1-Bit processing based model predictive control for fractionated satellite missions

In this thesis, a 1-bit processing based Model Predictive Control (OBMPC) structure is proposed for a fractionated satellite attitude control mission. Despite the appealing advantages of the MPC algorithm towards constrained MIMO control applications, implementing the MPC algorithm onboard a small satellite is certainly challenging due to the limited onboard resources. The proposed design is based on the 1-bit processing concept, which takes advantage of the affine relation between the 1-bit state feedback and multi-bit parameters to implement a multiplier free MPC controller. As multipliers are the major power consumer in online optimization, the OBMPC structure is proven to be more efficient in comparison to the conventional MPC implementation in term of power and circuit complexity. The system is in digital control nature, affected by quantization noise introduced by Δ∑ modulators. The stability issues and practical design criteria are also discussed in this work. Some other aspects are considered in this work to complete the control system. Firstly, the implementation of the OBMPC system relies on the 1-bit state feedbacks. Hence, 1-bit sensing components are needed to implement the OBMPC system. While the ∆∑ modulator based Microelectromechanical systems (MEMS) gyroscope is considered in this work, it is possible to implement this concept into other sensing components. Secondly, as the proposed attitude mission is based on the wireless inter-satellite link (ISL), a state estimator is required. However, conventional state estimators will once again introduce multi-bit signals, and compromise the simple, direct implementation of the OBMPC controller. Therefore, the 1-bit state estimator is also designed in this work to satisfy the requirements of the proposed fractionated attitude control mission. The simulation for the OBMPC is based on a 2U CubeSat model in a fractionated satellite structure, in which the payload and actuators are separated from the controller and controlled via the ISL. Matlab simulations and FPGA implementation based performance analysis shows that the OBMPC is feasible for fractionated satellite missions and is advantageous over the conventional MPC controllers

Rapid Temporal Modulation of Synchrony by Competition in Cortical Interneuron Networks

The synchrony of neurons in extrastriate visual cortex is modulated by selective attention even when there are only small changes in firing rate (Fries, Reynolds, Rorie, & Desimone, 2001). We used Hodgkin-Huxley type models of cortical neurons to investigate the mechanism by which the degree of synchrony can be modulated independently of changes in firing rates

Quantum and classical solutions for free particle in wedge billiards

We have studied the quantum and classical solutions of a particle constrained to move inside a sector circular billiard with angle $\theta_w$ and its pacman complement with angle $2\pi-\theta_w$. In these billiards rotational invariance is broken and angular momentum is no longer a conserved quantum number. The "fractional" angular momentum quantum solutions are given in terms of Bessel functions of fractional order, with indices $\lambda_p={p\pi \over {\theta_w}}$, $p=1,2,...$ for the sector and $\mu_q={q\pi \over {2\pi - \theta_w}}$, $q=1,2...$ for the pacman. We derive a ``duality'' relation between both fractional indices given by $\lambda_p={{p\mu_q} \over {2\mu_q - q}}$ and $\mu_q = {{q\lambda_p} \over {2\lambda_p - p}}$. We find that the average of the angular momentum $\hat L_z$ is zero but the average of $\hat L^2_z$ has as eigenvalues $\lambda_p^2$ and $\mu_q^2$. We also make a connection of some classical solutions to their quantum wave eigenfunction counterparts.Comment: 10 pages and two PostScript figure

Giant Shapiro steps for two-dimensional Josephson-junction arrays with time-dependent Ginzburg-Landau dynamics

Two-dimensional Josephson junction arrays at zero temperature are investigated numerically within the resistively shunted junction (RSJ) model and the time-dependent Ginzburg-Landau (TDGL) model with global conservation of current implemented through the fluctuating twist boundary condition (FTBC). Fractional giant Shapiro steps are found for {\em both} the RSJ and TDGL cases. This implies that the local current conservation, on which the RSJ model is based, can be relaxed to the TDGL dynamics with only global current conservation, without changing the sequence of Shapiro steps. However, when the maximum widths of the steps are compared for the two models some qualitative differences are found at higher frequencies. The critical current is also calculated and comparisons with earlier results are made. It is found that the FTBC is a more adequate boundary condition than the conventional uniform current injection method because it minimizes the influence of the boundary.Comment: 6 pages including 4 figures in two columns, final versio

Lattice effects on the current-voltage characteristics of superconducting arrays

The lattice effects on the current-voltage characteristics of two-dimensional arrays of resistively shunted Josephson junctions are investigated. The lattice potential energies due to the discrete lattice structure are calculated for several geometries and directions of current injection. We compare the energy barrier for vortex-pair unbinding with the lattice pinning potential, which shows that lattice effects are negligible in the low-current limit as well as in the high-current limit. At intermediate currents, on the other hand, the lattice potential becomes comparable to the barrier height and the lattice effects may be observed in the current-voltage characteristics.Comment: 5 pages including 5 figures in two columns, to appear in Phys. Rev.

Flux-noise spectra around the Kosterlitz-Thouless transition for two-dimensional superconductors

The flux-noise spectra around the Kosterlitz-Thouless transition are obtained from simulations of the two-dimensional resistively shunted junction model. In particular the dependence on the distance $d$ between the pick-up coil and the sample is investigated. The typical experimental situation corresponds to the large-$d$ limit and a simple relation valid in this limit between the complex impedance and the noise spectra is clarified. Features, which distinguish between the large- and small-$d$ limit, are identified and the possibility of observing these features in experiments is discussed.Comment: 12 pages including 8 figures, submitted to Phys. Rev.

Boundary Effects on Dynamic Behavior of Josephson-Junction Arrays

The boundary effects on the current-voltage characteristics in two-dimensional arrays of resistively shunted Josephson junctions are examined. In particular, we consider both the conventional boundary conditions (CBC) and the fluctuating twist boundary conditions (FTBC), and make comparison of the obtained results. It is observed that the CBC, which have been widely adopted in existing simulations, may give a problem in scaling, arising from rather large boundary effects; the FTBC in general turn out to be effective in reducing the finite-size effects, yielding results with good scaling behavior. To resolve the discrepancy between the two boundary conditions, we propose that the proper scaling in the CBC should be performed with the boundary data discarded: This is shown to give results which indeed scale well and are the same as those from the FTBC.Comment: RevTex, Final version to appear in Phys. Rev.

Orientational pinning and transverse voltage: Simulations and experiments in square Josephson junction arrays

We study the dependence of the transport properties of square Josephson Junctions arrays with the direction of the applied dc current, both experimentally and numerically. We present computational simulations of current-voltage curves at finite temperatures for a single vortex in the array ($Ha^2/\Phi_0=f=1/L^2$), and experimental measurements in $100\times1000$ arrays under a low magnetic field corresponding to $f\approx0.02$. We find that the transverse voltage vanishes only in the directions of maximum symmetry of the square lattice: the [10] and [01] direction (parallel bias) and the [11] direction (diagonal bias). For orientations different than the symmetry directions, we find a finite transverse voltage which depends strongly on the angle $\phi$ of the current. We find that vortex motion is pinned in the [10] direction ($\phi=0$), meaning that the voltage response is insensitive to small changes in the orientation of the current near $\phi=0$. We call this phenomenon orientational pinning. This leads to a finite transverse critical current for a bias at $\phi=0$ and to a transverse voltage for a bias at $\phi\not=0$. On the other hand, for diagonal bias in the [11] direction the behavior is highly unstable against small variations of $\phi$, leading to a rapid change from zero transverse voltage to a large transverse voltage within a few degrees. This last behavior is in good agreement with our measurements in arrays with a quasi-diagonal current drive.Comment: 9 pages, 9 figure

Vortex dynamics for two-dimensional XY models

Two-dimensional XY models with resistively shunted junction (RSJ) dynamics and time dependent Ginzburg-Landau (TDGL) dynamics are simulated and it is verified that the vortex response is well described by the Minnhagen phenomenology for both types of dynamics. Evidence is presented supporting that the dynamical critical exponent $z$ in the low-temperature phase is given by the scaling prediction (expressed in terms of the Coulomb gas temperature $T^{CG}$ and the vortex renormalization given by the dielectric constant $\tilde\epsilon$) $z=1/\tilde{\epsilon}T^{CG}-2\geq 2$ both for RSJ and TDGL and that the nonlinear IV exponent a is given by a=z+1 in the low-temperature phase. The results are discussed and compared with the results of other recent papers and the importance of the boundary conditions is emphasized.Comment: 21 pages including 15 figures, final versio

Portfolio of compositions

My Masters research has been to the aim of my development as a composer of original music with an individual voice that is nonetheless informed by the musical and aesthetic currents alive in our contemporary society. This paper is an exegesis on my portfolio of compositions, written during my Masters candidature from 2006-08, in which I pursue a generally-consistent language towards a music that situates itself across a number of dualities with the aim to resolve their opposing strands, while exploring a wide range of thematic and philosophical concerns. The musical analyses contained within demonstrate my compositional technical apparatus which bridges between microstructural cellular detail and an organically unified whole, and promotes a consideration of metaphorical issues that arise through further aesthetic contemplation