Nonuniform External Magnetic Field Research Articles

Quantum correlation of the Heisenberg xxz Hamiltonian with nonuniform external magnetic field and Dzyaloshinskii–Moriya interaction

Quantum correlation of the Heisenberg xxz Hamiltonian with nonuniform external magnetic field and Dzyaloshinskii–Moriya interaction

Zig-zag dynamics in a Stern–Gerlach spin measurement

The century-old Stern–Gerlach setup is paradigmatic for a quantum measurement. We visualize the electron trajectories following the Bohmian zig-zag dynamics. This dynamics was developed in order to deal with the fundamentally massless nature of particles (with mass emerging from the Brout–Englert–Higgs mechanism). The corresponding trajectories exhibit a stochastic zig-zagging, as the result of the coupling between left- and right-handed chiral Weyl states. This zig-zagging persists in the non-relativistic limit, which will be considered here, and which is described by the Pauli equation for a non-uniform external magnetic field. Our results clarify the different meanings of ‘spin’ as a property of the wave function and as a random variable in the Stern–Gerlach setup, and they illustrate the notion of effective collapse. We also examine the case of an EPR-pair. By letting one of the entangled particles pass through a Stern–Gerlach device, the non-local influence (action-at-a-distance) on the other particle is manifest in its trajectory, e.g. by initiating its zig-zagging.

Spectral approximation scheme for a hybrid, spin-density Kohn–Sham density-functional theory in an external (nonuniform) magnetic field and a collinear exchange-correlation energy

AbstractWe provide a mathematical justification of a spectral approximation scheme known as spectral binning for the Kohn–Sham spin density-functional theory in the presence of an external (nonuniform) magnetic field and a collinear exchange-correlation energy term. We use an extended density-only formulation for modeling the magnetic system. No current densities enter the description in this formulation, but the particle density is split into different spin components. By restricting the exchange-correlation energy functional to be of a collinear LSDA form, we prove a series of results which enable us to mathematically justify the spectral binning scheme using the method of Gamma-convergence, in conjunction with auxiliary steps involving recasting the electrostatic potentials, justifying the spectral approximation by making a spectral decomposition of the Hamiltonian and “linearizing" the latter Hamiltonian.

Multi-frequency and wide-angle nonreciprocity arising from non-uniform magnetic field

We investigate the effect of non-uniform external static magnetic field on the scattering nonreciprocity of a deep-subwavelength gyrotropic particle system. Based on a scattering matrix approach, we show analytically that asymmetrical extinction cross section of the scattering system for opposite illumination directions can be accessed at multi-frequency and wide-angle regimes, in the presence of magnetic field with weak spatial non-uniformity. A simplified dual-dipole model is further employed to capture the generic physics of nonreciprocal scattering, essentially attributed to the asymmetrical magneto-electric cross interactions. In addition, typical examples are provided with full-wave numerical verifications. Our finding may open a straightforward and efficient pathway to manipulate nonreciprocal scattering at the subwavelength scale.

Numerical modelling of HTS tapes under arbitrary external field and transport current via integral method: review and application to electrical machines *

Superconductors in practical use can be subjected to spatially non-uniform and time-varying external magnetic field as well as carrying a transport current, for example, in an electrical machine. This paper verifies that the integral method can be used in situations in which the external field is spatially non-uniform, by providing both theoretical reasoning and simulation results. Variations in the integral method are reviewed, such as how to impose transport current. Further, the integral method is applied to calculate ac loss in superconducting tapes in an air-cored electrical machine in a two-stage process: the external field is calculated in a COMSOL model without superconducting tapes, and exported into the integral method model that consists of the tapes only. The time taken by the integral method is a small fraction of the time taken by the full machine model in COMSOL, which uses the T-A formulation. There are good agreements between the full COMSOL model and two-stage method incorporating the integral method.

Analytical modeling of a magnetoactive elastomer unimorph

Magnetoactive elastomers (MAEs) are capable of large deformation, shape programming, and moderately large actuation forces when driven by an external magnetic field. These capabilities enable applications such as soft grippers, biomedical devices, and actuators. To facilitate complex shape deformation and enhanced range of motion, a unimorph can be designed with varying geometries, behave spatially varying multi-material properties, and be actuated with a non-uniform external magnetic field. To predict actuation performance under these complex conditions, an analytical model of a segmented MAE unimorph is developed based on beam theory with large deformation. The effect of the spatially-varying magnetic field is approximated using a segment-wise effective torque. The model accommodates spatially varying concentrations of magnetic particles and differentiates between the actuation mechanisms of hard and soft magnetic particles by accommodating different assumptions concerning the magnitude and direction of induced magnetization under a magnetic field. To validate the accuracy of the model predictions, four case studies are considered with various magnetic particles and matrix materials. Actuation performance is measured experimentally to validate the model for the case studies. The results show good agreement between experimental measurements and model predictions. A further parametric study is conducted to investigate the effects of the magnetic properties of particles and external magnetic fields on the free deflection. In addition, complex shape programming of the unimorph actuator is demonstrated by locally altering the geometric and material properties.

Effects of external magnetic field arrangements on thermomagnetic convection in ferrofluid around heated Micro-wire

Thermomagnetic convective cooling of a heated micro-wire in quiescent ferrofluid is experimentally investigated under various non-uniform external magnetic fields produced by permanent magnets. In the past studies, in most of the cases for this geometry the external magnetic field is applied under forced convection conditions. This work provides the first published data set of heat transfer from a microwire in quiescent ferrofluid (free convection conditions) under various arrangements of external magnetic fields produced by permanent magnets. For the different arrangements, magnetic flux density and Kelvin body force density are calculated to aid discussions of the observed effects. The experiment tracked the transient temperature rise of a heated micro-wire, highlighting effects of applied magnetic field orientation, symmetry, and strength. The results showed that greater non-uniformity in radial magnetic field could enhance the cooling effects with up to 7% reduction in the heated wire temperature rise. A magnetic field aligned with the heated wire axis produced only a minor enhancement of 3% in heat transfer in contrast to application of radial magnetic fields. Surprisingly, a stronger external magnetic field did not always result in better heat transfer. Magnetophoresis of ferro-particles induced by the external magnetic field was found to be an important consideration when using permanent magnets for ferrofluid applications.

Effects of electrically conductive walls on turbulent magnetohydrodynamic flow in a continuous casting mold

In the present study, we have performed a series of numerical simulations of the turbulent liquid metal flow in a laboratory-scale setup of the continuous casting. The liquid metal flow was subjected to an external non-uniform magnetic field reproducing a realistic electromagnetic brake (EMBr) effect. The focus of this research was on the effects of the finite electrical conductivity of Hartmann walls on the flow and turbulence in the mold. To be able to simulate distributions of the electric potential and current in both the fluid and solid wall domains, we applied our recently developed and validated in-house conjugate MHD solver based on the open-source code OpenFOAM. The dynamic Large Eddy Simulation (LES) method was used to simulate the turbulent flow. The results obtained for the neutral (non-MHD) and MHD cases over a range of the imposed EMBr strengths – all for the perfectly electrically insulated walls – were compared with the available Ultrasound Doppler Velocimetry (UDV) measurements. A good agreement between simulations and experiments was obtained for all simulated cases. Next, we completed a series of simulations including a wide range of the finite electric conductivities (ranging from a weakly to perfectly conducting wall conditions) of the Hartmann walls for a fixed value of the imposed EMBr. The obtained results demonstrated a significant influence of the electric wall conductivities on the flow and turbulence reorganization. It is expected that here provided insights can be applicable for the new generation of the laboratory- and real-scale continuous casting setups.

Strong Magnetic Field Dependence of Micro-YBCO Superconductor Levitated Above Halbach Guideway

For a regular-geometry superconductor, due to a nonuniform external magnetic field, the effect of the field dependence (i.e., <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">J_c</i> anisotropy and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">J_c</i> ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> ) property) on the levitation force is complex and indistinct. For a relative microsample, its applied field is uniform, and the phenomenon caused by the field dependence should be more obvious. A novel instrument with a parallel-structure is therefore developed to accurately measure the micro force, and the device achieves a 4 mN precision. Based on this specialized apparatus, the experimental results present several rare phenomena caused by the field dependence. (a) Force attenuation (near the guideway during the superconductor descent) occurs in the small-width superconductor at the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</i> -axis⊥ <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> condition, which is attributed to <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">J_c</i> ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> ). (b) The maximum levitation force (MLF) position offset of bulks do not appear in the stack. (c) For the stack, the MLF curve varies in a sinusoidal way with the lateral position and fits well with the applied field | <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B_z</i> |, which depicts that the anisotropic feature of the stack is much stronger than that of the bulk. An analytical critical-state model based on the assumptions of a uniform external field and saturated magnetization is proposed for describing these results that accurately reflect the experimental phenomenon. In addition, the finite element simulation of the micro superconductor in COMSOL is discussed, and a force formulation from this analytical model improves the calculated result.

Nonlinear self-focusing of an intense laser beam in non-Maxwellian plasma with a non-uniform magnetic field

The present article investigates the nonlinear self-focusing of an intense laser beam circularly polarized inside a non-Maxwellian magnetized plasma. It has been assumed that the plasma is embedded in a non-uniform axial magnetic field with a positive slope. Through applying relativistic fluid momentum and Maxwell's equations, the nonlinear equation of electromagnetic wave propagation for a circular polarized laser beam with right-and left-hand polarizations has been derived. Subsequently, a differential equation was obtained for the evolution of the laser spot-size through applying the source-dependent expansion method. The equation was then solved using the fourth-order Runge-Kutta method. Effects of the simultaneous presence of the superthermal particles and non-uniform magnetic field on the evolution of laser spot-size were studied, and variations of the normalized spot-size of the laser with respect to the variables κe and κi were discussed. It was also indicated that the solution of the present study confirms the results of the Maxwellian plasma in extreme conditions. Numerical results indicate that the self-focusing of the laser beam in the presence of an external nonuniform magnetic field inside non-Maxwellian plasma was improved in comparison with Maxwellian plasma. In addition, results show that an increase in the nonuniform external magnetic field leads to the reduction of the critical power required for the self-focusing of the laser beam inside the plasma.

Local quantum uncertainty in a two-qubit Heisenberg spin chain with intrinsic decoherence

Quantum correlation plays an important role in quantum information processing, for which various quantifiers have been proposed so far. In this paper, we address the dynamics of local quantum uncertainty (LQU) as a reliable quantifier of quantum correlation in a two-qubit Heisenberg spin chain in the presence of nonuniform external magnetic field and Dzyaloshinski-Moriya interaction with intrinsic decoherence. The influences of the initial states, external magnetic field strength, Dzyaloshinski-Moriya interaction strength and intrinsic decoherence rate on the dynamics of LQU have been in detail investigated. Our analytical results show that the dynamics of LQU is strongly depended on the form of initial states. For an initial correlated state, the dynamical behaviors of LQU exhibit either monotonic decay or damped oscillations with respect to time. While for an initial separable state, quantum correlation quantified by LQU can be created due to the Dzyaloshinski-Moriya interaction and Heisenberg anisotropic interaction. Besides, the relationship between LQU and l-norm coherence or concurrence is also demonstrated in the present model.

The effect of target position on Al plasma characteristics induced by a 355 nm nanosecond laser in the presence of an external non-uniform magnetic field

In this work, the effect of target position on Al plasma characteristics induced by a 355 nm nanosecond laser in the presence of an external non-uniform magnetic field was investigated by using the optical emission spectroscopy and fast imaging. The time-resolved spectra were recorded at various sample positions within the magnetic field at different time delays. It was observed that all spectral lines emitted from the Al ions or neutral atoms were enhanced in the presence of the magnetic field, and the emission intensity reached its maximum peak at delay time of 150 ns for Al II 281.6 nm and delay time of 600ns for Al I 394.6 nm. At the early stage of plasma plume expansion, the plasma plume front at M position is longer than that of at B position. As the delay time increasing, under the confinement of magnetic pressure, the plasma plume fronts for two position are near same. The observed differences in emission intensity at the various positions were attributed to the curvature and gradient of the magnetic field.

Dynamics of quantum correlations under intrinsic decoherence in a Heisenberg spin chain model with Dzyaloshinskii–Moriya interaction

By taking into account the effect of intrinsic decoherence and by using Milburn’s dynamical master equation, we study the temporal evolution of quantum correlations in a two-qubit XXZ Heisenberg spin chain model with Dzyaloshinskii–Moriya (DM) interaction and an external nonuniform magnetic field both directed along the z-axis. We use the concurrence (C) to detect entanglement and the local quantum uncertainty (LQU) to measure discord-like correlations. We consider three cases of initial quantum states: the mixed state, the Werner state and the pure state. For the mixed initial state and the Werner initial state, our results show that the external magnetic field strongly stimulates the effect of intrinsic decoherence which can highlight the entanglement sudden death phenomenon, while the LQU is resistant to sudden death. In addition, the DM interaction makes the effect of intrinsic decoherence more pronounced. However, a weak DM interaction can markedly improve quantum correlations and thus cause the phenomenon of entanglement sudden revival. On the other hand, and especially for the initial “uncorrelated” state (in terms of entanglement and LQU) with a zero nonuniform magnetic field and no DM interaction, it is easier to generate a strong entanglement, but it is difficult to generate LQU. Finally, we have found that when the system is initially “uncorrelated,” the nonuniform magnetic field can make the system strongly correlated for very remarkable steady-state values (in particular entanglement). Other results will also be discussed.

Triple diffusion of species in fluid regime using tangent hyperbolic rheology

This study discusses double diffusion of nanoparticles and solute presuming the impacts of diffusion thermo and thermal diffusion numerically by adapting finite element method. Complex models are solved in order to examine the role of Soret and Dufour parameters on the double diffusion mechanism. The imposition of external non-uniform magnetic field makes the fluid to be capable of controlling the flow field. Consequently, such flow situations may be used in control-based applications in the field of hydro-magnetic power generation and electromagnetic metal casting phenomenon. The Brownian and thermophoresis effects have shown significant impact on double diffusion phenomenon in Weissenberg rheological fluid regime. Further, any flowing material is imperiled to magnetic field and ostensible viscous effects enhance. It can be concluded that unsteadiness effects enhance the molecular movement which results in the increment in the velocity of fluid.

Effects of applying uniform and non-uniform external magnetic fields on the optimal design of microchannel heat sinks

A numerical study is performed to investigate the effects of an external uniform and non-uniform magnetic field on the optimal geometric design and thermal performance of a microchannel heat sink. Fe3O4 nanoparticles suspended in water is used as the cooling fluid. The optimization process has been utilized for three cases: (1) in the absence of the magnetic field, (2) in the presence of a uniform magnetic field, and (3) in the presence of a non-uniform magnetic field generated by a current-carrying wire. The numerical results are validated with existing experimental and numerical works. The results indicated that; for the off-design (non-optimal) geometries, imposing a uniform magnetic field decreased the thermal resistance up to 21% and improved the heat sink performance. However, for the on-design (optimal) geometries, no significant improvement was achieved by applying a uniform magnetic field. In this case, imposing the magnetic field did not change the optimal geometry of the heat sink compared to the reference case (in the absence of a magnetic field). On the other hand, imposing a non-uniform magnetic field improved the heat sink performance up to 10% for the on-design geometries. In this case, the optimal geometry of the heat sink changed in comparison with the reference case.

The effect of external magnetic field on the collisional power absorption in helicon plasma sources

The paper reports on the effects of uniform and non-uniform external magnetic field on the power absorption in a helicon plasma source, which are computationally investigated by the CST Microwave Studio code. RF (13.56 MHz) power deposition was studied using one designs of antennas, namely, the Nagoya type-III. Argon was used as the plasma working gas at the operating pressure of 15 mTorr. We have focused on the collisional power absorption utilizing WKB approximation to describe the plasma inhomogeneity. We put discrete plasma density layers in CST. The obtained results show that the radial inhomogeneity has different effects on the power absorption at the uniform and the non-uniform external magnetic fields. It is found that at uniform external magnetic fields (i.e., B0 = 200 G), there is a specific density (nc) ranging from 1 × 1018 m−3 to 5 × 1018 m−3, before and after which the radial inhomogeneity decreases and increases the absorbed power, respectively. On the other hand, at uniform external magnetic fields (i.e., B0 = 900 G), the inhomogeneity has no regular effect on the power absorption in various plasma densities. In addition, for a given plasma density (e.g., n = 1018 m−3), as the magnetic field increases, the radial inhomogeneity effect on the power absorption would decrease for the Nagoya type-III.

Boundary-layer separation in circular diffuser flows in the presence of an external non-uniform magnetic field

Abstract. The focus of the present work is on the investigation of the separation point and its relative location in a circular diffuser carrying incompressible laminar flow in the presence of a non-uniform external magnetic field. Two different approaches are deployed in the present analysis. In the first approach, a similarity transform is applied to reduce the momentum equation to the nonlinear ordinary differential equation (ODE). The ODE is solved by a dual integral–numerical method and the separation position is directly determined. In this combined numerical–integral methodology, the integration is applied followed by a numerical method. In the second approach, the equation is solved by the least square method (LSM), and the separation position is indirectly specified. In this study it is shown that the magnetic field intensity can be manipulated to postpone the separation such that it could be eliminated totally. Comparing the results yields a good agreement. It has been concluded that by increasing the magnetic field intensity, as the Lorentz force increases, increased shear stress on the wall and delay in the occurrence of the separation position are observed.

Study of thermal performance of a ferrofluid with multivariable dependence viscosity within a wavy duct with external magnetic force

Ferrofluids are type of colloidal systems which are known as an important group of smart materials. Their physical properties adaptively change with magnetic strength. These characteristics of ferrofluid must be applied for improving the efficiency. In this work, thermal performance of a type of ferrofluid with a viscosity correlation dependence on temperature, magnetic field and volume fraction was scrutinized. FVM is applied for solving momentum, conservation and heat transfer equation. To consider the effect of solid part in thermal behavior of system, the conjugate heat transfer was considered. The wire is placed in the bottom of channel, and the equation of non-uniform external magnetic field is defined as user function. The results indicated in a comparison of studied parameters as non-dimensional variables, it is demonstrated magnetic number and wave amplitude result in the maximum impact on improving Nu and the worst impact on friction coefficient and pressure loss correspondence to volume fraction and Reynolds number. The results also predicted significant changes in viscosity under influence of effective parameters, especially Kelvin force.

Natural convection of a non-Newtonian ferrofluid in a porous elliptical enclosure in the presence of a non-uniform magnetic field

In the present study, laminar natural convection of a non-Newtonian ferrofluid inside an elliptical porous cavity was numerically simulated in the presence of a non-uniform external magnetic field. This natural convection problem was relevant to the cooling of micro-sized electronic devices. The well-known finite volume method was employed to discretize the governing equations for ferrofluid flow under the effect of an external magnetic field. The effects of pertinent non-dimensional numbers including the Rayleigh number, the magnetic number, the power-law index, and the Darcy number were studied on the flow pattern and the heat transfer rate of the non-Newtonian ferrofluid. The results showed that by applying the magnetic field by a wire, the overall heat transfer rate increased significantly. Moreover, to achieve the maximum heat transfer enhancement, the wire should have been placed at the center of the elliptical walls of the enclosure. It was also shown that the impact of the power-law index on the heat transfer rate was considerable, and using a shear-thinning liquid increased the average Nusselt number in the porous elliptical enclosure.

The Features of Ring-Shaped Deposit Formation upon Evaporation of Magnetic Colloid Droplets in a Magnetic Field

The structure of deposits resulting from the evaporation of magnetic colloid droplets has been experimentally studied. It has been shown that the deposit has the largest thickness in the center and at the boundary of a droplet; i.e., a ring-shaped deposit is formed. The width of the ring-shaped (boundary) region of the deposit has been measured and shown to depend on colloid concentration and the action of a nonuniform external magnetic field. In particular, it has been found that, under the action of a magnetic field having a gradient directed to the droplet center, the thickness and width of the ring-shaped region of the deposit decrease.