Based on the inverse scattering method, the formulae of one higher‐order pole solitons and multiple higher‐order poles solitons of the nonlinear Schrödinger equation (NLS) equation are obtained. ...Their denominators are expressed as det(I+Ω∗Ω), where Ω is a matrix frequently constructed for solving the Riemann‐Hilbert problem, and the asterisk denotes complex conjugate. We take two methods for proving I+Ω∗Ω is invertible. The first one shows matrix Ω is equivalent to a self‐adjoint Hankel matrix Δ, proving det(I+Ω∗Ω)=det(I+Δ†Δ)≥1. The second one considers the block‐matrix form of det(I+Ω∗Ω), proving |det(I+Ω∗Ω)|≥1. In addition, we prove that the dimension of Ω is equivalent to the sum of the orders of pole points of the transmission coefficient and its diagonal entries compose a set of basis.
This paper investigates the influence of stator/rotor pole number combinations and permanent magnet (PM) numbers on electromagnetic performance of consequent-pole hybrid excited flux reversal ...machines (CP-HEFRMs), which have different numbers of PM poles and iron poles and concentrated AC and DC windings on the stator and a salient pole rotor. PMs in the slots of one stator pole are magnetized radially in the same direction, while opposite on adjacent stator poles. Magnetic field paths of DC, PM, and hybrid excitations are investigated. The phenomenon of flux cancellation, i.e., PM and DC MMFs in CP-HEFRMs are of opposite polarities in the flux-enhancing operating mode, is revealed and verified, for the first time, as the key feature that makes CP-HEFRMs different from other hybrid excited machines. Consequently, the saturation in stator pole and yoke can be mitigated and hence the overload capability of DC excitation is enhanced, which is verified by finite element analysis (FEA). Global optimizations are utilized to obtain the optimal rotor and stator pole number combinations and PM numbers for each stator pole. Torque, torque ripple, inductance, unbalanced magnetic force, and flux regulation capability are compared for different PM numbers and rotor pole numbers. Comparisons are made on consequent-pole and non-consequent-pole topologies in terms of torque capacity, flux regulation capability, and PM consumption to further illustrate the advantages of consequent-pole topology. A prototype machine is built and tested to validate the analyses.
In this article, we present the scalar-diquark-scalar-diquark-antiquark type and scalar-diquark-axialvector-diquark-antiquark type pentaquark configurations in the diquark model, and study the masses ...and pole residues of the Formula omitted hidden-charm pentaquark states in detail with the QCD sum rules by extending our previous work on the Formula omitted and Formula omitted hidden-charm pentaquark states. We calculate the contributions of the vacuum condensates up to dimension-10 in the operator product expansion by constructing both the scalar-diquark-scalar-diquark-antiquark type and the scalar-diquark-axialvector-diquark-antiquark type interpolating currents. The present predictions of the masses can be confronted to the LHCb experimental data in the future.
Developing a permanent magnet synchronous machine (PMSM) for direct-drive electric vehicle (EV) has challenges such as obtaining high torque density and low torque ripple. The PMSM should have high ...pole numbers owing to low-speed operation, thereby increasing the use of rare earth magnets and cost. Therefore, in this article a consequent pole (CP) rotor topology is proposed in which the permanent magnet (PM) volume is reduced when compared with conventional surface PMSM (SPMSM). However, replacing south poles in an SPMSM with induced steel poles can increase torque ripple and reduce torque density. In order to improve torque density in a CP PMSM, structural modifications such as multilayer windings and non-ferromagnetic barriers have been proposed in the literature. These modifications increased the torque density while increasing the torque ripple. Therefore, this article proposes a novel two-level optimization method based on gradient descent algorithm, to address the challenges of improving torque density and reducing torque ripple simultaneously in a CP PMSM. Initially, an expression for the magnet pole arc angle is derived for CP PMSM based on magnetic equivalent circuit. A two-level optimization is performed on a baseline CP PMSM to determine the optimal magnet pole arc. The torque production and torque ripples of the optimized design are validated by simulation and experimental results.
•A method for uncertainty minimisation using active control is proposed.•The method does not require knowledge of the system since receptances are used.•Pole spreads, due to parameter variability, ...are minimised by global optimisation.•Uncertainty is quantified globally by variances taken via polynomial chaos expansion.•Uncertainty is modelled as modifications to a randomly measured nominal system.
The problem of pole placement in dynamic systems with uncertainties is addressed using a global optimisation approach. Variability between nominally identical systems, which arises from manufacturing tolerances, wear and environmental variability, is considered. In the proposed method, receptances are measured from one of the open-loop, nominal systems chosen at random. In this case, in addition to the variability about the parameter means, the parameter means are also random. The receptance method is then used to place the poles of the measured system such that their spread, due to parameter uncertainty, is minimised. The measure used to assess the spread is the variance, determined efficiently by a polynomial chaos expansion. Among the advantages of the method are: (i) there is no requirement to model the system since experimental receptances are used, (ii) it is not necessary to measure the mean system, and (iii) uncertainty in poles is quantified across its full range by using variances. Numerical and experimental examples are provided to illustrate the working of the proposed method.
Consequent-pole permanent magnet (PM) synchronous machines (PMSMs) provide especial features by the use of alternate PM and ferromagnetic poles. The design of these types of electric machines ...requires an accurate model due to the asymmetrical flux distribution in the air gap under adjacent poles. The equivalent magnetic circuit technique can hardly offer an accurate model for consequent-pole PMSMs. To this end, a 2-D analytical model is presented for consequent-pole slotted stator PMSMs to accurately compute the magnetic field distribution due to PMs and armature reaction. The slotting effects and the tooth-tip effects are taken into consideration by using the subdomain technique. The proposed model is used to calculate the magnetic flux density distributions of three consequent-pole PMSMs: an 8-pole, 9-slot machine with a non-overlapping winding; a 4-pole, 15-slot machine with an overlapping winding; and a 10-pole, 12-slot machine with a non-overlapping winding, each with three different magnetization patterns, i.e., radial, parallel, and Halbach. Based on the magnetic flux distribution, the electromagnetic torque, the self- and mutual-inductances, and the unbalanced magnetic forces have been analytically calculated. The analytical results are compared with those obtained from the finite-element method to show the accuracy and efficacy of the proposed 2-D analytical model.
The Earth’s three poles, the North Pole, South Pole, and Third Pole (i.e., the Tibetan Plateau and its surroundings), hold the largest amount of fresh water on Earth as glaciers, sea ice, and snow. ...They are sensitive to climate change. However, the linkages between climate variations of the three poles, particularly between the South Pole and Third Pole, remain largely unknown. The temperatures at 200 hPa over the three poles are the highest in the summer and are less affected by surface conditions, which could reflect large-scale dynamic linkages. Temperatures at 200 hPa peak the three poles during their respective hemispheric summer and exhibit in-phase variations on interdecadal timescales (10-100 years). The 200 hPa temperatures over the North Pole and South Pole were significantly correlated with the Brewer-Dobson circulation (BDC), which transports stratospheric ozone poleward, heating the air at 200 hPa. Tropopause warming over the Third Pole was found to enhance the poleward BDC, particularly to the South Pole, linking the Third Pole’s climate to the other two poles. Additionally, the Interdecadal Pacific Oscillation (IPO) also exhibits links with the 200 hPa temperatures of the three poles.
Hydrophilic materials immersed in aqueous solutions show near-surface zones that exclude suspended colloids and dissolved molecules. These exclusion zones (EZs) can extend for tens to hundreds of ...micrometers from hydrophilic surfaces and show physicochemical properties that differ from bulk water. Here we report that exposure of standard aqueous microsphere suspensions to static magnetic fields creates similar microsphere-free zones adjacent to magnetic poles. The EZs build next to both north and south poles; and they build whether the microspheres are of polystyrene or carboxylate composition. EZ formation is accompanied by ordered motions of microspheres, creating dense zones some distance from the magnetic poles and leaving microsphere-free zones adjacent to the magnet. EZ size was larger next to the north pole than the south pole. The difference was statistically significant when polystyrene microspheres were used, although not when carboxylate microspheres were used. In many ways, including both size and dynamics, these exclusion zones resemble those found earlier next to various hydrophilic surfaces. The ability to create EZs represents a feature of magnets not previously revealed.
Dual-pole line start permanent magnet (PM) synchronous machine is an emerging technology for replacing induction machines in two-speed applications, such as air coolers, compressors, and pumps. The ...machine structure includes two magnetic pole numbers on a single rotor layout and two separate sets of stator windings. Due to the unconventional and complex rotor structure, to this date, the design and analysis have solely been based on finite element (FE) method. This article aims to analytically validate the theory and the overall functionality of dual-pole PM machines in both steady state and transient regime. For this propose, a detailed magnetic circuit model is developed for calculating the PM flux distribution and the back electromotive force waveform. However, a single magnetic circuit cannot adequately represent the flux flow of the armature reaction, since the path of the armature flux is a function of rotor position. This is even more challenging in dual-pole machines, where the armature flux is originated from two different sets of stator winding. To avoid the necessity of having multiple magnetic circuits, the concept of magnetic islands is employed to capture the motor response at the loaded condition. For verification, analytical results are all supported via FE, and partially with experimental tests.
It has been long known that the Venusian bow shock (BS) location is asymmetric from the observations of the long‐lived Pioneer Venus Orbiter mission. The Venus Express (VEX) mission crossed BS near ...perpendicularly not only in the terminator region but also in the near‐subsolar and tail regions. Taking the advantage of VEX orbit geometry, we examined a large data set of BS crossings observed during the long‐lasting solar minimum between solar cycles 23 and 24 and found that the Venusian BS asymmetries exhibit dependence of solar zenith angle. In the terminator and tail regions, both the magnetic pole‐equator and north‐south asymmetries are observed in Venusian BS location, which is similar to the Pioneer Venus Orbiter (PVO) observation near terminator. However, in the near‐subsolar region, only the magnetic north‐south is observed; i.e., the BS shape is indented inward over magnetic south pole and bulged outward over magnetic north pole. The absence of the magnetic pole‐equator asymmetry in the near‐subsolar region suggests that the magnetic pole‐equator asymmetry is mainly caused by the asymmetric wave propagation rather than the ion pickup process. The evident magnetic north‐south asymmetry in solar minimum, which is not observed by PVO, suggests that even during the low long‐lasting solar minimum, the ion pickup process is very important in Venusian space environment.
Key Points
The north‐south asymmetry in Venusian BS location is observed in solar minimum
The pole‐equator asymmetry is absent in subsolar BS location
The pole‐equator asymmetry is caused by the asymmetric wave propagation
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