An equivalent magnetic dipoles model for quantitative damage recognition of broken wire

By simplifying saturatedly magnetized wire-rope to magnetic dipoles of the same magnetic field strength, an equivalent magnetic dipoles model is developed and the measuring principle for recognising damage of broken wire was presented. The relevant calculation formulas were also deduced. A composite solution method about nonlinear optimization was given. An example was given to illustrate the use of the equivalent magnetic dipoles method for quantitative damage recognition, and demonstrates that the result of this method is consistent with the real situation, so the method is valid and practical. wire-rope, damage of broken wires, quantitative recognition, equivalent magnetic dipoles, simulate

Aggregation-induced suppression of quantum tunneling by manipulating intermolecular arrangements of magnetic dipoles

The relaxation time under zero field reflects the memory retention capabilities of single-molecule magnets(SMMs)when used as storage devices.Intermolecular magnetic dipole interaction is ubiquitous in aggregates of magnetic molecules and can greatly influence relaxation times.However,such interaction is often considered harmful and challenging to manipulate in molecular solids,especially for high-performance lanthanide single-ion magnets(SIMs).By an elaborately designed combination of ion pairing and hydrogen bonding,we have synthesized two pseudo-D5h SIMs with supramolecular arrangements of magnetic dipoles in staggered and side-by-side patterns,the latter of which exhibits a 104-fold slower zero-field relaxation time at 2 K.Intriguingly,the side-by-side complex exhibits a significantly accelerated magnetic relaxation upon diamagnetic dilution,contrary to the general trend observed in the staggered complex.This strongly reveals the presence of aggregation-induced suppression of quantum tunneling in a side-by-side arrangement,which has not been observed in mononuclear SMMs.By leveraging ion-pairing aggregation and converting to a side-by-side pattern,this study successfully demonstrates an approach to transform a harmful intermolecular dipole interaction into a beneficial one,achieving aτQTM of 980 s ranking among the best-performance SMMs.

Numerical Analysis of the Magnetic Dipole Effect on a Radiative Ferromagnetic Liquid Flowing over a Porous Stretched Sheet

The effects of a magnetic dipole on a nonlinear thermally radiative ferromagnetic liquidflowing over a stretched surface in the presence of Brownian motion and thermophoresis are investigated.By means of a similarity transformation,ordinary differential equations are derived and solved afterwards using a numerical(the BVP4C)method.The impact of various parameters,namely the velocity,temperature,concentration,is presented graphically.It is shown that the nanoparticles properties,in conjunction with the magnetic dipole effect,can increase the thermal conductivity of the engineered nanofluid and,consequently,the heat transfer.Comparison with earlier studies indicates high accuracy and effectiveness of the numerical approach.An increase in the Brow-nian motion parameter and thermophoresis parameter enhances the concentration and the related boundary layer.The skin-friction rises when the viscosity parameter is increased.A larger value of the ferromagnetic para-meter results in a higher skin-friction and,vice versa,in a smaller Nusselt number.

Impact of a Magnetic Dipole on Heat Transfer in Non-Conducting Magnetic Fluid Flow over a Stretching Cylinder

The thermal behavior of an electrically non-conducting magnetic liquid flowing over a stretching cylinder under the influence of a magnetic dipole is considered.The governing nonlinear differential equations are solved numerically using a finite element approach,which is properly validated through comparison with earlier results available in the literature.The results for the velocity and temperature fields are provided for different values of the Reynolds number,ferromagnetic response number,Prandtl number,and viscous dissipation parameter.The influence of some physical parameters on skin friction and heat transfer on the walls of the cylinder is also investigated.The applicability of this research to heat control in electronic devices is discussed to a certain extent.

A Simple Mechanism for Generating a Geomagnetic Field

On the basis of the ideal gas model, the polarization of charges in the mantle was obtained, a physical and mathematical model was constructed, and estimated calculations of the dipole mode of the Earth’s magnetic field were performed, taking into account the speed of its angular rotation, the parameters of density and temperature, the chemical composition, the ionization potential, the dielectric constant and the percentage of the main chemical compounds of the mantle substance.

Moments of Inertia, Magnetic Dipole Moments, and Electric Quadrupole Moments of the Lithium Isotopes

The single-particle Schrödinger fluid model is designed mainly to calculate the moments of inertia of the axially symmetric deformed nuclei by assuming that each nucleon in the nucleus is moving in a single-particle potential which is deformed with time t, through its parametric dependence on a classical shape variable α(t). Also, the Nilsson model is designed for the calculations of the single-particle energy levels, the magnetic dipole moments, and the electric quadrupole moments of axially symmetric deformed nuclei by assuming that all the nucleons are moving in the field of an anisotropic oscillator potential. On the other hand, the nuclear superfluidity model is designed for the calculations of the nuclear moments of inertia and the electric quadrupole moments of deformed nuclei which have no axes of symmetry by assuming that the nucleons are moving in a quadruple deformed potential. Furthermore, the cranked Nilsson model is designed for the calculations of the total nuclear energy and the quadrupole moments of deformed nuclei which have no axes of symmetry by modifying the Nilsson potential to include second and fourth order oscillations. Accordingly, to investigate whether the six p-shell isotopes 6Li, 7Li, 8Li, 9Li, 10Li, and 11Li have axes of symmetry or not, we applied the four mentioned models to each nucleus by calculating their moments of inertia, their magnetic dipole moments, and their electric quadrupole moments by varying the deformation parameter β and the non-axiality parameter γ in wide ranges of values for this reason. Hence for the assumption that these isotopes are deformed and have axes of symmetry, we applied the single-particle Schrödinger fluid model and the Nilsson model. On the other hand, for the assumption that these isotopes are deformed and have no axes of symmetry, we applied the cranked Nilsson model and the nuclear super fluidity model. As a result of our calculations, we can conclude that the nucleus 6Li may be assumed to be deformed and has an axis of symmetry.

Numerical Analysis on Magnetic-induced Shear Modulus of Magnetorheological Elastomers Based on Multi-chain Model

Based on the magnetic interaction energy, using derivative of the magnetic energy density, a model is proposed to compute the magnetic-induced shear modulus of magnetorheological elastomers. Taking into account the influences of particles in the same chain and the particles in all adjacent chains, the traditional magnetic dipole model of the magnetorheological elastomers is modified. The influence of the ratio of the distance etween adjacent chains to the distance between adjacent particles in a chain on the magnetic induced shear odulus is quantitatively studied. When the ratio is large, the multi-chain model is compatible with the single chain model, but when the ratio is small, the difference of the two models is significant and can not be neglected. Making certain the size of the columns and the distance between adjacent columns, after constructing the computational model of BCT structures, the mechanical property of the magnetorheological elastomers composed of columnar structures is analyzed. Results show that, conventional point dipole model has overrated the magnetic-induced shear modulus of the magnetorheological elastomers. From the point of increasing the magnetic-induced shear modulus, when the particle volume fraction is small, the chain-like structure exhibits better result than the columnar structure, but when the particle volume fraction is large,the columnar structure will be better.

Calculation of Constitutive Parameters from Electric and Magnetic Field Measurements in an Anisotropic Medium with a Triaxial Instrument

A hypothetical electric and magnetic induction tensor is considered in an anisotropic medium. The sources are magnetic dipoles. In such a medium, constitute parameters can be calculated by combining electric and magnetic field measurements. Constitutive parameters are not a scalar in this case. They are tensors, so parameters have at least both horizontal and vertical components in a uniaxial medium. These calculated parameters from the field measurement are horizontal and vertical conductivity, permittivity, and magnetic permeability. Operating frequency range is also quite large. It is up to 4 GHz. A hypothetical instrument should measure gradient fields both electric and magnetic types as well.

Characterization of the Elastic-plastic Region Based on Magnetic Memory Effect

Detecting stress concentration, especially critical stress state leading to structure damage or failure, is one of the most important tasks of equipment diagnosis. Metal magnetic memory technique needs further research to evaluate stress concentration quantitatively due to ambiguous physical mechanism, though it has potential to detect early defects in ferromagnetic materials. Mild Q235 steel defective specimens in demagnetization state were loaded in tension up to visible necking, with magnetic memory signals measurement made at increasing stress levels. Magnetic signals varied greatly under first several loadings and subsequently tended to stability in the elastic region, which showed that the magnetization always approaches the anhysteretic magnetization curve and was explained by the theory of magnetomechanical effect. In the plastic stage, an abnormal wave occurred in the stress concentration zone and its height value was sensitive to plastic deformation levels and dependent on the distance between the probe and defect, in accordance with the simulation results based on the magnetic dipole model. Different magnetic signal characteristics in the elastic-plastic region indicate that the magnetic memory technique can identify macroyielding and early damage, which is of profound significance for ensuring safe operation of equipment in service.

Calculation and correction of magnetic object positioning error caused by magnetic field gradient tensor measurement

Magnetic field gradient tensor measurement is an important technique to obtain position information of magnetic objects. When using magnetic field sensors to measure magnetic field gradient as the coefficients of tensor, field differentiation is generally approximated by field difference. As a result, magnetic objects positioning by magnetic field gradient tensor measurement always involves an inherent error caused by sensor sizes, leading to a reduction in detectable distance and detectable angle. In this paper, the inherent positioning error caused by magnetic field gradient tensor measurement is calculated and corrected by iterations based on the systematic position error distribution patterns. The results show that, the detectable distance range and the angle range of an ac magnetic object（2.44 Am^2@1 kHz） can be increased from（0.45 m, 0.75 m）,（0？, 25？） to（0.30 m, 0.80 m）,（0？,80？）, respectively.

Shim coil design for Halbach magnet by equivalent magnetic dipole method

Low-field nuclear magnetic resonance magnet（2 MHz） is required for rock core analysis. However, due to its low field strength, it is hard to achieve a high uniform B0 field only by using the passive shimming. Therefore, active shimming is necessarily used to further improve uniformity for Halbach magnet. In this work, an equivalent magnetic dipole method is presented for designing shim coils. The minimization of the coil power dissipation is considered as an optimal object to minimize coil heating effect, and the deviation from the target field is selected as a penalty function term. The lsqnonlin optimization toolbox of MATLAB is used to solve the optimization problem. Eight shim coils are obtained in accordance with the contour of the stream function. We simulate each shim coil by ANSYS Maxwell software to verify the validity of the designed coils. Measurement results of the field distribution of these coils are consistent with those of the target fields.The uniformity of the B0 field is improved from 114.2 ppm to 26.9 ppm after using these shim coils.

3-D Magnetic Sensor Module for Locating and Tracking MEMS Swallowable Capsule Based on Scalar Form of Magnetic Dipole Model

MEMS swallowable capsule is a novel technology in the non-invasive surgery. This technology provides a way to diagnose directly into the deep intestinal where the traditional invasive technology implemented, such as X-Ray, endoscopy. It is a key for us to locate and track the position of a MEMS capsule in clinical applications. To solve this problem, we implemented a magnetic sensor module based on the scalar form of the magnetic dipole model,which was designed with very small size （5.2 ＊ 2. 1 ＊ 1.2 em） and easy to assemble to satisfy the system requirement. Here we discuss in detail the principle of magnetic dipole model, rules of selecting sensor and functions of the module. Some trials are established to test the characteristic of the module. The results of the Cm experiment demonstrates that the module follows the rules of the new magnetic dipole model form.

Energy levels and magnetic dipole transition parameters for the nitrogen isoelectronic sequence

Theoretical calculations of the energy levels and magnetic dipole transition parameters for the 1s^(2)2s^(2)2p^(3) and 1s^(2)2p^(5) configurations of nitrogen isoelectronic sequence with Z=21-30 are performed using multi-congfiguration Dirac-Fock(MCDF)method.Based on the relativistic computational code GRASP2k compiled within the framework of MCDF method,the electron correlations,Breit interaction and QED effects are well treated in detail.The energy levels,line strengths and transition rates of magnetic dipole transition are obtained and compared with the experimental data avail-able.For most cases,good agreements are achieved and the relative differences of them are less than 0.114%,8.43% and 9.80%,respectively.The scaling laws of the fine structure splitting and transition rate are obtained on the isoelec-tronic sequence and the corresponding physical mechanisms are discussed.The data sets for tables are openly available at https://www.doi.org/10.57760/sciencedb.j00113.00022.

Interaction forces between soft magnetic particles in uniform and non-uniform magnetic fields

The influence of the magnetization of a soft magnetic sphere on the surrounding magnetic field is measured and characterized.The interaction force between two soft magnetic particles is directly measured using an ultra precision load sensor in uniform and non-uniform magnetic fields. The interaction force largely follows an inverse fourth power law as a function of separation distance between particle centers. At small distances,the effect of magnetization of one particle on the magnetization of its adjacent particle causes the attractive（repulsive） force to be larger（smaller） than that predicted by the inverse fourth power law.The theoretical prediction based on a modified dipole model,that takes into account the coupling effect of the magnetization among soft magnetic particles,gives excellent agreement with the measured force in a uniform magnetic field.The interaction force under a non-uniform applied magnetic field can be reasonably predicted using the dipole-dipole interaction model when the local magnetic field is used to determine the magnetization.

Angular dependence of vertical force and torque when magnetic dipole moves vertically above flat high-temperature superconductor

The interaction between a permanent magnet(PM)assumed as a magnetic dipole and a flat high-temperature superconductor(HTS)is calculated by the advanced frozen-image model.When the dipole vertically moves above the semiinfinite HTS,the general analytical expression of vertical force and that of torque are obtained for an arbitrary angle between the magnetization direction of the PM and the c axis of the HTS.The variations of the force and torque are analyzed for angle and vertical movements in both zero-field cooling(ZFC)condition and field cooling(FC)condition.It is found that the maximum vertical repulsive or attractive force has the positive or negative cosine relation with the angle.However,the maximum torque has the positive or negative sine relation.From the viewpoint of the rotational equilibrium,the orientation of the magnetic dipole with zero angle is deemed to be an unstable equilibrium point in ZFC,but the same orientation is considered as a stable equilibrium point in FC.In addition,both of the variation cycles of the maximum force and torque with the angle areπ.

Gauge Invariance of a Time-Dependent Harmonic Oscillator in Magnetic Dipole Approximation

A manifestly gauge-invariant formulation of non-relativistic quantum mechanics is applied to the case of time-dependent harmonic oscillator in the magnetic dipole approximation. A general equation for obtaining gauge-invariant transition probability amplitudes is derived.

Equivalent magnetic dipole method used to design gradient coil for unilateral magnetic resonance imaging

The conventional magnetic resonance imaging(MRI)equipment cannot measure large volume samples nondestructively in the engineering site for its heavy weight and closed structure.In order to realize the mobile MRI,this study focuses on the design of gradient coil of unilateral magnet.The unilateral MRI system is used to image the local area above the magnet.The current density distribution of the gradient coil cannot be used as a series of superconducting nuclear magnetic resonance gradient coils,because the region of interest(ROI)and the wiring area of the unilateral magnet are both cylindrical side arc surfaces.Therefore,the equivalent magnetic dipole method is used to design the gradient coil,and the algorithm is improved for the special case of the wiring area and the ROI,so the X and Y gradient coils are designed.Finally,a flexible printed circuit board(PCB)is used to fabricate the gradient coil,and the magnetic field distribution of the ROI is measured by a Gauss meter,and the measured results match with the simulation results.The gradient linearities of x and y coils are 2.82%and 3.56%,respectively,less than 5%of the commercial gradient coil requirement.

Ray-tracing simulations of whistler-mode wave propagation in different rescaled dipole magnetic fields

Kinetic simulation is a powerful tool to study the excitation and propagation of whistler-mode waves in the Earth’s inner magnetosphere.This method typically applies a scaled-down dipole magnetic field to save computational time.However,it remains unknown whether whistler wave propagation in the scaled-down dipole field is consistent with that in the realistic dipole field.In this work,we develop a ray-tracing code with a scalable dipole magnetic field to address this concern.The simulation results show that parallel whistler waves at different frequencies gradually become oblique after leaving the equator and propagate in different raypaths in a dipole magnetic field.During their propagation,the higher frequency waves tend to have larger wave normal angles at the same latitude.Compared with the wave propagation in a realistic dipole field,the wave raypath and wave normal remain the same,whereas the wave amplification or attenuation is smaller because of the shorter propagation time in a scaled-down dipole field.Our study provides significant guidance for kinetic simulations of whistler-mode waves.

Strong near-field couplings of anapole modes and formation of higher-order electromagnetic modes in stacked all-dielectric nanodisks

We theoretically study the near-field couplings of two stacked all-dielectric nanodisks,where each disk has an electric anapole mode consisting of an electric dipole mode and an electric toroidal dipole(ETD)mode.Strong bonding and anti-bonding hybridizations of the ETD modes of the two disks occur.The bonding hybridized ETD can interfere with the dimer’s electric dipole mode and induce a new electric anapole mode.The anti-bonding hybridization of the ETD modes can induce a magnetic toroidal dipole(MTD)response in the disk dimer.The MTD and magnetic dipole resonances of the dimer form a magnetic anapole mode.Thus,two dips associated with the hybridized modes appear on the scattering spectrum of the dimer.Furthermore,the MTD mode is also accompanied by an electric toroidal quadrupole mode.The hybridizations of the ETD and the induced higher-order modes can be adjusted by varying the geometries of the disks.The strong anapole mode couplings and the corresponding rich higher-order mode responses in simple all-dielectric nanostructures can provide new opportunities for nanoscale optical manipulations.

Observation of Magnetic Dipole Forbidden Transitions in LHD and Its Application to Burning Plasma Diagnostics

Magnetic dipole forbidden （M1） transition was studied in large helical device （LHD） and F-, Si- and Ti-like M1 transitions are successfully observed for highly ionized Ar, Kr, Mo and Xe ions. The wavelengths measured in visible range for the heavy elements, which are carefully determined with extremely small uncertainties of 0.02 - 0.05 A as a standard wavelength of usual electric dipole （El） plasma emissions, are compared with theoretical predictions. The result shows a good agreement with recent Hatree-Fock calculation including semi-empirical adjustment. The M1 intensity for the F-like ions is examined by analyzing the intensity ratio of M1 to El. Density dependence of the ratio is experimentally verified by comparing with collisional- radiative model calculation on level population. The M1/E1 line ratio for the F-like ions is applied to the α （He^2＋） particle diagnostics in ITER, in which a steady-state operation of burning plasmas based on D-T fusion reaction is expected with α particle heating. Unfortunately, the present estimation suggests a negative result for the α particle measurement because the ratio is largely enhanced by the collisional excitation with bulk ions due to high ion temperature of ITER of 10 keV as assumed and the resultant effect of the collisional excitation with α particles becomes less. Meanwhile, the M1 transition, in particular, Ti-like WLIII （W^52＋） transition （3627 A） emitted in visible range, is very useful for diagnostics of the impurity behavior and the core plasma parameters in ITER.