, the band structures of the extraordinary mode will be similar to those obtained from the same structure containing the pure magnetized plasma spheres. In this case, the band structures also will not be affected by the inserted core spheres. It is also provided that the upper edges of two flatbands regions will not depend on the topology of lattice. However, the frequencies of lower edges of two flatbands regions will be convergent to the different constants for different lattices, as the thickness of magnetized plasma shell is close to zero.

Magneto-optical Faraday effects in dispersive properties for three-dimensional magnetized plasma photonic crystals

The dispersive properties of three-dimensional magnetized plasma photonic crystals composed of homogeneous magnetized plasma spheres immersed in isotropic dielectric host with face-centered-cubic lattices are theoretically studied based on plane wave expansion method, as the magneto-optical Faraday effects of magnetized plasma are considered. The equations for calculating the band structures are theoretically deduced. The photonic band gap and a flatbands region can be obtained. The influences of host dielectric constant, plasma collision frequency, filling factor, external magnetic field and plasma frequency on the dispersive properties are investigated in detail, respectively, and some corresponding physical explanations are also given. The numerical results show that the photonic band gap can be manipulated by the plasma frequency, filling factor, external magnetic field and host dielectric constant, respectively. However, the plasma collision frequency has no effects on photonic band gap. The location of flatbands region cannot be tuned by any parameters except for the plasma frequency and external magnetic field.

Magneto-Optical Faraday Effects in Dispersive Properties and Unusual Surface Plasmon Modes in the Three-Dimensional Magnetized Plasma Photonic Crystals

The dispersive properties and unusual surface plasmon modes in three-dimensional (3-D) magnetized plasma photonic crystals (MPPCs) with face-centered-cubic lattices that are composed of the core tellurium (Te) spheres surrounded by the magnetized plasma shells inserted in the air are theoretically studied in detail by the plane-wave expansion method, as the magneto-optical Faraday effects of magnetized plasma are considered. Our analysis shows that the proposed 3-D MPPCs can obtain the complete photonic band gaps, which can be manipulated by the radius of core Te sphere, the plasma density, and the external magnetic field, respectively. We also find that a flatband region can be achieved, which is determined by the existence of surface plasmon modes. If the thickness of the magnetized plasma shell is less than a threshold value, the band structures of such 3-D MPPCs will be similar to those obtained from the same structure containing the pure magnetized plasma spheres. In this case, the inserted core sphere also will not affect the band structures. It is also noticed that the upper edge of flatband region does not depend on the topology of lattice.