Magnetized Sphere Research Articles

Nondipole interaction between two uniformly magnetized spheres and its relation to superconducting levitation

Analytically solving the magnetostatic Maxwell equations in the bispherical coordinates, we calculate the magnetic field around two uniformly magnetized spheres oriented so that their magnetic moments are parallel to the axis passing through the centers of the spheres. We demonstrate that, contrary to what is often claimed in the literature, the magnetic interaction between such spheres is not equivalent to the interaction between two point magnetic dipoles placed in the centers of the spheres. The nonzero levitation force acting on a uniformly magnetized sphere or a point magnetic dipole above a superconducting sphere in the ideal Meissner state is a clear manifestation of the non-equivalence.

Magnetic field calculation of a uniformly magnetized sphere using solid angles

A new method to calculate the magnetic field of a uniformly magnetized sphere or spherical shell with surface current density K=Kosinθ using the solid angle concept is presented. The field can be shown easily to be constant inside the shell and dipole-like outside with a direct integral of Biot-Savart’s law without invoking magnetic vector potential or special scalar functions typically used for this classical problem.

Hybrid finite-amplitude periodic modes for two uniformly magnetized spheres.

We analyze a system of two uniformly magnetized spheres, one fixed and the other free to slide in frictionless contact with the surface of the first. The centers of the two magnets, and their magnetic moments, are restricted to a plane. We search for sets of initial conditions that yield finite-amplitude oscillatory periodic solutions. We extend two small-amplitude base modes, one with orbital and spin motions that are in phase and the other out of phase, to finite amplitudes and show that the motion for arbitrary oscillatory solutions can be considered to be a nonlinear superposition of these base modes. Some solutions are pure periodic finite-amplitude extensions of one base mode, while others are hybrid finite-amplitude superpositions of the two modes. Hybrid modes with rational frequency ratios are periodic and come in families defined by their frequency ratios. We further characterize hybrid periodic modes by identifying two symmetry classes that describe their relative phases. We see continuous transitions between one finite-amplitude base mode and the other, with one mode gradually transforming into the other. We also calculate frequency spectra of nonperiodic modes, show that the two base modes have well-defined frequencies even for nonperiodic states, and show that periodic solutions can give clues about the behavior of nearby nonperiodic solutions. In the limit of small amplitudes, we confirm that the computed frequencies of these modes agree with small-amplitude analytical results. We also generate a Lyapunov exponent heatmap that reflects periodic and nonperiodic regions of state space.

Non-similar modeling and numerical simulations of microploar hybrid nanofluid adjacent to isothermal sphere

Abstract In today’s era of rapid technological development, there is an increasing requirement for high-functioning investiture solutions, working liquids and materials that can satisfy the benchmarks of energy efficacy. Specifically, within the domain of heat transference-based industries, an essential challenge is to fabricate a cooling medium that can effectually cope with dissipation of substantial heat flux engendered by high-energy utilizations. At present, nanoliquids are extensively deliberated as some of the most promising aspirants for such effectual cooling mediums. The current investigation features hybrid nanoliquid flow adjacent to magnetized non-isothermal incompressible sphere. Rheological expressions representing micropolar liquid are accounted for flow formulation. The rheological analysis is developed using the boundary-layer concept. Buoyancy impact is accounted for heat transference analysis. Nanoparticles with distinct shapes are considered. The developed nonlinear systems are computed numerically and non-similar simulations are performed.

Multimode microdimer robot for crossing tissue morphological barrier

Swimming microrobot energized by magnetic fields exhibits remotely propulsion and modulation in complex biological experiment with high precision. However, achieving high environment adaptability and multiple tasking capability in one configuration is still challenging. Here, we present a strategy that use oriented magnetized Janus spheres to assemble the microdimer robots with two magnetic distribution configurations of head-to-side configuration (HTS-config) and head-to-head configuration (HTH-config), achieving performance of multiple tasks through multimode transformation and locomotion. Modulating the magnetic frequency enables multimode motion transformation between tumbling, rolling, and swing motion with different velocities. The dual-asynchronization mechanisms of HTS-config and HTH-config robot dependent on magnetic dipole-dipole angle are investigated by molecular dynamic simulation. In addition, the microdimer robot can transport cell crossing morphological rugae or complete drug delivery on tissues by switching motion modes. This microdimer robot can provide versatile motion modes to address environmental variations or multitasking requirements.

A magnetic falling-sphere viscometer

We present a falling-sphere viscometer with a magnetized sphere and fluxgate magnetometers continuously measuring the magnetic field produced at the sensor positions by the falling sphere. With a fluid volume of 15 ml and within a few seconds, we directly measure dynamic viscosities in a range between 200 and 3000 cP with a precision of 3%.

Moore–Gibson–Thompson Photothermal Model with a Proportional Caputo Fractional Derivative for a Rotating Magneto-Thermoelastic Semiconducting Material

By considering the Moore–Gibson–Thompson (MGT) equation, the current work introduces a modified fractional photothermal model. The construction model is based on the proportional Caputo fractional derivative, which is a new definition of the fractional derivative that is simple and works well. In addition, the theory of heat transfer in semiconductor materials was used in the context of optical excitation transfer and plasma processes. The proposed model was used to investigate the interaction of light and heat within a magnetized semiconductor sphere rotating at a constant angular speed. The Laplace transform was used to obtain solutions for optical excitation induced by physical field variables. Using a numerical method, Laplace transforms can be reversed. The figures show the effects of carrier lifetime, conformable fractional operator, and rotation on thermal and mechanical plasma waves, which are shown in the graphs. The theory’s predictions were compared and extensively tested against other existing models.

Diffusion separation of submicron particles by using magnetized spheres

The diffusion capture of submicron-sized particles in the gradient field formed by the magnetized ferromagnetic spheres in the external homogeneous magnetic field has been theoretically investigated. Magnetic field measurements were made with a specially designed prototype magnetometer. The simple semi-empirical formula of the magnetic force acting on the submicron particle was determined. The analytical solution of the diffusion equation for steady states was obtained. The concentration distribution of the particles in capturing regions was determined. A formula was obtained to evaluate the critical size of the submicron particles captured in this area. The effects of magnetic, hydrodynamic and geometric parameters of the investigated system on the critical size of the particles in the diffusion event were evaluated. The critical size of the particles decreased with the increase of the external magnetic field and was found to be independent of the dimensions of the spheres. As a result; the diffusion separation phenomenon in the gradient field formed by the magnetized ferromagnetic spheres is more effective than in the gradient magnetic field formed by the wires. The results obtained contribute to the development of the theory of magnetic separators using ferromagnetic matrix elements.

Angular momentum conservation and core superfluid dynamics for the pulsar J1734‐3333

AbstractPulsars emit pulsed radiation at well‐defined frequencies. In the canonical model, a pulsar is assumed to be a rotating, highly magnetized sphere made mostly of neutrons that has a magnetic dipole misaligned with respect to its rotation axis, which would be responsible for the emission of the observed pulses. The measurement of the pulse frequency and its first two derivatives allows the calculation of the braking index, n. One limitation of the canonical model is that, for all pulsars, it yields n = 3, a result that does not correspond to observational values of n. In order to contribute to the solution of this problem, we proposed a model for pulsars' rotation frequency decay assuming that the star's total moment of inertia would vary with time due to mass motions inside the core. As a result, we found that the pulsar J1734‐3333 has total angular momentum practically conserved, a phenomenon that we explain by relating the motion of neutron superfluid vortices in the core to torques associated with radiation emission.

Gravitomagnetic resonance in the field of a gravitational wave

Using the construction of the Fermi frame, the field of a gravitational wave can be described in terms of gravito-electromagnetic fields that are transverse to the propagation direction and orthogonal to each other. In particular, the gravito-magnetic field acts on spinning particles and we show that, due to the action of the gravitational wave field, a new phenomenon, that we call gravito-magnetic resonance, may appear. We give both a classical and a quantum description of this phenomenon and suggest that it can be used as the basis for a new type of gravitational wave detectors. Our results highlight the effectiveness of collective spin excitations, e.g. spin waves in magnetized materials, in detecting high frequency gravitational waves. Here we suggest that, when gravitational waves induce a precession of the electron spin, power is released in the ferromagnetic resonant mode endowed with quadrupole symmetry of a magnetized sphere. This offers a possible path to the detection of the gravito-magnetic effects of a gravitational wave.

Modeling of magnetic anomalies generated by simple geological structures through Genetic-Price inversion algorithm

A new approach to the interpretation of magnetic anomalies generated by geological structures resembling simple geometrical bodies is presented. The method is based on the Genetic-Price hybrid Algorithm (GPA) recently proposed by the authors for the inversion of potential-field data, specifically of self-potential signals. In this paper, the effectiveness of the proposed algorithm is tested on magnetic data for retrieving the parameters of the anomaly causative sources. First, the testing is performed on synthetic noise-free and noisy signals due to magnetized sphere-, dike- and fault-like models, then the analysis is extended to field magnetic anomalies. Concerning the synthetic data analyses, a very good agreement is obtained between assumed and retrieved source parameters. Specifically, the error between true and inverted parameter sets was found to be no higher than 9% even by adding 15% of Gaussian white random noise to the initial dataset. As for the study of field data, the values of depth, horizontal position, effective magnetization intensity and angle provided by the proposed GPA method compare well with those obtained by other interpretative approaches. Finally, the results of the GPA application to the inversion of magnetic data measured in the Mt. Somma-Vesuvius volcanic area are reported. In particular, the interpretation of the magnetic anomalies along a SW-NE profile in terms of multiple dikes provides information about depth and location of buried volcanic structures that match well those from other geophysical and geological analyses.

Contribution of Magnetism to the Origin of Saturn’s Rings

Abstract In this paper, we derive the magnetization relationships for magnetically uniform spherical particles of Saturn’s rings, and solve the problem of a solitary magnetized sphere and a spherical particle among identical particles scattered in a disk-like structure. We also derive differential equations of collisionless motion of particles in the gravitational and magnetic fields. A special approximation of these equations is solved exactly, and its solution suggests that the superposition of the gravitational and magnetic fields acting on diamagnetic ice particles can account for the stability of Saturn’s rings in its equatorial plane.

Braking of a Magnetized Body at the Interaction of Its Magnetic Field with a Rarified Plasma Flow

The features of the flow around and the dynamic interaction of a magnetized sphere with a hypersonic flow of a rarefied plasma are studied via physical simulation. The dependences of the coefficients of the electromagnetic drag of a sphere on the ratio of the magnetic pressure to the dynamic pressure are obtained for the axial and orthogonal orientations of the plasma flow vectors and of the body’s own magnetic field. At an magnetic field of the sphere of 0.8–1.5 T, the electromagnetic force generated in the “magnetic field of the sphere–surrounding plasma” system is comparable to the pulse injected by plasma accelerators of special spacecraft designed for forced (“active”) removal of objects of space debris from the near-Earth space via their braking with a plasma jet, removing to lower orbits, and disposal by combustion in the dense layers of the Earth’s atmosphere. Small, permanent magnets can be used arranged in a particular manner (Halbach magnetic arrays) to create energy-efficient, compact sources of the magnetic field of these objects with an induction of 0.8–1.5 T.

Metric of a rotating charged magnetized sphere

Stationary axisymmetric metric describing the exterior field of a rotating, charged sphere endowed with magnetic dipole moment is presented and discussed. It has a remarkably simple multipole structure defined by only four nonzero Hoenselaers-Perjés relativistic moments.

Periodic bouncing modes for two uniformly magnetized spheres. I. Trajectories.

We consider a uniformly magnetized sphere that moves without friction in a plane in response to the field of a second, identical, fixed sphere, making elastic hard-sphere collisions with this sphere. We seek periodic solutions to the associated nonlinear equations of motion. We find closed-form mathematical solutions for small-amplitude modes and use these to characterize and validate our large-amplitude modes, which we find numerically. Our Runge-Kutta integration approach allows us to find 1243 distinct periodic modes with the free sphere located initially at its stable equilibrium position. Each of these modes bifurcates from the finite-amplitude radial bouncing mode with infinitesimal-amplitude angular motion and supports a family of states with increasing amounts of angular motion. These states offer a rich variety of behaviors and beautiful, symmetric trajectories, including states with up to 157 collisions and 580 angular oscillations per period.

Periodic bouncing modes for two uniformly magnetized spheres. II. Scaling.

A uniformly magnetized sphere moves without friction in a plane in response to the field of a second, identical, fixed sphere and makes elastic hard-sphere collisions with this sphere. Numerical simulations of the threshold energies and periods of periodic finite-amplitude nonlinear bouncing modes agree with small-amplitude closed-form mathematical results, which are used to identify scaling parameters that govern the entire amplitude range, including power-law scaling at large amplitudes. Scaling parameters are combinations of the bouncing number, the rocking number, the phase, and numerical factors. Discontinuities in the scaling functions are found when viewing the threshold energy and period as separate functions of the scaling parameters, for which large-amplitude scaling exponents are obtained from fits to the data. These discontinuities disappear when the threshold energy is viewed as a function of the threshold period, for which the large-amplitude scaling exponent is obtained analytically and for which scaling applies to both in-phase and out-of-phase modes.

Influence of uniform magnetic field on elastic modulus in polyacrylamide ferrogels with embedded nickel nanoparticles

Polyacrylamide ferrogels with embedded nickel magnetic nanoparticles were synthesized by radical polymerization in water. The elastic modulus of ferrogels was measured under unidirectional compression in a uniform magnetic field with a strength of 0, 165, 220 and 275 Oe. With an increase in the content of nickel particles in ferrogel from 0 to 5.3% by weight, the elastic modulus in zero magnetic field increased by 60%. The application of magnetic field parallel to the direction of compression resulted in the increase of modulus, and if the field was applied perpendicular to the compression, the modulus tends to decrease. Such trends are in good agreement with the features of magnetostriction of a non-compressible uniformly magnetized sphere in a constant magnetic field.

Magnetic Field of a Compact Spherical Star under f(R, T) Gravity

We present the interior solutions of distributions of magnetized fluid inside a sphere in f(R,T) gravity. The magnetized sphere is embedded in an exterior Reissner–Nordström metric. We assume that all physical quantities are in static equilibrium. The perfect fluid matter is studied under a particular form of the Lagrangian density f(R,T). The magnetic field profile in modified gravity is calculated. Observational data of neutron stars are used to plot suitable models of magnetized compact objects. We reveal the effect of f(R,T) gravity on the magnetic field profile, with application to neutron stars, especially highly magnetized neutron stars found in x-ray pulsar systems. Finally, the effective potential Veff and innermost stable circular orbits, arising out of the motion of a test particle of negligible mass influenced by attraction or repulsion from the massive center, are discussed.

Ferromagnetic linewidth measurements employing electrodynamic model of the magnetic plasmon resonance

The mode of uniform precession, or Kittel mode, in a magnetized ferromagnetic sphere, has recently been proven to be the magnetic plasmon resonance. In this paper we show how to apply the electrodynamic model of the magnetic plasmon resonance for accurate measurements of the ferromagnetic resonance linewidth ΔH. Two measurement methods are presented. The first one employs Q-factor measurements of the magnetic plasmon resonance coupled to the resonance of an empty metallic cavity. Such coupled modes are known as magnon-polariton modes, i.e. hybridized modes between the collective spin excitation and the cavity excitation. The second one employs direct Q-factor measurements of the magnetic plasmon resonance in a filter setup with two orthogonal semi-loops used for coupling. Q-factor measurements are performed employing a vector network analyser. The methods presented in this paper allow one to extend the measurement range of the ferromagnetic resonance linewidth ΔH well beyond the limits of the commonly used measurement standards in terms of the size of the samples and the lowest measurable linewidths. Samples that can be measured with the newly proposed methods may have larger size as compared to the size of samples that were used in the standard methods restricted by the limits of perturbation theory.

Diamagnetic expulsion as a possible cause of the origin and stability of saturn’s rings

In this work, the problems of a uniformly magnetized sphere in magnetic field are solved for modeling the magnetic properties of Saturn’s rings particles, with the problem of a sphere in an infinite “disk” of evenly distributed identical spheres being formulated and solved for the first time. The found magnetic moments of the spheres are used in deriving the equations of motion of the particles in the gravitational and magnetic field. The solutions of two special cases of these equations indicate that the diamagnetic expulsion in combination with the gravitational attraction to the planet is a plausible cause of stability of Saturn’s rings, and the semi-analytically calculated formation time of the stable orbits is some tens of millennia.