Analysis of cogging torque in brushless machines having nonuniformly distributed stator slots and stepped rotor magnets

A simple analytical technique is proposed for synthesizing the cogging torque waveform of a permanent magnet brushless machine from the cogging torque waveform that is associated with a single stator slot. The machine may have either uniformly or nonuniformly distributed stator slots and/or a skewed rotor, in which the skew is realized by circumferentially displacing the magnets of each pole. The technique is validated by finite element analysis and measurements

Influence of design parameters on the starting torque of a single-phase PM brushless DC motor

The starting torque of a single-phase permanent magnet brushless DC motor is investigated, for both radial and parallel magnetization. Finite element analysis is used to assess the relative merits of alternative methods of introducing the required air gap asymmetry, viz. tapered air gap, stepped air gap, asymmetric air gap, and slotted teeth. The predicted results are validated experimentall

The Fractional Quantum Hall States at ν=13/5\nu=13/5 and 12/512/5 and their Non-Abelian Nature

We investigate the nature of the fractional quantum Hall (FQH) state at filling factor $\nu=13/5$, and its particle-hole conjugate state at $12/5$, with the Coulomb interaction, and address the issue of possible competing states. Based on a large-scale density-matrix renormalization group (DMRG) calculation in spherical geometry, we present evidence that the physics of the Coulomb ground state (GS) at $\nu=13/5$ and $12/5$ is captured by the $k=3$ parafermion Read-Rezayi RR state, $\text{RR}_3$. We first establish that the state at $\nu=13/5$ is an incompressible FQH state, with a GS protected by a finite excitation gap, with the shift in accordance with the RR state. Then, by performing a finite-size scaling analysis of the GS energies for $\nu=12/5$ with different shifts, we find that the $\text{RR}_3$ state has the lowest energy among different competing states in the thermodynamic limit. We find the fingerprint of $\text{RR}_3$ topological order in the FQH $13/5$ and $12/5$ states, based on their entanglement spectrum and topological entanglement entropy, both of which strongly support their identification with the $\text{RR}_3$ state. Furthermore, by considering the shift-free infinite-cylinder geometry, we expose two topologically-distinct GS sectors, one identity sector and a second one matching the non-Abelian sector of the Fibonacci anyonic quasiparticle, which serves as additional evidence for the $\text{RR}_3$ state at $13/5$ and $12/5$.Comment: 12 pages, 8 figure

Topological Characterization of Non-Abelian Moore-Read State using Density-Matrix Renormailzation Group

The non-Abelian topological order has attracted a lot of attention for its fundamental importance and exciting prospect of topological quantum computation. However, explicit demonstration or identification of the non-Abelian states and the associated statistics in a microscopic model is very challenging. Here, based on density-matrix renormalization group calculation, we provide a complete characterization of the universal properties of bosonic Moore-Read state on Haldane honeycomb lattice model at filling number $\nu=1$ for larger systems, including both the edge spectrum and the bulk anyonic quasiparticle (QP) statistics. We first demonstrate that there are three degenerating ground states, for each of which there is a definite anyonic flux threading through the cylinder. We identify the nontrivial countings for the entanglement spectrum in accordance with the corresponding conformal field theory. Through inserting the $U(1)$ charge flux, it is found that two of the ground states can be adiabatically connected through a fermionic charge-$\textit{e}$ QP being pumped from one edge to the other, while the ground state in Ising anyon sector evolves back to itself. Furthermore, we calculate the modular matrices $\mathcal{S}$ and $\mathcal{U}$, which contain all the information for the anyonic QPs. In particular, the extracted quantum dimensions, fusion rule and topological spins from modular matrices positively identify the emergence of non-Abelian statistics following the $SU(2)_2$ Chern-Simons theory.Comment: 5 pages; 3 figure

Reduction of cogging torque in interior-magnet brushless machines

An investigation into the cogging torque in a four-pole interior-magnet brushless machines having either a six-slot stator and a short-pitched nonoverlapping winding or a 12-slot stator and a full-pitched overlapping winding is described. It is shown by finite-element analyses and measurements that, by appropriately defining the pole-arc to pole-pitch ratio, the optimal pole-arc to pole-pitch ratio for minimum cogging torque, which has been derived for surface-mounted magnet machines, is equally applicable to interior-magnet machines

Diquarks, Pentaquarks and Dibaryons

We explore the connection between pentaquarks and dibaryons composed of three diquarks in the framework of the diquark model. With the available experimental data on H dibaryon, we estimate the Pauli blocking and annihilation effects and constrain the $P=-$ pentaquark $SU(3)_F$ singlet mass. Using the $\Theta^+$ pentaquark mass, we estimate $P=-$ dibaryon mass