Low Power Magnetic Bearing Design for High Speed Rotating Machinery

Magnetic suspension technology has advanced to the point of being able to offer a number of advantages to a variety of applications in the rotating machinery and aerospace fields. One strong advantage is the decrease in power consumption. The design and construction of a set of permanent magnet biased, actively controlled magnetic bearing for a flexible rotor are presented. Both permanent magnets and electromagnets are used in a configuration which effectively provides the necessary fluxes in the appropriate air gaps, while simultaneously keeping the undesirable destabilizing forces to a minimum. The design includes two radial bearings and a thrust bearing. The theoretical development behind the design is briefly discussed. Experimental performance results for a set of operating prototype bearings is presented. The results include measurements of load capacity, bearing stiffness and damping, and the dynamic response of the rotor. With few exceptions, the experimental results matched very well with the predicted performance. The power consumption of these bearings was found to be significantly reduced from that for a comparable set of all electromagnetic bearings

Phase diagram of the su(8) quantum spin tube

We calculate the phase diagram of an integrable anisotropic 3-leg quantum spin tube connected to the su(8) algebra. We find several quantum phase transitions for antiferromagnetic rung couplings. Their locations are calculated exactly from the Bethe Ansatz solution and we discuss the nature of each of the different phases.Comment: 10 pages, RevTeX, 1 postscript figur

Sampling Theorem and Discrete Fourier Transform on the Riemann Sphere

Using coherent-state techniques, we prove a sampling theorem for Majorana's (holomorphic) functions on the Riemann sphere and we provide an exact reconstruction formula as a convolution product of $N$ samples and a given reconstruction kernel (a sinc-type function). We also discuss the effect of over- and under-sampling. Sample points are roots of unity, a fact which allows explicit inversion formulas for resolution and overlapping kernel operators through the theory of Circulant Matrices and Rectangular Fourier Matrices. The case of band-limited functions on the Riemann sphere, with spins up to $J$, is also considered. The connection with the standard Euler angle picture, in terms of spherical harmonics, is established through a discrete Bargmann transform.Comment: 26 latex pages. Final version published in J. Fourier Anal. App

High Performance Magnetic Bearings for Aero Applications

Several previous annual reports were written and numerous papers published on the topics for this grant. That work is not repeated here in this final report. Only the work completed in the final year of the grant is presented in this final report. This final year effort concentrated on power loss measurements in magnetic bearing rotors. The effect of rotor power losses in magnetic bearings are very important for many applications. In some cases, these losses must be minimized to maximize the length of time the rotating machine can operate on a fixed energy or power supply. Examples include aircraft gas turbine engines, space devices, or energy storage flywheels. In other applications, the heating caused by the magnetic bearing must be removed. Excessive heating can be a significant problem in machines as diverse as large compressors, electric motors, textile spindles, and artificial heart pumps

Magnetization Plateaux in Bethe Ansatz Solvable Spin-S Ladders

We examine the properties of the Bethe Ansatz solvable two- and three-leg spin-$S$ ladders. These models include Heisenberg rung interactions of arbitrary strength and thus capture the physics of the spin-$S$ Heisenberg ladders for strong rung coupling. The discrete values derived for the magnetization plateaux are seen to fit with the general prediction based on the Lieb-Schultz- Mattis theorem. We examine the magnetic phase diagram of the spin-1 ladder in detail and find an extended magnetization plateau at the fractional value $= {1/2}$ in agreement with the experimental observation for the spin-1 ladder compound BIP-TENO.Comment: 11 pages, 1 figur

Spectral Analysis of the Supreme Court

The focus of this paper is the linear algebraic framework in which the spectral analysis of voting data like that above is carried out. As we will show, this framework can be used to pinpoint voting coalitions in small voting bodies like the United States Supreme Court. Our goal is to show how simple ideas from linear algebra can come together to say something interesting about voting. And what could be more simple than where our story begins— with counting

Note on the thermodynamic Bethe Ansatz approach to the quantum phase diagram of the strong coupling ladder compounds

We investigate the low-temperature phase diagram of the exactly solved su(4) two-leg spin ladder as a function of the rung coupling $J_{\perp}$ and magnetic field $H$ by means of the thermodynamic Bethe Ansatz (TBA). In the absence of a magnetic field the model exhibits three quantum phases, while in the presence of a strong magnetic field there is no singlet ground state for ferromagnetic rung coupling. For antiferromagnetic rung coupling, there is a gapped phase in the regime H H_{c2} and a Luttinger liquid magnetic phase in the regime H_{c1} < H < H_{c2}. The critical behaviour derived using the TBA is consistent with the existing experimental, numerical and perturbative results for the strong coupling ladder compounds. This includes the spin excitation gap and the critical fields H_{c1} and H_{c2}, which are in excellent agreement with the experimental values for the known strong coupling ladder compounds (5IAP)_2CuBr_4 2H_2 O, Cu_2(C_5 H_{12} N_2)_2 Cl_4 and (C_5 H_{12} N)_2 CuBr_4. In addition we predict the spin gap $\Delta \approx J_{\perp}-{1/2}J_{\parallel}$ for the weak coupling compounds with $J_{\perp} \sim J_{\parallel}$, such as (VO)_2 P_2 O_7, and also show that the gap opens for arbitrary $J_{\perp}/ J_{\parallel}$.Comment: 10 pages, 3 figure

Celebrating Cercignani's conjecture for the Boltzmann equation

Cercignani's conjecture assumes a linear inequality between the entropy and entropy production functionals for Boltzmann's nonlinear integral operator in rarefied gas dynamics. Related to the field of logarithmic Sobolev inequalities and spectral gap inequalities, this issue has been at the core of the renewal of the mathematical theory of convergence to thermodynamical equilibrium for rarefied gases over the past decade. In this review paper, we survey the various positive and negative results which were obtained since the conjecture was proposed in the 1980s.Comment: This paper is dedicated to the memory of the late Carlo Cercignani, powerful mind and great scientist, one of the founders of the modern theory of the Boltzmann equation. 24 pages. V2: correction of some typos and one ref. adde

GenTAC registry report: Gender differences among individuals with genetically triggered thoracic aortic aneurysm and dissection

Previous data suggest women are at increased risk of death from aortic dissection. Therefore, we analyzed data from the GenTAC registry, the NIH‐sponsored program that collects information about individuals with genetically triggered thoracic aortic aneurysms and cardiovascular conditions. We performed cross‐sectional analyses in adults with Marfan syndrome (MFS), familial thoracic aortic aneurysm or dissection (FTAAD), bicuspid aortic valve (BAV) with thoracic aortic aneurysm or dissection, and subjects under 50 years of age with thoracic aortic aneurysm or dissection (TAAD <50 years). Women comprised 32% of 1,449 subjects and were 21% of subjects with BAV, 34% with FTAAD, 22% with TAAD <50 years, and 47% with MFS. Thoracic aortic dissections occurred with equal gender frequency yet women with BAV had more extensive dissections. Aortic size was smaller in women but was similar after controlling for BSA. Age at operation for aortic valve dysfunction, aneurysm or dissection did not differ by gender. Multivariate analysis (adjusting for age, BSA, hypertension, study site, diabetes, and subgroup diagnoses) showed that women had fewer total aortic surgeries (OR = 0.65, P  < 0.01) and were less likely to receive angiotensin converting enzyme inhibitors (ACEi; OR = 0.68, P  < 0.05). As in BAV, other genetically triggered aortic diseases such as FTAAD and TAAD <50 are more common in males. In women, decreased prevalence of aortic operations and less treatment with ACEi may be due to their smaller absolute aortic diameters. Longitudinal studies are needed to determine if women are at higher risk for adverse events. © 2013 Wiley Periodicals, Inc.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/97193/1/35836_ftp.pd