Adaptive and Supertwisting Adaptive Spacecraft Orbit Control Around Asteroids

This paper addresses the development of control systems for the orbit control of spacecraft around irregularly shaped rotating asteroids with uncertain parameters. The objective is to steer the spacecraft along prescribed orbits. First, a nonlinear adaptive law for orbit control was designed. This was followed by the design of a supertwisting adaptive (STWA) control system. In the closed-loop system, which includes the adaptive law or the STWA law, all the signals remain bounded, and the trajectory tracking error asymptotically converges to zero for any initial condition. Finally, under the assumption of boundedness of the derivative of the uncertain functions of the model in a region of the state space, a supertwisting control (STW) law for finite-time convergence of the trajectory was obtained. Based on the Lyapunov theory, stability properties of the closed-loop systems were analyzed. Simulation results for 433 Eros and Ida asteroids were presented for illustration. The results showed that control of spacecraft along closed orbits or to a fixed point is accomplished using each of these controllers, despite uncertainties in the parameters of the asteroid models

Polarization Structures in the Thomson-Scattered Emission Lines in Active Galactic Nuclei

A line photon incident in an electron-scattering medium is transferred in a diffusive way both in real space and in frequency space, and the mean number of scatterings changes as the wavelength shifts from the line center. This leads to the profile broadening and polarization dependence on the wavelength shift as a function of the Thomson optical depth $\tau_T$. We find that the polarization of the Thomson-scattered emission lines has a dip around the line center when $\tau_T$ does not exceed a few. Various structures such as the polarization flip are also seen. An application to an ionized halo component surrounding the broad emission line region in active galactic nuclei is considered and it is found that the polarization structures may still persist. Brief discussions on observational implications are given.Comment: 14 pages, 3 figures, accepted for publication in ApJ Letter

Computer programs for prediction of structural vibrations due to fluctuating pressure environments. Volume 1 - Theoretical analyses Final report

Theoretical analyses for computer program to calculate random vibrations of reinforced rectangular cylindrical panels in fluctuating pressure environmen

Conquest of the ghost pyramid of the superstring

We give a new Becchi-Rouet-Stora-Tyutin operator for the superstring. It implies a quadratic gauge-fixed action, and a new gauge-invariant action with first-class constraints. The infinite pyramid of spinor ghosts appears in a simple way through ghost gamma matrices.Comment: 30 pages, 1 figure, Late

State space collapse and diffusion approximation for a network operating under a fair bandwidth sharing policy

We consider a connection-level model of Internet congestion control, introduced by Massouli\'{e} and Roberts [Telecommunication Systems 15 (2000) 185--201], that represents the randomly varying number of flows present in a network. Here, bandwidth is shared fairly among elastic document transfers according to a weighted $\alpha$-fair bandwidth sharing policy introduced by Mo and Walrand [IEEE/ACM Transactions on Networking 8 (2000) 556--567] [$\alpha\in (0,\infty)$]. Assuming Poisson arrivals and exponentially distributed document sizes, we focus on the heavy traffic regime in which the average load placed on each resource is approximately equal to its capacity. A fluid model (or functional law of large numbers approximation) for this stochastic model was derived and analyzed in a prior work [Ann. Appl. Probab. 14 (2004) 1055--1083] by two of the authors. Here, we use the long-time behavior of the solutions of the fluid model established in that paper to derive a property called multiplicative state space collapse, which, loosely speaking, shows that in diffusion scale, the flow count process for the stochastic model can be approximately recovered as a continuous lifting of the workload process.Comment: Published in at http://dx.doi.org/10.1214/08-AAP591 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Ferromagnetism below 10 K in Mn doped BiTe

Ferromagnetism is observed below 10 K in [Bi0.75Te0.125Mn0.125]Te. This material has the BiTe structure, which is made from the stacking of two Te-Bi-Te-Bi-Te blocks and one Bi-Bi block per unit cell. Crystal structure analysis shows that Mn is localized in the Bi2 blocks, and is accompanied by an equal amount of TeBi anti-site occupancy in the Bi2Te3 blocks. These TeBi anti-site defects greatly enhance the Mn solubility. This is demonstrated by comparison of the [Bi1-xMnx]Te and [Bi1-2xTexMnx]Te series; in the former, the solubility is limited to x = 0.067, while the latter has xmax = 0.125. The magnetism in [Bi1-xMnx]Te changes little with x, while that for [Bi1-2xTexMnx]Te shows a clear variation, leading to ferromagnetism for x > 0.067. Magnetic hysteresis and the anomalous Hall Effect are observed for the ferromagnetic samples.Comment: Accepted for publication in Phys. Rev.

Modulation of the Curie Temperature in Ferromagnetic/Ferroelectric Hybrid Double Quantum Wells

We propose a ferromagnetic/ferroelectric hybrid double quantum well structure, and present an investigation of the Curie temperature (Tc) modulation in this quantum structure. The combined effects of applied electric fields and spontaneous electric polarization are considered for a system that consists of a Mn \delta-doped well, a barrier, and a p-type ferroelectric well. We calculate the change in the envelope functions of carriers at the lowest energy sub-band, resulting from applied electric fields and switching the dipole polarization. By reversing the depolarizing field, we can achieve two different ferromagnetic transition temperatures of the ferromagnetic quantum well in a fixed applied electric field. The Curie temperature strongly depends on the position of the Mn \delta-doped layer and the polarization strength of the ferroelectric well.Comment: 9 pages, 5 figures, to be published in Phys. Rev. B (2006) minor revision: One of the line types is changed in Fig.

The 1D interacting Bose gas in a hard wall box

We consider the integrable one-dimensional delta-function interacting Bose gas in a hard wall box which is exactly solved via the coordinate Bethe Ansatz. The ground state energy, including the surface energy, is derived from the Lieb-Liniger type integral equations. The leading and correction terms are obtained in the weak coupling and strong coupling regimes from both the discrete Bethe equations and the integral equations. This allows the investigation of both finite-size and boundary effects in the integrable model. We also study the Luttinger liquid behaviour by calculating Luttinger parameters and correlations. The hard wall boundary conditions are seen to have a strong effect on the ground state energy and phase correlations in the weak coupling regime. Enhancement of the local two-body correlations is shown by application of the Hellmann-Feynman theorem.Comment: 23 pages, 7 figures. Improved version. Extra figure added for the weak coupling regime. New expression for the interaction-dependent cloud size and additional reference