Control Theory: The Double Pendulum Inverted on a Cart

In this thesis the Double Pendulum Inverted on a Cart (DPIC) system is modeled using the Euler-Lagrange equation for the chosen Lagrangian, giving a second-order nonlinear system. This system can be approximated by a linear first-order system in which linear control theory can be used. The important definitions and theorems of linear control theory are stated and proved to allow them to be utilized on a linear version of the DPIC system. Controllability and eigenvalue placement for the linear system are shown using MATLAB. Linear Optimal control theory is likewise explained in this section and its uses are applied to the DPIC system to derive a Linear Quadratic Regulator (LQR). Two different LQR controllers are then applied to the full nonlinear DPIC system, which is concurrently modeled in MATLAB. Also, an in-depth look is taken at the Riccati equation and its solutions. Finally, results from various MATLAB simulations are shown

Neutron inelastic scattering investigation of the magnetic excitations in Cu_2Te_2O_5X_2 (X=Br, Cl)

Neutron inelastic scattering investigations have been performed on the spin tetrahedral system Cu_2Te_2O_5X_2 (X = Cl, Br). We report the observation of magnetic excitations with a dispersive component in both compounds, associated with the 3D incommensurate magnetic order that develops below $T^{Cl}_{N}$=18.2 K and $T^{Br}_{N}$=11.4 K. The excitation in Cu_2Te_2O_5Cl_2 softens as the temperature approaches $T^{Cl}_{N}$, leaving diffuse quasi-elastic scattering above the transition temperature. In the bromide, the excitations are present well above $T^{Br}_{N}$, which might be attributed to the presence of a degree of low dimensional correlations above $T^{Br}_{N}$ in this compound

Pressure coefficients of Raman modes of carbon nanotubes resolved by chirality: Environmental effect on graphene sheet

Studies of the mechanical properties of single-walled carbon nanotubes are hindered by the availability only of ensembles of tubes with a range of diameters. Tunable Raman excitation spectroscopy picks out identifiable tubes. Under high pressure, the radial breathing mode shows a strong environmental effect shown here to be largely independent of the nature of the environment . For the G-mode, the pressure coefficient varies with diameter consistent with the thick-wall tube model. However, results show an unexpectedly strong environmental effect on the pressure coefficients. Reappraisal of data for graphene and graphite gives the G-mode Grueuneisen parameter gamma = 1.34 and the shear deformation parameter beta = 1.34.Comment: Submitted to Physical Review

Raman excitation spectroscopy of carbon nanotubes: effects of pressure medium and pressure

Raman excitation and emission spectra for the radial breathing mode (RBM) are reported, together with a preliminary analysis. From the position of the peaks on the two-dimensional plot of excitation resonance energy against Raman shift, the chiral indices (m, n) for each peak are identified. Peaks shift from their positions in air when different pressure media are added - water, hexane, sulphuric acid - and when the nanotubes are unbundled in water with surfactant and sonication. The shift is about 2 - 3 cm-1 in RBM frequency, but unexpectedly large in resonance energy, being spread over up to 100meV for a given peak. This contrasts with the effect of pressure. The shift of the peaks of semiconducting nanotubes in water under pressure is orthogonal to the shift from air to water. This permits the separation of the effects of the pressure medium and the pressure, and will enable the true pressure coefficients of the RBM and the other Raman peaks for each (m, n) to be established unambiguously.Comment: 6 pages, 3 Figures, Proceedings of EHPRG 2011 (Paris

Deep Space Network information system architecture study

The purpose of this article is to describe an architecture for the Deep Space Network (DSN) information system in the years 2000-2010 and to provide guidelines for its evolution during the 1990s. The study scope is defined to be from the front-end areas at the antennas to the end users (spacecraft teams, principal investigators, archival storage systems, and non-NASA partners). The architectural vision provides guidance for major DSN implementation efforts during the next decade. A strong motivation for the study is an expected dramatic improvement in information-systems technologies, such as the following: computer processing, automation technology (including knowledge-based systems), networking and data transport, software and hardware engineering, and human-interface technology. The proposed Ground Information System has the following major features: unified architecture from the front-end area to the end user; open-systems standards to achieve interoperability; DSN production of level 0 data; delivery of level 0 data from the Deep Space Communications Complex, if desired; dedicated telemetry processors for each receiver; security against unauthorized access and errors; and highly automated monitor and control

Precision control of thermal transport in cryogenic single-crystal silicon devices

We report on the diffusive-ballistic thermal conductance of multi-moded single-crystal silicon beams measured below 1 K. It is shown that the phonon mean-free-path $\ell$ is a strong function of the surface roughness characteristics of the beams. This effect is enhanced in diffuse beams with lengths much larger than $\ell$, even when the surface is fairly smooth, 5-10 nm rms, and the peak thermal wavelength is 0.6 $\mu$m. Resonant phonon scattering has been observed in beams with a pitted surface morphology and characteristic pit depth of 30 nm. Hence, if the surface roughness is not adequately controlled, the thermal conductance can vary significantly for diffuse beams fabricated across a wafer. In contrast, when the beam length is of order $\ell$, the conductance is dominated by ballistic transport and is effectively set by the beam area. We have demonstrated a uniformity of $\pm$8% in fractional deviation for ballistic beams, and this deviation is largely set by the thermal conductance of diffuse beams that support the micro-electro-mechanical device and electrical leads. In addition, we have found no evidence for excess specific heat in single-crystal silicon membranes. This allows for the precise control of the device heat capacity with normal metal films. We discuss the results in the context of the design and fabrication of large-format arrays of far-infrared and millimeter wavelength cryogenic detectors

Incommensurate magnetic ordering in Cu2Te2O5X2 (X=Cl, Br) studied by single crystal neutron diffraction

Polarized and unpolarized neutron diffraction studies have been carried out on single crystals of the coupled spin tetrahedra systems Cu2Te2O5X2 (X=Cl, Br). A model of the magnetic structure associated with the propagation vectors k'Cl ~ -0.150,0.422,1/2 and k'Br ~ -0.172,0.356,1/2 and stable below TN=18 K for X=Cl and TN=11 K for X=Br is proposed. A feature of the model, common to both the bromide and chloride, is a canted coplanar motif for the 4 Cu2+ spins on each tetrahedron which rotates on a helix from cell to cell following the propagation vector. The Cu2+magnetic moment determined for X=Br, 0.395(5)muB, is significantly less than for X=Cl, 0.88(1)muB at 2K. The magnetic structure of the chloride associated with the wave-vector k' differs from that determined previously for the wave vector k~0.150,0.422,1/2 [O. Zaharko et.al. Phys. Rev. Lett. 93, 217206 (2004)]

Electron-impact ionization of atomic hydrogen at 2 eV above threshold

The convergent close-coupling method is applied to the calculation of fully differential cross sections for ionization of atomic hydrogen by 15.6 eV electrons. We find that even at this low energy the method is able to yield predictive results with small uncertainty. As a consequence we suspect that the experimental normalization at this energy is approximately a factor of two too high.Comment: 10 page

Optical measurement of blood flow changes in spinal cord injury

Little is known about cell death in spinal cord tissue following compression injury, despite compression being a key component of spinal injuries. Currently models are used to mimic compression injury in animals and the effects of the compression evaluated by observing the extent and duration of recovery of normal motor function in the days and weeks following the injury. A fibreoptic photoplethysmography system was used to investigate whether pulsation of the small arteries in the spinal cord occurred before, during and after compressive loads were applied to the tissue. It was found that the signal amplitudes were reduced and this reduction persisted for at least five minutes after the compression ceased. It is hoped that results from this preliminary study may improve knowledge of the mechanism of spinal cord injury