5 research outputs found
Piecewise Linear Models for the Quasiperiodic Transition to Chaos
We formulate and study analytically and computationally two families of
piecewise linear degree one circle maps. These families offer the rare
advantage of being non-trivial but essentially solvable models for the
phenomenon of mode-locking and the quasi-periodic transition to chaos. For
instance, for these families, we obtain complete solutions to several questions
still largely unanswered for families of smooth circle maps. Our main results
describe (1) the sets of maps in these families having some prescribed rotation
interval; (2) the boundaries between zero and positive topological entropy and
between zero length and non-zero length rotation interval; and (3) the
structure and bifurcations of the attractors in one of these families. We
discuss the interpretation of these maps as low-order spline approximations to
the classic ``sine-circle'' map and examine more generally the implications of
our results for the case of smooth circle maps. We also mention a possible
connection to recent experiments on models of a driven Josephson junction.Comment: 75 pages, plain TeX, 47 figures (available on request
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Improvement of Azimuthal Homogeneity in Permanent-Magnet Bearing Rotors
Permanent magnets that are levitated and rotating over a bulk high-temperature superconductor (HTS) form the basis of many superconducting bearing designs. Experiments have shown that the rotational-loss``coefficient of friction`` for thrust bearings of this type can be as low as 8 {times} 10{sup {minus}6}. While the loss mechanisms of such bearings are not well understood, the azimuthal homogeneity of the rotating permanent magnet is believed to play an important role in determining the loss. One possible loss mechanism is magnetic hysteresis in the HTS, where the energy loss E per cycle is derived from the critical state model and given by E = K ({Delta}B{sup 3}/J{sub c}) where K is a geometric coefficient, {Delta}B is the variation in magnetic field at the surface of the HTS experienced during a rotation of the levitated magnet, and J{sub c} is the critical current density of the HTS. It is clear that a small decrease in {Delta}B (i.e., decreasing the azimuthal inhomogeneity of the rotating magnetic field) could have profound effects on decreasing E and the rotational coefficient of friction. The role of {Delta}B is also expected to be significant in reducing losses from eddy currents and other mechanisms. Low rotational losses in HTS bearings have been demonstrated only for levitated masses of several grams. For practical bearings, it is important to obtain these low losses with larger levitated masses. There are two main routes toward decreasing {Delta}B. The first is to improve the alignment of the magnetic particles during fabrication and to maintain close tolerances on grinding angles during manufacture of the permanent magnet. The second, the subject of this paper, is to provide correctional procedures after the magnet is fabricated
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Improvement of Azimuthal Homogeneity in Permanent-Magnet Bearing Rotors
Permanent magnets that are levitated and rotating over a bulk high-temperature superconductor (HTS) form the basis of many superconducting bearing designs. Experiments have shown that the rotational-loss coefficient of friction'' for thrust bearings of this type can be as low as 8 [times] 10[sup [minus]6]. While the loss mechanisms of such bearings are not well understood, the azimuthal homogeneity of the rotating permanent magnet is believed to play an important role in determining the loss. One possible loss mechanism is magnetic hysteresis in the HTS, where the energy loss E per cycle is derived from the critical state model and given by E = K ([Delta]B[sup 3]/J[sub c]) where K is a geometric coefficient, [Delta]B is the variation in magnetic field at the surface of the HTS experienced during a rotation of the levitated magnet, and J[sub c] is the critical current density of the HTS. It is clear that a small decrease in [Delta]B (i.e., decreasing the azimuthal inhomogeneity of the rotating magnetic field) could have profound effects on decreasing E and the rotational coefficient of friction. The role of [Delta]B is also expected to be significant in reducing losses from eddy currents and other mechanisms. Low rotational losses in HTS bearings have been demonstrated only for levitated masses of several grams. For practical bearings, it is important to obtain these low losses with larger levitated masses. There are two main routes toward decreasing [Delta]B. The first is to improve the alignment of the magnetic particles during fabrication and to maintain close tolerances on grinding angles during manufacture of the permanent magnet. The second, the subject of this paper, is to provide correctional procedures after the magnet is fabricated
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A permanent-magnet rotor for a high-temperature superconducting bearing
Design, fabrication, and performance, of a 1/3-m dia., 10-kg flywheel rotor with only one bearing is discussed. To achieve low-loss energy storage, the rotor`s segmented-ring permanent-magnet (PM) is optimized for levitation and circumferential homogeneity. The magnet`s carbon composite bands enable practical energy storage