Evaluation of quasi-square wave inverter as a power source for induction motors

The relative merits of quasi-square wave inverter-motor technology versus a sine wave inverter-motor system were investigated. The empirical results of several tests on various sizes of wye-wound induction motors are presented with mathematical analysis to support the conclusions of the study. It was concluded that, within the limitations presented, the quasi-square wave inverter-motor system is superior to the more complex sine wave system for most induction motor applications in space

Uniform Approximation from Symbol Calculus on a Spherical Phase Space

We use symbol correspondence and quantum normal form theory to develop a more general method for finding uniform asymptotic approximations. We then apply this method to derive a result we announced in an earlier paper, namely, the uniform approximation of the $6j$-symbol in terms of the rotation matrices. The derivation is based on the Stratonovich-Weyl symbol correspondence between matrix operators and functions on a spherical phase space. The resulting approximation depends on a canonical, or area preserving, map between two pairs of intersecting level sets on the spherical phase space.Comment: 18 pages, 5 figure

A tree-decomposed transfer matrix for computing exact Potts model partition functions for arbitrary graphs, with applications to planar graph colourings

Combining tree decomposition and transfer matrix techniques provides a very general algorithm for computing exact partition functions of statistical models defined on arbitrary graphs. The algorithm is particularly efficient in the case of planar graphs. We illustrate it by computing the Potts model partition functions and chromatic polynomials (the number of proper vertex colourings using Q colours) for large samples of random planar graphs with up to N=100 vertices. In the latter case, our algorithm yields a sub-exponential average running time of ~ exp(1.516 sqrt(N)), a substantial improvement over the exponential running time ~ exp(0.245 N) provided by the hitherto best known algorithm. We study the statistics of chromatic roots of random planar graphs in some detail, comparing the findings with results for finite pieces of a regular lattice.Comment: 5 pages, 3 figures. Version 2 has been substantially expanded. Version 3 shows that the worst-case running time is sub-exponential in the number of vertice

The X-ray outburst of the Galactic Center magnetar over six years of Chandra observations

The magnetar SGR J1745-2900 discovered at parsecs distance from the Milky Way central black hole, Sagittarius A*, represents the closest pulsar to a supermassive black hole ever detected. Furthermore, its intriguing radio emission has been used to study the environment of the black hole, as well as to derive a precise position and proper motion for this object. The discovery of SGR J1745-2900 has opened interesting debates about the number, age and nature of pulsars expected in the Galactic center region. In this work, we present extensive X-ray monitoring of the outburst of SGR J1745-2900 using the Chandra X-ray Observatory, the only instrument with the spatial resolution to distinguish the magnetar from the supermassive black hole (2.4" angular distance). It was monitored from its outburst onset in April 2013 until August 2019, collecting more than fifty Chandra observations for a total of more than 2.3 Ms of data. Soon after the outburst onset, the magnetar emission settled onto a purely thermal emission state that cooled from a temperature of about 0.9 to 0.6 keV over 6 years. The pulsar timing properties showed at least two changes in the period derivative, increasing by a factor of about 4 during the outburst decay. We find that the long-term properties of this outburst challenge current models for the magnetar outbursts.Comment: 11 pages, 6 figures. Accepted by Ap

The X-ray outburst of the Galactic Centre magnetar SGR J1745-2900 during the first 1.5 year

In 2013 April a new magnetar, SGR 1745-2900, was discovered as it entered an outburst, at only 2.4 arcsec angular distance from the supermassive black hole at the Centre of the Milky Way, Sagittarius A*. SGR 1745-2900 has a surface dipolar magnetic field of ~ 2x10^{14} G, and it is the neutron star closest to a black hole ever observed. The new source was detected both in the radio and X-ray bands, with a peak X-ray luminosity L_X ~ 5x10^{35} erg s^{-1}. Here we report on the long-term Chandra (25 observations) and XMM-Newton (8 observations) X-ray monitoring campaign of SGR 1745-2900, from the onset of the outburst in April 2013 until September 2014. This unprecedented dataset allows us to refine the timing properties of the source, as well as to study the outburst spectral evolution as a function of time and rotational phase. Our timing analysis confirms the increase in the spin period derivative by a factor of ~2 around June 2013, and reveals that a further increase occurred between 2013 Oct 30 and 2014 Feb 21. We find that the period derivative changed from 6.6x10^{-12} s s^{-1} to 3.3x10^{-11} s s^{-1} in 1.5 yr. On the other hand, this magnetar shows a slow flux decay compared to other magnetars and a rather inefficient surface cooling. In particular, starquake-induced crustal cooling models alone have difficulty in explaining the high luminosity of the source for the first ~200 days of its outburst, and additional heating of the star surface from currents flowing in a twisted magnetic bundle is probably playing an important role in the outburst evolution.Comment: 16 pages, 12 figures; accepted for publication on MNRA

A strongly magnetized pulsar within grasp of the Milky Way's supermassive black hole

The center of our Galaxy hosts a supermassive black hole, Sagittarius (Sgr) A*. Young, massive stars within 0.5 pc of SgrA* are evidence of an episode of intense star formation near the black hole a few Myr ago, which might have left behind a young neutron star traveling deep into SgrA*'s gravitational potential. On 2013 April 25, a short X-ray burst was observed from the direction of the Galactic center. Thanks to a series of observations with the Chandra and the Swift satellites, we pinpoint the associated magnetar at an angular distance of 2.4+/-0.3 arcsec from SgrA*, and refine the source spin period and its derivative (P=3.7635537(2) s and \dot{P} = 6.61(4)x10^{-12} s/s), confirmed by quasi simultaneous radio observations performed with the Green Bank (GBT) and Parkes antennas, which also constrain a Dispersion Measure of DM=1750+/-50 pc cm^{-3}, the highest ever observed for a radio pulsar. We have found that this X-ray source is a young magnetar at ~0.07-2 pc from SgrA*. Simulations of its possible motion around SgrA* show that it is likely (~90% probability) in a bound orbit around the black hole. The radiation front produced by the past activity from the magnetar passing through the molecular clouds surrounding the Galactic center region, might be responsible for a large fraction of the light echoes observed in the Fe fluorescence features.Comment: ApJ Letters in pres

Asymptotes in SU(2) Recoupling Theory: Wigner Matrices, 3j3j Symbols, and Character Localization

In this paper we employ a novel technique combining the Euler Maclaurin formula with the saddle point approximation method to obtain the asymptotic behavior (in the limit of large representation index $J$) of generic Wigner matrix elements $D^{J}_{MM'}(g)$. We use this result to derive asymptotic formulae for the character $\chi^J(g)$ of an SU(2) group element and for Wigner's $3j$ symbol. Surprisingly, given that we perform five successive layers of approximations, the asymptotic formula we obtain for $\chi^J(g)$ is in fact exact. This result provides a non trivial example of a Duistermaat-Heckman like localization property for discrete sums.Comment: 36 pages, 3 figure

Identification campaign of supernova remnant candidates in the Milky Way - I: Chandra observation of G308.3-1.4

ROSAT all-sky survey (RASS) data have provided another window to search for supernova remnants (SNRs). In reexamining this data archive, a list of unidentified extended X-ray objects have been suggested as promising SNR candidate. However, most of these targets have not yet been fully explored by the state-of-art X-ray observatories. For selecting a pilot target for a long-term identification campaign, we have observed the brightest candidate, G308.3-1.4, with Chandra X-ray observatory. An incomplete shell-like X-ray structure which well-correlated with the radio shell emission at 843 MHz has been revealed. The X-ray spectrum suggests the presence of a shock-heated plasma. All these evidences confirm G308.3-1.4 as a SNR. The brightest X-ray point source detected in this field-of-view is also the one locates closest to the geometrical center of G308.3-1.4, which has a soft spectrum. The intriguing temporal variability and the identification of optical/infrared counterpart rule out the possibility of an isolated neutron star. On the other hand, the spectral energy distribution from Ks band to R band suggests a late-type star. Together with a putative periodicity of \sim1.4 hrs, the interesting excesses in V, B bands and H-alpha suggest this source as a promising candidate of a compact binary survived in a supernova explosion (SN).Comment: 19 pages, 10 figures, 2 tables, accepted for publication in Ap