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Magnetometers have received considerable attention in recent years. Magnetic components offer an alternative methodology to improve the sensitivity. Due to their exceedingly small structural dimensions, metasurfaces exhibit significant competitiveness in field modulation. A magnetic field concentration phenomenon of spheres at the nanoscale is presented in this paper. The sensitivity of a magnetometer is, therefore, improved through the enhanced static or quasistatic magnetic field by the nanosphere concentrator. Magnetic field redistribution due to the assistance of nanospheres is discussed in this paper using the finite element method. The numerical method is verified with classical analytical equations with a single sphere. The simulation results show that the magnetic field concentrates in the near field behind the nanosphere along the direction of the magnetic flux density. The radius, material or permeability exactly, and distribution are critical parameters to the concentration strength. The magnetic gain of a single nanosphere with typical positive permeability of the typical soft magnetic material reaches 3, and thus, the field along the magnetic flux direction concentrates. Furthermore, the amplification factor is more prominent with the nanosphere arrays compared to a single sphere with the same scale of size, and amplification improves with the sphere numbers and distributions in the array arrangement, which provides a novel approach for the designing of the magnetic flux concentrator being monolithically integrated with the magnetometer probe. Our simulation results provide a new degree of freedom by using nanoscale structures to manipulate magnetic fields. [ABSTRACT FROM AUTHOR]

The study of the behavior of magnetic skyrmions in local magnetic fields' nanometric length-scale has gained increasing interest in recent years due to the theoretical proposal of magnetic skyrmion–superconducting vortex pairs as potential hosts for topologically protected bound states, which hold high promise for applications in quantum computing. From a magnetic interaction point-of-view, the key interest lies in understanding the skyrmion dynamics triggered by the magnetic energy landscape generated by the superconducting vortex. Here, we present a micromagnetic study of the dynamics of nanometric skyrmions inside a Gaussian magnetic field profile, which is used as a simplified version of the vortex magnetic flux. On the one hand, our calculations show that local non-linear magnetic fields can be very effective in controlling the dynamics of magnetic skyrmions; in particular, they offer the appealing possibility to manipulate skyrmions in a two dimensional space. On the other hand, they also show that the dynamics of a skyrmion in a local magnetic field can be manipulated via a uniform external magnetic field without any change in the magnetic field gradient. An analytical expression for the skyrmion velocity is given, and the corresponding microscopic dynamics are confirmed by the micromagnetic simulations. This work is expected to motivate more theoretical and experimental studies of the behavior of magnetic skyrmions in proximity to superconducting vortices. [ABSTRACT FROM AUTHOR]

Although high-temperature superconducting induction motors have a simple structure, they are distinguished by their high efficiency and high power density. However, an accurate theoretical model that defines the primary electrical characteristics controlling the motor has not been established because of the nonlinear characteristics of high-temperature superconducting squirrel-cage rotor winding. As part of establishing such a model, an experiment was conducted to analyze the relationship between the induced voltage of the rotor bar in a high-temperature superconducting squirrel-cage rotor winding and stator-side quantities (voltage and transport current), as well as its rotation characteristics. A subject was a 1.5 kW class induction motor using Bi–Sr–Ca–Cu–O high-temperature superconducting rotor bars and the experiment was performed at a temperature and a frequency of 77 K and 60 Hz, respectively. The induced voltages of the rotor bars were measured by applying a rotating magnetic field and exhibited a distorted waveform characterized by a third-order harmonic in a magnetic flux flow state. Despite the distorted voltage waveform of the rotor bar, the stator transport current responsible for driving the induction motor remained unaffected and the motor initiated rotation in a slip rotation mode. From the above results, it was experimentally clarified that a stator voltage exceeding the critical current of the rotor bar must be applied when starting the induction motor. It was also shown that the rotor bar can be regarded as a constant resistance for a constant effective value of the stator current when transitioning the motor into a slip rotation state. [ABSTRACT FROM AUTHOR]

By the Aharonov–Casher theorem, the Pauli operator P has no zero eigenvalue when the normalized magnetic flux α satisfies | α | < 1 , but it does have a zero energy resonance. We prove that in this case a Lieb–Thirring inequality for the γ -th moment of the eigenvalues of P + V is valid under the optimal restrictions γ ≥ | α | and γ > 0 . Besides the usual semiclassical integral, the right side of our inequality involves an integral where the zero energy resonance state appears explicitly. Our inequality improves earlier works that were restricted to moments of order γ ≥ 1 . [ABSTRACT FROM AUTHOR]

In this paper, we introduce the dual magnetic trajectories traced by the dual Frenet vectors of any dual curves in dual space via the dual Lorentz force, and then we give the characterizations of dual magnetic curves. Moreover, we define the dual flux ruled surfaces corresponding to the Killing vectors on the dual unit sphere and identify the conditions for these surfaces to be minimal or developable. Additionally, we present certain characterizations related to these surfaces. We demonstrate the visual representations of some dual flux ruled surfaces in some examples. [ABSTRACT FROM AUTHOR]

This study examines how fractional derivatives affect the theory of curves and related surfaces, an application area that is expanding daily. There has been limited research on the geometric interpretation of fractional calculus. The present study applied the Caputo fractional calculation method, which has the most suitable structure for geometric computations, to examine the effect of fractional calculus on differential geometry. The Caputo fractional derivative of a constant is zero, enabling the geometric solution and understanding of many fractional physical problems. We examined flux tubes, which are magnetic surfaces that incorporate these lines of magnetic fields as parameter curves. Examples are visualized using mathematical programs for various values of Caputo fractional analysis, employing theory‐related examples. Fractional derivatives and integrals are widely utilized in various disciplines, including mathematics, physics, engineering, biology, and fluid dynamics, as they yield more numerical results than classical solutions. Also, many problems outside the scope of classical analysis methods can be solved using the Caputo fractional calculation approach. In this context, applying the Caputo fractional analytic calculation method in differential geometry yields physically and mathematically relevant findings, particularly in the theory of curves and surfaces. [ABSTRACT FROM AUTHOR]

In this paper, we study (0,2) two-dimensional theories in type IIB configurations with D5 branes wrapping blow-up P 1 cycles of deformed resolutions for A n singularities or in T-dual IIA configurations with suspended D4 branes. We consider deformations of four-dimensional = 2 , ∏ i = 1 n U (N i) theories with general superpotentials for the adjoint and bifundamental fields together with fundamental flavors and reduce to two dimensions on a two-torus in the presence of magnetic fluxes and FI terms. [ABSTRACT FROM AUTHOR]

As the simplest free-living animal, Trichoplax adhaerens (Placozoa) is emerging as a powerful paradigm to decipher molecular and cellular bases of behavior, enabling integrative studies at all levels of biological organization in the context of metazoan evolution and parallel origins of neural organization. However, the progress in this direction also depends on the ability to maintain a long-term culture of placozoans. Here, we report the dynamic of Trichoplax cultures over 11 years of observations from a starting clonal line, including 7 years of culturing under antibiotic (ampicillin) treatment. This study revealed very complex population dynamics, with seasonal oscillation and at least partial correlations with the solar radio emission flux and the magnetic field disturbance parameters. Notable, the analysis of the distribution of Fe2+ in living animals revealed not only its high abundance across most cells but also asymmetric localizations of Fe2+ in unidentified cells, suggesting that these Fe2+ intracellular patterns might be coupled with the animal's bioenergetics. We hypothesize that placozoans might have magnetoreception, which can be experimentally tested in future studies. In sum, Trichoplax , in particular, and Placozoa, in general, can be viewed as prospective reference species in traditional evolutionary and system biology but have the yet unexplored potential for planetary ecology and space biomedicine. [ABSTRACT FROM AUTHOR]

Recent high angular resolution ALMA observations have revealed rich information about protoplanetary discs, including ubiquitous substructures and three-dimensional gas kinematics at different emission layers. One interpretation of these observations is embedded planets. Previous 3D planet–disc interaction studies are either based on viscous simulations or non-ideal magnetohydrodynamics (MHD) simulations with simple prescribed magnetic diffusivities. This study investigates the dynamics of gap formation in 3D non-ideal MHD discs using non-ideal MHD coefficients from the look-up table that is self-consistently calculated based on the thermochemical code. We find a concentration of the poloidal magnetic flux in the planet-opened gap (in agreement with previous work) and enhanced field-matter coupling due to gas depletion, which together enable efficient magnetic braking of the gap material, driving a fast accretion layer significantly displaced from the disc mid-plane. The fast accretion helps deplete the gap further and is expected to negatively impact the planet growth. It also affects the corotation torque by shrinking the region of horseshoe orbits on the trailing side of the planet. Together with the magnetically driven disc wind, the fast accretion layer generates a large, persistent meridional vortex in the gap, which breaks the mirror symmetry of gas kinematics between the top and bottom disc surfaces. Finally, by studying the kinematics at the emission surfaces, we discuss the implications of planets in realistic non-ideal MHD discs on kinematics observations. [ABSTRACT FROM AUTHOR]

In traditional inductor design with planar windings, the magnetic field distribution may not be well-organized, leading to significant winding loss, particularly at high switching frequencies. This study explores the relationship between current distribution and magnetic field distribution in the winding region. Unlike conventional magnetic flux distribution, which directs a large portion of the magnetic field vertically through the windings in the winding region, this work introduces a structure that maintains most of the magnetic flux parallel to the foil windings through the application of quasi-distributed air gaps. This paper presents a design methodology for a high-frequency foil winding inductor with high flux variation. Building on this concept, a high-power density, low loss inductor with foil windings is designed based on the four-switch buck-boost (FSBB) converter. Experimental results demonstrate that the proposed inductor design significantly reduces winding loss in inductors with planar windings. [ABSTRACT FROM AUTHOR]

Magnetic flux ropes are a fundamental component in both space and laboratory plasmas. We present a Hall-MHD simulation exploring the interaction between two isolated magnetic flux ropes under mesoscale solar wind conditions. The interaction interface is resolved with a resolution approaching the kinetic scale, to reveal unprecedented details of this process. As we replicate previous findings that such interactions can lead to the formation of two new ropes, we also find that magnetic reconnection occurs in multiple locations inside the central current sheet, leading to transient small flux ropes, which is qualitatively consistent with previous magnetospheric multiscale observations. Consequently, each field line undergoes multiple reconnections that alter its connectivity before it exits the current sheet. Later, each flux rope divides into two branches: the reconnected flux moving away from the current sheet to form the transition regions of the new ropes and the remnant flux sustaining the current sheet. For each magnetic flux rope (MFR), the core field reconnects after most surface fields are reconnected so that the reconnecting MFRs maintain a relatively symmetric shape. These results in unprecedented detail highlight the complex internal dynamics and call for further observational and theoretical studies. [ABSTRACT FROM AUTHOR]

The use of segmented stator and rotor designs in AC electric machine construction offers several significant advantages, including a high-copper fill factor, increased torque density, improved field-weakening performance, simplified manufacturing processes, and enhanced mechanical strength. Additionally, segmented designs allow for the incorporation of oriented steel—either partially or fully—which exhibits excellent magnetic properties in the rolling direction, resulting in more efficient machine performance. However, lamination segmentation also introduces challenges. Parasitic air gaps between segments and an increased number of cut edges in the assembled stack can alter the magnetic properties of the machine, potentially leading to degraded performance. Furthermore, the use of oriented steel remains complex, as its highly nonlinear magnetic properties vary depending on the direction of the magnetic flux. This paper reviews the widely adopted stator and rotor segmentation techniques available in the literature, discussing their potential benefits and limitations. It also covers key aspects such as popular manufacturing approaches, the impact of segmentation on machine performance, advanced finite-element analysis (FEA) techniques for numerical modeling, and experimental methods for evaluating the performance of segmented stator and rotor constructions in AC machines. By addressing these areas, this work provides a comprehensive resource for machine designers seeking to develop AC machines with segmented stators and rotors. [ABSTRACT FROM AUTHOR]

This paper proposes a novel consequent‐pole dual‐stator linear permanent magnet vernier machine (DS‐LPMVM) with PM in the mover slot opening, which has a bi‐directional flux modulation effect. The novelty of the proposed machine consists of consequent‐pole double‐sided topology with toroidal windings placed in the mover slot, as well as PMs both on the stator and mover slot to improve the air gap magnetic field. The dual‐stator adopts misalignment structure to suppress detent force and produce steady thrust. The electromagnetic parameters of the proposed DS‐LPMVM are evaluated and quantitatively compared with the conventional linear permanent magnet vernier machine (C‐LPMVM) in terms of air‐gap flux density, no‐load back EMF, inductance, and thrust. The geometrical parameters are designed to reduce the detent force. By analyzing the optimized structure parameters of the two machines, the good electromagnetic performances of the proposed machine are verified by the finite element method (FEM) and semi‐analytical method, and both results of the two methods are basically the same. It is found that the amount of PMs for the proposed machine is reduced by 20% compared to the C‐LPMVM, but the average thrust is increased by 20.7% and the thrust ripple is reduced to 4.04%. The results show that the proposed DS‐LPMVM has better flux modulation effect and thrust characteristics than C‐LPMCM. Finally, a 12‐slot, 10‐pole pairs prototype was manufactured and tested. © 2024 Institute of Electrical Engineers of Japan and Wiley Periodicals LLC. [ABSTRACT FROM AUTHOR]

The problem of axisymmetric steady magnetic field continuation from flat boundary surface of ferromagnetic is formulated for magnetic flux and scalar potential. Boundary conditions for magnetic flux are not classical because on boundary magnetic flux is unknown and its normal derivative equal zero. The formulation for scalar potential is Cauchy's problem for elliptical partial differential equation. Analytical solutions of the problem are obtained by method of partial solutions, which depend on parameter continuously, and Hankel's integral transformation. It is shown that there are similar properties in problems of axisymmetric fields continuation from flat boundaries of ideal conductor for magnetic field and conductor for steady electric field. It is fixed that field lines, which bound unknown profile, are determined directly by solution of Cauchy's problem for one from two functions. Equipotential lines are calculated to determine of electromagnetic pole profile [ABSTRACT FROM AUTHOR]

In this paper, a two-DOF L-shaped yoke spherical actuator based on the principle of traditional voice coil actuators is developed. By utilizing the shape characteristics of the yoke and the magnetization direction of the magnet, the magnetic flux is concentrated and the magnet is shared, thereby improving the performance of the actuator. In the design process, SOLIDWORKS 2018 software is used for design modeling and assembly simulation, ANSYS Maxwell 2018 software is employed for magnetic circuit analysis and electromagnetic simulation, while MATLAB is utilized for analyzing the dynamic characteristics through a mathematical model. A prototype was also fabricated, and torque measurement experiments were conducted to verify the performance and feasibility of the proposed design. [ABSTRACT FROM AUTHOR]

The applications of magneto-rheological fluids have become many, and important. Especially the valves used in dampers and hydraulic systems. Including the pressure relief valve. But all of these valves are type normally open. However, the pressure relief valve should be of the normally closed type. This study presents the concept of a magneto-rheological pressure relief valve using a permanent magnetic, along with a comprehensive analysis. Using FEMM software the design analysis was performed, to determine the efficiency of its performance and work. As a result of the work, the appropriate current value was determined, which is 0.17 amps, along with the number of turns of the electric coil, the best of which was 240 turns, which was applied to open the valve at the appropriate pressure. The maximum pressure was about 2500 kPa, which can be tolerated in the valve also calculated. Through the analysis, it was also determined that 1 mm is the best thickness for the gap. As well as choose the type and dimension of the proper permanent magnet. With this work, the design is considered very suitable and efficient, and it can be developed in the future based on the same principle and method. [ABSTRACT FROM AUTHOR]

This paper investigates the differentiable dynamic modeling of mobile manipulators to facilitate efficient motion planning and physical design of actuators, where the actuator design is parameterized by physically meaningful motor geometry parameters. The proposed differentiable modeling comprises two major components. First, the dynamic model of the mobile manipulator is derived, which differs from the state‐of‐the‐art in two aspects: (1) the model parameters, including magnetic flux, link mass, inertia, and center‐of‐mass, are represented as analytical functions of actuator design parameters; (2) the dynamic coupling between the base and the manipulator is captured. Second, the state and control constraints, such as maximum angular velocity and torque capacity, are established as analytical functions of actuator design parameters. This paper further showcases two typical use cases of the proposed differentiable modeling work: integrated locomotion and manipulation planning; simultaneous actuator design and motion planning. Numerical experiments demonstrate the effectiveness of differentiable modeling. That is, for motion planning, it can effectively reduce computation time as well as result in shorter task completion time and lower energy consumption, compared with an established sequential motion planning approach. Furthermore, actuator design and motion planning can be jointly optimized toward higher performance. [ABSTRACT FROM AUTHOR]

The demand for non‐invasive health monitoring with wearables poses challenges in developing sustainable, self‐powered systems, as current energy harvesters face issues like complex fabrication, low robustness, and insufficient power density for continuous biosensing. In this study, a wearable self‐powered biosensing platform combining a electromagnetic‐triboelectric hybrid generator (ETHG) with an advanced electrochemical sweat‐ion‐sensing patch is proposed. A Halbach magnet array within the electromagnetic generator (EMG) enhances magnetic flux concentration and power output, while advanced Nylon@polyallylamine and polyvinylidene fluoride@Co3O4 nanofiber films significantly boost the triboelectric generator's performance. Mechanical and theoretical modeling reveals an optimized power output of 328 mW for the EMG and 0.65 mW for the triboelectric component at 6 Hz. This hybrid approach not only enhances the power density but also simplifies the fabrication process and improves the charging performance and robustness of the system. To address potential drift in solid‐contact ion‐selective electrodes, nanoporous carbon ‐modified electrodes increase hydrophobicity, enhancing sensitivity for Na+ (56.1 mV dec−1), K+ (55.2 mV dec−1), and Ca2+ (30.8 mV dec−1), along with excellent performance in pH (69.7 mV dec−1) sensing. Integrating ETHG with a flexible microfluidics‐enabled patch enables real‐time on‐body sweat monitoring, with data wirelessly transmitted via Bluetooth, offering an efficient and robust platform for continuous health monitoring applications. [ABSTRACT FROM AUTHOR]

A theoretical investigation of spin-orbit coupling effect on magnetotransport of a monolayer graphene system having the geometry of Aharonov–Bohm interferometer is presented. The spin-orbit interaction is considered in the form of Rashba spin-orbit (RSO) coupling. The problem is studied within atomistic tight-binding approximation in combination with non-equilibrium Green's functions formalism. The influence of RSO coupling on quantum interference effects is investigated within linear response limit in terms of transmission function and magnetoconductance as functions of Fermi energy, RSO coupling, magnetic flux and the number of transmission-modes as well as beyond this limit in terms of current-flow, under finite bias conditions. The Fourier power spectra of corresponding response functions are also obtained. The possibility of an effective control the two-terminal spin resolved resistances of the system and the spin polarization of equilibrium charge current as well as a nonequilibrium net current by means of RSO coupling and magnetic flux through the system, leading to an increase of the functionality of graphene in potential electronic applications, has been demonstrated. [ABSTRACT FROM AUTHOR]

Magnetorheological (MR) fluids can be utilized in one of the fundamental operating modes of which the gradient pinch mode has been the least explored. In this unique mode non-uniform magnetic field distributions are taken advantage of to develop a so-called Venturi-like contraction in MR fluids. By adequately directing magnetic flux the material can be made solidified in the regions near the flow channel wall, thus creating a passage in the middle of the channel for the fluid to pass through. This leads to unique variations of the slope in the pressure-flow rate characteristics. It can be stated that the effect of the MR fluid composition on the behaviour of the MR fluid in gradient pinch mode has not been thoroughly investigated yet. In this study, the behaviour of MR fluids was assessed with a dedicated pinch mode MR valve that provided a valuable insight into the contraction mechanism using fluorescence microscopy. Briefly, seven MR fluid samples were prepared with different particle concentrations (10%, 22% and 32 vol%) and mean particle sizes (2, 4.5 and 8.2 μm). It was found that the MR fluid sample with the larger particle size exhibits a significantly larger slope change observed in the pressure-flow rate characteristics. Increasing the particle size from 2 μm (base) to 8 μm resulted in the slope increase by a factor of 2.6 compared to the base sample. Increasing the particle concentration has a negligible effect on the pinch mode effect. Finally, these results were analysed using the modified Wuest equation, which is commonly used for characterizing sharp-edged orifices in low Reynolds number flow regimes. The simple equation was determined to describe the behaviour of MR fluids in gradient pinch mode with adequate accuracy. [ABSTRACT FROM AUTHOR]

The Dungey cycle is considered from the formation of a magnetic barrier and necessary for dayside reconnection conditions till the electric field generation around the Birkeland current loop and magnetic flux circulation balance. Data-based modeling of the magnetosheath magnetic field makes it possible to quantitatively assess the main factors that control formation and destruction of the magnetospheric magnetic barrier, such as the field line draping and the field intensity increase from the bow shock to the magnetopause, as well as their dependence on the orientation of the interplanetary magnetic field (IMF). The Dungey cycle has been revised to take into account the essentially time-dependent effects of magnetic reconnection. It is shown by means of the Stokes' theorem that a powerful electric field with an effective potential difference of several tens of kV is generated around the developing substorm current system. The emerging Birkeland current loop is an important particle acceleration element in the magnetosphere, contributing to the energization of ring current protons and electrons. The electric field that arises in the dipolarization zone magnifies the already existing ring current, and the closure of its amplified part through the ionosphere generates the Region 2 field-aligned currents. The motion of the expanding partial ring current around the magnetosphere, combined with the particle drift, transfers the magnetic flux from the night side of the magnetosphere to the dayside. At the dayside magnetopause, the reconnection is also responsible for the creation of the Birkeland loop, but now the electric field in the loop area decelerates the ring current particles, and regions of weakened ring current are formed. Closure of these weakened loop currents results in a transfer of the magnetic flux from the dayside to the night side, thus ensuring its overall balance and completing the Dungey cycle. [ABSTRACT FROM AUTHOR]

ABSTRACT Electrically driven unmanned aerial vehicles (UAVs) are gaining popularity due to use in industrial, military, and civil applications. The UAVs have to execute complicated maneuvers in the air requires accurate control of the BLDC motor propeller systems. In this study, we propose easy to implement field‐oriented adaptive input‐output feedback linearizing control (AIOFL) for controlling propellers as per demand of flight controller. This study aims to compare the proposed field‐oriented AIOFL with usual six step control architecture with a focus on the typical back‐electromotive force (back‐EMF) shapes featured in the propeller motor. The proposed control architecture that does not only regulate speed and torque of the propeller with acceptable torque ripple but it also estimates the rotor magnetic flux and the stator resistance of the BLDC motor to know about stator/rotor condition monitoring, motor fault detection, and temperature rise. To ensure reliable operation in all operational conditions, closed loop stability of proposed speed controller is analyzed based on the Lyapunov method. Particle swarm optimization (PSO) is utilized to accurately tune the PI controller since the trial‐and‐error technique used to choose the PI controller gains resulted in the low stability and poor transient response of the controller. Finally, comprehensive numerical and experimental tests are performed and compared with conventional field‐oriented control to evaluate the effectiveness and robustness of the proposed control system. [ABSTRACT FROM AUTHOR]

In this paper, a three-dimensional (3D) solution of static behavior of simply supported doubly curved functionally graded multilayered (FGM) magneto-electro-elastic shells subjected to mechanical, electric displacement, magnetic flux, electric potential and magnetic potential loads is presented. A coupling procedure based on the state space and the Runge–Kutta methods is elaborated for the 3D magneto-electro-elastic governing equations. An efficient semi-analytical approach is resulted for arbitrary functionally graded shells in thickness direction. The proposed mathematical modeling has been validated by several numerical tests. The obtained results are in good agreement with the available ones given by the three-dimensional asymptotic approach, the state space approach and a meshless collocation method. It has been revealed that, the loading conditions, the materials properties gradient index, the span-to-thickness ratio and the radius-to-thickness ratio remarkably influence the static response of FGM shells. [ABSTRACT FROM AUTHOR]

A three‐dimensional particle‐in‐cell simulation is performed to study secondary reconnection between two interlinked flux tubes produced by neighboring guide field reconnection x‐lines. The reconnecting magnetic fields of this secondary reconnection is enhanced toward the diffusion region, agree well with that in observations. The magnetic field pileup is attributed to the upstream magnetic tension force, that smashes the flux tubes into each other. We propose that the primary reconnection x‐line length is a key parameter to determine the formation of interlinked flux tubes and secondary reconnection therein. Interlinked flux tubes will form only if the x‐line is short; when the x‐line is long enough, the regular flux ropes are formed instead. The critical x‐line length to form interlinked flux tubes is determined by the distance between two neighbor x‐lines and the magnetic shear angle of the primary reconnection. The results provide a novel scenario of secondary reconnection generation during three‐dimensional reconnection. Plain Language Summary: Magnetic reconnection is a fundamental energy conversion process in plasmas, and exists in varieties of space environments. Recent observations find magnetic reconnection occurring in the current sheet between two elbow like flux tubes interlinked with each other. The observational features of such a kind of event are very similar to that of a flux rope, which is a helical magnetic field structure. However, the formation condition for interlinked flux tubes and magnetic reconnection between them is not well understood, the relation between interlinked flux tubes and flux ropes is also not very clear. In this letter, we use three‐dimensional particle‐in‐cell simulation to study the formation of magnetic reconnection between interlinked flux tubes, and propose an explanation for its formation. Key Points: Interlinked flux tubes can form during multiple x‐line guide field reconnection when the x‐line is shortSecondary reconnection can be triggered in the current sheet formed between interlinked flux tubesThe upstream magnetic field pileup is caused by the magnetic tension force [ABSTRACT FROM AUTHOR]

This paper presents another model of a flare filament with a force-free magnetic field structure. The distribution of the magnetic field and currents within the volume of the rope is defined by the so-called flux function. To obtain a force-free solution, the Laplacian of this function must strictly depend only on the function itself. However, there are a large number of such functions, which raises the question: how does the choice of a particular flux function affect the physical properties of the magnetic flux rope constructed based on it? In previous studies, the author generally used an exponential dependence of the flux function on the coordinates, but in this article, a power function was used, and it turned out that the physical parameters of the flare ropes almost coincide. All force-free magnetic flux ropes have one common physical property: as the rope loop apex extends into the corona, the external pressure that prevents its lateral expansion steadily decreases, and upon reaching a certain critical reduction, the longitudinal magnetic field of the rope turns to zero at the current inversion surface (CIS). At this point, the force-free parameter and the azimuthal electric current experience a discontinuity at this surface, causing their values in the vicinity of the CIS to grow indefinitely (in magnitude). The electron drift velocity here inevitably exceeds the ion acoustic velocity, leading to the excitation of plasma ion-acoustic instability, a sharp drop in plasma conductivity within the rope, and the generation of a super-Dreicer electric field. Parker's effect (alignment, with some delay, of the torque along the rope axis due to the transfer of azimuthal field to the energy release region) leads to quasi-periodic pulsations of hard flare radiation and ultimately ensures the flare release of a significant portion of the free magnetic energy stored in the long loop of the magnetic flux rope. [ABSTRACT FROM AUTHOR]

In this work, we studied the formation of a large-scale magnetic field. For this, we used the surface flux transport (SFT) model. We have studied the model's accuracy and its sensitivity to uncertainties in its key parameters and input data. We also compared the simulated magnetic field with observations of the SDO/HMI and STOP/Kislovodsk magnetic fields. Overall there is good agreement between the simulations and observations. Although the model cannot reproduce fine details of the magnetic field, the long-term evolution of the polar field is very similar in simulations and observations. During even one activity cycle, large-scale field drift waves to high latitudes change polarity. Magnetic field drift waves, the sign of which corresponds to the magnetic polarity of the trailing parts of the active regions, often exist during the decline phase of activity. This does not quite correspond to the idea of mutual compensation of the leading fields of active regions across the equator. We also looked at the magnetic field flux across the equator. We confirmed that the flux across the equator does not show a clear predominance of leading sunspot polarity. The results are discussed to test dynamo models. [ABSTRACT FROM AUTHOR]

We propose a model of a light bridge as a current-carrying magnetic flux tube formed by convection. It is shown that convection in the sunspot penumbra provides the electric current necessary to heat the flux rope plasma and forms structures of a light bridge type. The steady-state heating mode of the light bridge is considered, since the light bridge life time (days) is much longer than the typical heating time (minutes). Radiation losses determine the current value I > 1011A required to heat the light bridge to a temperature up to 6800 K. The parameters of the light bridge plasma are presented, and the observed double structure of the light bridge emission is explained. [ABSTRACT FROM AUTHOR]

The characteristics of solar cycles important for the development of dynamo theory can manifest themselves differently when different activity indices are used. To study the features of the north–south (N–S) asymmetry of solar activity, a comparison was made of the time profiles of active regions (ARs) of the 23rd and 24th cycles based on data on their number (the most accessible and frequently used) and magnetic flux (allowing a more complete assessment about the generative function of the dynamo process). We used data on 3047 ARs that appeared on the disk from June 1996 to December 2020 according to the MMC ARs CrAO (magneto-morphological classification of ARs of the Crimean Astrophysical Observatory) catalog (http://sun.crao.ru/databases/catalog-mmc-ars). The attribution of AR to the classes of the regular and irregular sunspot groups was taken into account in accordance with the MMC ARs CrAO. Analysis of the results showed the following. Variations of ARs of both MMC classes are associated with a cycle, which confirms their relationship with the action of the global dynamo. Due to the overlap of multipeak ARs profiles of different classes, a classic double-peak cycle structure is formed in the two hemispheres. Variations in the relative position of profiles for the number and magnetic flux of ARs (for groups of each class in each hemisphere) during the cycle can be associated with changes in the sizes of ARs. This makes it possible to suggest the multicomponent nature of the dynamo process, which consists in joint manifestation of global (responsible for the production of ARs) and turbulent (associated with the fragmentation of magnetic structures due to turbulence in the convection zone) components of the dynamo. The strongest magnetic fluxes observed for the irregular groups in the maximum of the cycle may also indicate action of the turbulent component of the dynamo distorting the regular flux tube. The pronounced N–S asymmetry of these fluxes agrees with the hypothesis on the possibility of weakening of the toroidal field in one of the hemispheres due to the interaction of the dipole and quadrupole components. [ABSTRACT FROM AUTHOR]

We present the first model aimed at understanding how the Meissner effect in a young neutron star affects its macroscopic magnetic field. In this model, field expulsion occurs on a dynamical time-scale, and is realized through two processes that occur at the onset of superconductivity: fluid motions causing the dragging of field lines, followed by magnetic reconnection. Focusing on magnetic fields weaker than the superconducting critical field, we show that complete Meissner expulsion is but one of four possible generic scenarios for the magnetic-field geometry, and can never expel magnetic flux from the centre of the star. Reconnection causes the release of up to |$\sim 5\times 10^{46}\, \mathrm{erg}$| of energy at the onset of superconductivity, and is only possible for certain favourable early-phase dynamics and for pre-condensation fields |$10^{12}\, \mathrm{G}\lesssim B\lesssim 5\times 10^{14}\, \mathrm{G}$|⁠. Fields weaker or stronger than this are predicted to thread the whole star. [ABSTRACT FROM AUTHOR]

Magnetorheological (MR) brakes are flourishing in low-torque applications due to their dynamic controllability nature. Researchers have introduced multi-layer and multipole concepts to increase the torque–volume ratio (TVR) of the MR brake. However, the combination of these two ideas did not exist due to the design limitations. Therefore, this study aims to design a brake that combines the multipole magnetic field and multi-layered structure concepts. The axial slots were introduced on the brake rotor and the stator drum axial surfaces to achieve a high TVR. These slots stop the flux bypass in the inner layers; therefore, the magnetic flux can also reach the brake's outer layers. This brake was designed with multiple stator and rotor drums and MR fluid layers. The number of poles was placed so that the magnetic field from these poles traveled in a closed loop via the stator, rotor, and MR layers. A 3D model of the brake was prepared for the virtual study. Electromagnetic simulations were conducted to analyze the effect of axial slots' and other design parameters of the brake. According to those simulation results, the axial slots' width and position significantly affect the brake output torque. The maximum torque obtained from the brake is 38 Nm, and the TVR value of the brake is 41 Nm/dm3. Additionally, multiphysics simulations were performed to understand the Joule-heating effect of the magnetic coil and the frictional heating in MR fluid. Results showed that the maximum possible temperature in the brake is under the MR fluid temperature limits. Therefore, this multipole multi-layered (MPML) MR brake with axial slots idea is very useful for high-torque MR brake growth. [ABSTRACT FROM AUTHOR]

The restructuring of the power grid calls for various energy harvesting technologies to power prospective remote electronic sensors, data loggers, and communication devices that could be installed at locations with restricted access. Magnetic energy harvesting stands out as a promising technology that is well suited for such applications while also being able to provide a significant amount of power. In this paper, a clamped-type overhead line magnetic energy harvester in configuration with passive and active rectifiers loaded with a constant voltage load is investigated. Here, an approximate piecewise linear model of the magnetic core is applied to represent the operation of the joint harvester–rectifier system. The main findings of this study include design-oriented analysis that easily lends itself to engineering applications. Based on the proposed analytical results, design guidelines are suggested to establish the key parameters of the harvester's magnetic structure such as core size and number of secondary turns. Design examples are presented and verified using both simulation and experimental results. A good agreement of the results was found. The offered approach is simple and suitable for engineering purposes. [ABSTRACT FROM AUTHOR]

Magnetic Gears (MG), which can operate under antifriction and unlubricated conditions, have the potential to meet the needs of many areas, especially the aviation and defense sectors. In this context, it is very important to develop MG designs that can meet the specific requirements in these areas. With this motivation, a coaxial MG with a power transmission ratio of 5.33 has been designed and optimized in this study by incorporating Flux-Concentrated Halbach Array (FCHA) magnets, and a power transmission mechanism that can be utilized especially in Fin Actuation System (FAS) is developed by performing Numerical Electromagnetic Analysis (NEA). Different geometric parameters are determined as variables in the FCHA design and the performance improvement study is carried out by developing various models. Accordingly, by comparing the effects of design parameters on the MG performance, the geometric model in which the Volumetric Torque Density (VTD) reached the highest value is determined. Numerical analysis results showed that the optimized FCHA increases VTD by 32% compared to the Halbach array. As a result of parametric analysis studies, MG system with VTD value of 225.7 Nm/L, which satisfies ideal design criteria, is obtained. Considering the optimized MD design, torque ripple and flux density are examined and also the effects of different magnet grades on the performance and the structural analysis of the middle rotor are investigated. [ABSTRACT FROM AUTHOR]

Solar eruptions, primarily manifested as solar flares, filament eruptions and coronal mass ejections, represent explosive releases of magnetic energy stored in the solar corona, with the potential to drive severe space weather. The initiation of solar eruptions remains an open question, leading to various theoretical models that are inferred from observations. However, these models are subjects of debate due to the absence of direct measurements of the three-dimensional (3D) magnetic fields in the corona. Numerical simulations, based on solving magnetohydrodynamics (MHD) equations that govern the macroscopic dynamics of solar corona, serve as a touchstone for testing these theoretical models. One early proposed model suggested that eruptions could be triggered by reconnection within a single sheared magnetic arcade, which is known as the tether-cutting reconnection model, but it was never confirmed through 3D MHD simulations until very recently. Consequently, two models have gained more popularity: one involving the eruption of a twisted magnetic flux rope (MFR) due to ideal instability (or loss of equilibrium), and the other known as the breakout eruption, which requires a quadrupolar configuration with a delicately located magnetic null point. Other mixed mechanisms, involving both ideal instability and reconnection, are also proposed in association with localized magnetic flux emergence. Now with the validation of the tether-cutting model, the fundamental mechanisms are boiled down to two types of models, one primarily based on the ideal instability of a pre-existing MFR, and the other based on the reconnection of sheared field lines with or without an MFR. Recently, the modelling of the birth of solar eruption using observed data-based MHD simulations has advanced rapidly, becoming a crucial research tool in the study of the initiation mechanisms. These realistic modellings reveal a higher level of complexity compared to all currently available theories and idealized models. [ABSTRACT FROM AUTHOR]

In this analysis, thermal and solutal stratifications in three-dimensional mixed convection flow of second grade fluid along an irregular cylinder through porous medium is demonstrated. Effect of induced magnetic induction is considered to deal many technological and scientific problems like crude oil purification, plasma confinement, rotating magnetic stars and power generation. The flow narrating continuity, magnetic flux, momentum, magnetic induction, concentration and heat equations are modeled in the form of PDEs. Set of dimensionless conversions are introduced to replace non-linear PDEs into a set of ODEs. To predict numerical solution of considering model, we used an efficient numerical technique Bvp4c. The consequential outcomes are sketched for unlike values of dimensionless parameters. Parameters like mixed convection, second grade parameter, magnetic parameter, porosity parameter and buoyancy ratio parameter are initiated to control the flow field. Further, temperature and solutal stratification parameters, Prandtl, magnetic Prandtl and Schmidt numbers are found to control energy, magnetic induction and concentration distributions. Skin drag coefficients, heat and mass fluxes are investigated for inflating values of some sundry parameters. For justification of the model, we compared present numerical outcomes with previous published results. [ABSTRACT FROM AUTHOR]

We study the spectrum of the Landau Hamiltonian with a periodic electric potential. In the case of a rational magnetic flux, we present examples of nonconstant zero-mean periodic electric potentials for which the spectrum has an eigenvalue at the second Landau level. [ABSTRACT FROM AUTHOR]

The superconducting sigma neuron is a single-junction interferometer, with a part of the circuit shunted by an additional inductance, which is also used to generate the output signal. It was previously predicted that the transfer function of this device would be close to the sigmoidal one at a certain relation between the values of inductance of its parts. This interferometer can be fabricated as a multilayer thin-film structure over a superconducting screen, which allows measuring the output magnetic flux in a single element. An analysis of the experimental data showed that the use of a superconducting screen did not ensure complete independence of the sigma neuron elements, as was assumed in the theoretical model. This paper presents a generalized model of the stationary state of a sigma neuron that takes into account the interaction between all its parts, including the input and readout elements. [ABSTRACT FROM AUTHOR]

Reluctance actuators (RA) are a type of electromagnetic actuator that offers high forces for short-range motions. The RA takes advantage of the electromagnetic reluctance force property in air gaps between the stator core and mover parts. The stator generates a magnetic flux that produces a magnetic attraction force between the stator and the mover, where the output force is dependent on the air gap displacement nonlinearly. It is demonstrated that the RA can produce a force that is effective and suitable for millimeter-range high-acceleration applications. One application for the RA is the short-stroke stage of photolithography or lithography machines, for example. The RA is available in a wide variety of configurations, such as C-Core, E-Core, Maxwell, and Plunger-type designs. The RA requires precise dynamic models and control algorithms to help linearize the RA for better control and optimization. Some nonlinear dynamics include magnetic hysteresis, flux fringing, and eddy currents. The RA is shown to have a larger force density than any other traditional actuator designs, with the main disadvantage being the nonlinear and hysteresis nonlinearities, making it difficult to control precision motion applications without proper dynamic and control models in place. This review documents currently available knowledge of the RA such as available applications, configurations, dynamic models, measurement systems, and control systems for the RA. • Provides a consolidated overview of available applications, configurations, dynamic models, measurement systems, and control methodologies for RAs. • Explores the unique electromagnetic properties of RAs for high-force, short- range motions. • Discusses various RA configurations and their suitability for different applications. • Addresses challenges posed by nonlinearities such as magnetic hysteresis, flux fringing, and eddy currents. • Emphasizes the importance of precise dynamic models and control algorithms for linearizing and optimizing RA performance. [ABSTRACT FROM AUTHOR]

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The optimization of a contact-less magnetoelastic sensing setup designed to detect substances/agents accumulating in its environment is presented. The setup is intended as a custom-built, low-cost yet effective magnetoelastic sensor for pest/bug detection in constrained places (small museums, labs, etc.). It involves a short, thin, and flexible polymer slab in a cantilever arrangement, with a short Metglas® 2826 MB magnetoelastic ribbon attached on part of its surface. A mobile phone both supports and supplies low-amplitude vibration to the slab's free end. When vibrating, the magnetoelastic ribbon generates variable magnetic flux, thus inducing voltage in a contact-less manner into a pick-up coil suspended above the ribbon. This voltage carries specific characteristic frequencies of the slab's vibration. If substances/agents accumulate on parts of the (suitably coated) slab surface, its mass distribution and, hence, characteristic frequencies change. Then, simply monitoring shifts of such frequencies in the recorded voltage enables the detection of accumulating substances/agents. The current work uses extensive testing via various vibration profiles and load positions on the slab, for statistically evaluating the sensitivity of the mass detection of the setup. It is shown that, although this custom-built substance/agent detector involves limited (low-cost) hardware and a simplified design, it achieves promising results with respect to its cost. [ABSTRACT FROM AUTHOR]

The Inverse Faraday Effect (IFE) is a phenomenon that enables non-thermal magnetization in various types of materials through the interaction with circularly polarized light. This study investigates the impact of single defects on the ability of circularly polarized radiation to switch between distinct superconducting current states, when the magnetic flux through a superconducting ring equals half the quantum flux, Φ 0 / 2 . Using both analytical methods within the standard Ginzburg–Landau theory and numerical simulations based on the stochastic time-dependent Ginzburg–Landau approach, we demonstrate that while circularly polarized light can effectively switch between current-carrying superconducting states, the presence of a single defect significantly affects this switching mechanism. We establish critical temperature conditions above which the switching effect completely disappears, offering insights into the limitations imposed by a single defect on the dynamics of light-induced IFE-based magnetization in superconductors. [ABSTRACT FROM AUTHOR]

We compute the one-loop vacuum energy in 10-dimensional (10D) super Yang–Mills theory compactified on |$\mathbb {R}^{1,3}\times (\mathbb {T}^2)^3$| in the presence of the Abelian magnetic fluxes. Regularization of the infinite Kaluza–Klein (KK) sum is achieved by the use of Barnes |$\zeta$| -functions, which can be applied to the case in which the KK mass spectrum has the Landau level structure. We apply the technique to two different models of the 10D super Yang–Mills theory: One is to introduce the magnetic flux background to the 10D super Yang–Mills action. The other is to first embed the 10D super Yang–Mills action into 4D |$\mathcal {N}=1$| superspace and to introduce magnetic fluxes. The two models built result in different KK mass spectra as well as tree level potentials, and we compute the one-loop vacuum energy of each case. Nevertheless, both of the KK mass spectra have the Landau level structure and we can apply the regularization method in the same way. It turns out that the former model shows UV finite one-loop vacuum energy whereas the latter shows UV divergent one-loop potential that vanish when 4D |${\cal N}=1$| supersymmetry is not broken by magnetic fluxes. We discuss the origin of the differences from a higher-dimensional-supersymmetry viewpoint. [ABSTRACT FROM AUTHOR]

Inductance is an important parameter for motor design and control, and the performance of the motor is closely related to the inductance parameter. To solve the problem of the complex magnetic circuit structure of search coil mutual inductance, this paper takes an 8-pole and 48-slot interior permanent magnet synchronous motor (IPMSM) as the object to carry out the relevant research on the formula of search coil mutual inductance, illustrates the method of calculating the mutual inductance of the search coil, and compares and verifies the proposed method through finite element analysis and the actual measurement results. By setting up a procedure for calculating the magnetic flux of the search coil, the magnetic flux of each sub-coil of the search coil is analyzed and calculated. The mutual inductance of the search coil is calculated by summing up the magnetic chains of different sub-coils between the phases of the search coil. Lastly, the finite element simulation of the permanent magnet synchronous motor (PMSM) with the placement of the search coil is carried out, the inductance of the search coil in the experimental prototype is measured practically, and the finite element simulation results of the mutual inductance of the search coil are compared with the actual measurement results, which proves the correctness of the theoretical analysis. [ABSTRACT FROM AUTHOR]

The main objective of the research described in the article was to determine the following: Is it possible to estimate the magnetic flux linkage in the core of a voltage transformer using analogue or digital methods? Will it be possible to estimate it approximately both in the normal state and in the state of deep core saturation (ferroresonant state)? The research aimed to identify the advantages and disadvantages of both proposed estimation methods. As part of the research described in this paper, a simulation model was developed and executed in the MATLAB/Simulink environment to generate a series of secondary voltage and flux waveforms in voltage transformers. The secondary voltage and flux waveforms were modelled under ground fault conditions, initiating ferroresonance oscillations in the medium-voltage network. To determine the associated flux from the simulated secondary voltages of the voltage transformers, an analogue integration circuit, a voltage analogue input circuit and a numerical integration algorithm with offset elimination were developed and implemented in an STM32 microcontroller. The obtained reference flux waveforms were used to verify the accuracy of the estimation of flux waveforms obtained using the analogue and digital methods. As a result, it was determined that both methods allow for a relatively accurate estimation of the periodic component of the magnetic flux. It also presented how both methods respond to the presence of slowly changing (aperiodic) components. Possible applications were proposed in order to create an innovative criterion for detecting ferroresonance oscillations. [ABSTRACT FROM AUTHOR]

Recently, there has been a significant focus on developing various energy harvesting technologies to power remote electronic sensors, data loggers, and communication devices for smart grid systems. Among these technologies, magnetic energy harvesting stands out as one straightforward method to extract substantial power from current-carrying overhead lines. Due to the relatively small size of the harvester, the high currents in the distribution system quickly saturate its magnetic core. Consequently, the magnetic harvester operates in a highly nonlinear manner. The nonlinear nature of the downstream AC to DC converters further complicates the process, making precise analytical modeling a challenging task. In this paper, a clamped type overhead line magnetic energy harvester with a controlled active rectifier generating significant DC output power is investigated. A piecewise nonlinear analytical model of the magnetic harvester is derived and reported. The modeling approach is based on the application of the Froelich equation. The chosen approximation method allowed for a complete piecewise nonlinear analytical treatise of the harvester's behavior. The main findings of this study include a closed-form solution that accounts for both the core and rectifiers' nonlinearities and provides an accurate quantitative prediction of the harvester's key parameters such as the transfer window width, optimal pulse location, average DC output current, and average output power. To facilitate the study, a nonlinear model of the core was developed in simulation software, based on parameters extracted from core experimental data. Furthermore, theoretical predictions were verified through comparison with a computer simulation and experimental results of a laboratory prototype harvester. Good agreement between the theoretical, simulation, and experimental results was found. [ABSTRACT FROM AUTHOR]

Inrush current is still a persistent problem affecting the quality of the power system. This paper presents the theoretical aspects of this transient phenomenon, the simulation of the phenomenon for prediction purposes and its measurement in a test laboratory. In the operation of power transformers, there may also be cases where electrical phenomena affecting the operation of transformers may overlap. When power transformers are in operation, there may also be cases where electrical phenomena affecting their operation overlap. This paper includes a study describing such a situation, where the maximum value of the inrush current is amplified by the fact that the series resonance condition has been met. The intersection of these electrical phenomena resulted in internal and external electrical discharges that led to the overhaul of a 440 MVA transformer; the description of this situation is based on field data. The paper focuses on real information and situations that support the development of a maintenance management schedule based on accurate and up-to-date data. The information presented in this paper will be particularly useful to personnel specializing in power transformer design and/or those monitoring/operating high power transformers in the energy sector, but can also be a teaching aid for students interested in such transient phenomena. [ABSTRACT FROM AUTHOR]

We analyze the structure and composition of 248 ICMEs observed by the Wind spacecraft from February 1995 to December 2015. We group each event based on their doubly ionized Helium concentration within the magnetic cloud region into either the high‐concentration (i.e., >8% for at least 25% of the magnetic cloud) or nominal‐concentration (i.e., <8% for at least 75% of the magnetic cloud) group. We then perform an epoch analysis on plasma and magnetic field parameters within each distinct region of the ICME structure to identify similarities and/or differences associated with each group of events. Results show that the sheath region of ICMEs with high Helium concentration exhibits a two‐part structure, which is indicative of the compression and expansion of the sheath as it propagates. We further investigate the effect of high Helium concentration within ICMEs on resulting geomagnetic activity by comparing the average Sym‐H geomagnetic index between the two groups. We find that the Sym‐H achieves a greater minimum for high‐concentration events by a factor of ∼1.6. We suggest that this effect is related to the increase in dynamic pressure within the sheath region for ICMEs with high Helium content. Results indicate that high Helium content in ICMEs may play a non‐trivial role in both the evolution of the ICME sheath throughout interplanetary space and the resulting geomagnetic activity induced by Earthward‐directed ICMEs. Plain Language Summary: Interplanetary coronal mass ejections (ICMEs) are transient solar events during which large amounts of plasma and magnetic flux is violently expelled from the Sun. ICMEs can result in significant geomagnetic activity as they impact Earth's magnetosphere. Some ICMEs contain enhanced concentrations of Helium ions which may result in differing interactions of the ICME with the surrounding solar wind plasma as well as Earth's magnetosphere. In this work we compare ICMEs with high Helium content to ICMEs with nominal Helium content in order to study differences in their structure and their resulting effects on geomagnetic activity at Earth. This work motivates the need for more in‐depth studies of how enhanced Helium in ICMEs affects the underlying structure of the ICME itself, as well as dayside processes at Earth's magnetosphere such as ion heating at the bow shock and magnetic reconnection at the magnetopause. Key Points: ICMEs with high doubly ionized Helium concentration exhibit a two‐part sheath structureICMEs with high Helium concentration drive stronger geomagnetic disturbances at Earth than those with low Helium concentrationThe dynamic pressure within the sheath region of the ICME correlates to the strength of the Sym‐H index at Earth [ABSTRACT FROM AUTHOR]