Nonlinear analysis of phased-locked loops with rapidly varying phase

The performance of command and telemetry systems, useful in deep-space communications, is frequently affected by the radio-frequency phase error which is introduced at the point of reception by means of the carrier tracking loop. In low data rate communications, this phase error may vary rapidly over the duration of the signaling interval. In this paper such phase variation is characterized by a sinusoidal input phase, K sin (omega sub o t+, pi/6), which models a typical phase variation in communication over turbulent media. Conditions for synchronization stability and the acquisition behavior are examined by detailed computer study of the phase-plane trajectories for the second and third-order loops with perfect integrator. It is demonstrated that for the phase variation considered the third-order loop has no real advantage over the second-order loop. Finally, it is shown that nonzero initial conditions may result in large steady-state phase error

An algorithm for clock synchronization with the gradient property in sensor networks

We introduce a distributed algorithm for clock synchronization in sensor networks. Our algorithm assumes that nodes in the network only know their immediate neighborhoods and an upper bound on the network's diameter. Clock-synchronization messages are only sent as part of the communication, assumed reasonably frequent, that already takes place among nodes. The algorithm has the gradient property of [2], achieving an O(1) worst-case skew between the logical clocks of neighbors. As in the case of [3,8], the algorithm's actions are such that no constant lower bound exists on the rate at which logical clocks progress in time, and for this reason the lower bound of [2,5] that forbids constant skew between neighbors does not apply

SU(N) Coherent States

We generalize Schwinger boson representation of SU(2) algebra to SU(N) and define coherent states of SU(N) using $2(2^{N-1}-1)$ bosonic harmonic oscillator creation and annihilation operators. We give an explicit construction of all (N-1) Casimirs of SU(N) in terms of these creation and annihilation operators. The SU(N) coherent states belonging to any irreducible representations of SU(N) are labelled by the eigenvalues of the Casimir operators and are characterized by (N-1) complex orthonormal vectors describing the SU(N) manifold. The coherent states provide a resolution of identity, satisfy the continuity property, and possess a variety of group theoretic properties.Comment: 25 pages, LaTex, no figure

Timing Features of the Accretion--driven Millisecond X-Ray Pulsar XTE J1807--294 in 2003 March Outburst

In order to probe the activity of the inner disk flow and its effect on the neutron star surface emissions, we carried out the timing analysis of the Rossi X-Ray Timing Explorer (RXTE) observations of the millisecond X-ray pulsar XTE J1807--294, focusing on its correlated behaviors in X-ray intensities, hardness ratios, pulse profiles and power density spectra. The source was observed to have a serial of broad "puny" flares on a timescale of hours to days on the top of a decaying outburst in March 2003. In the flares, the spectra are softened and the pulse profiles become more sinusoidal. The frequency of kilohertz quasi-periodic oscillation (kHz QPO) is found to be positively related to the X-ray count rate in the flares. These features observed in the flares could be due to the accreting flow inhomogeneities. It is noticed that the fractional pulse amplitude increases with the flare intensities in a range of $\sim 2$, comparable to those observed in the thermonuclear bursts of the millisecond X-ray pulsar XTE J1814--338, whereas it remains at about 6.5% in the normal state. Such a significant variation of the pulse profile in the "puny" flares may reflect the changes of physical parameters in the inner disk accretion region. Furthermore, we noticed an overall positive correlation between the kHz QPO frequency and the fractional pulse amplitude, which could be the first evidence representing that the neutron-star surface emission properties are very sensitive to the disk flow inhomogeneities. This effect should be cautiously considered in the burst oscillation studies.Comment: Accepted by ApJ, 23 pages, 7 figures, 3 table