Analysis and test for space shuttle propellant dynamics: 1/60th scale model test results

During the abort sequence, the ET and orbiter separate under aerodynamic loading, with propellant remaining in the ET. The separation event included a seven second decelerating coast period during which the residual propellant accelerates relative to the ET/orbiter. At separation, ET clearance was primarily provided by aerodynamics acting on the ET to move it away. The motion of the propellant, primarily LOX, significantly influenced the resulting ET motion and could cause the ET to recontact the orbiter. A test program was conducted involving thirty-two drops with 1/60th scale models of the ET LOX tank. The objective was to acquire data on the nature of low g propellant reorientation, in the ET LOX tank, and to measure the forces exerted on the tank by the moving propellant

Expectations for extreme-mass-ratio bursts from the Galactic Centre

When a compact object on a highly eccentric orbit about a much more massive body passes through periapsis it emits a short gravitational wave signal known as an extreme-mass-ratio burst (EMRB). We consider stellar mass objects orbiting the massive black hole (MBH) found in the Galactic Centre. EMRBs provide a novel means of extracting information about the MBH; an EMRB from the Galactic MBH could be highly informative regarding the MBH's mass and spin if the orbital periapsis is small enough. However, to be a useful astronomical tool EMRBs must be both informative and sufficiently common to be detectable with a space-based interferometer. We construct a simple model to predict the event rate for Galactic EMRBs. We estimate there could be on average ~2 bursts in a two year mission lifetime for LISA. Stellar mass black holes dominate the event rate. Creating a sample of 100 mission realisations, we calculate what we could learn about the MBH. On average, we expect to be able to determine the MBH mass to ~1% and the spin to ~0.1 using EMRBs.Comment: 22 pages, 5 figures, 2 appendices. Minor changes to reflect published versio

Observing the Galaxy's massive black hole with gravitational wave bursts

An extreme-mass-ratio burst (EMRB) is a gravitational wave signal emitted when a compact object passes through periapsis on a highly eccentric orbit about a much more massive object, in our case a stellar mass object about a 10^6 M_sol black hole. EMRBs are a relatively unexplored means of probing the spacetime of massive black holes (MBHs). We conduct an investigation of the properties of EMRBs and how they could allow us to constrain the parameters, such as spin, of the Galaxy's MBH. We find that if an EMRB event occurs in the Galaxy, it should be detectable for periapse distances r_p < 65 r_g for a \mu = 10 M_sol orbiting object, where r_g = GM/c^2 is the gravitational radius. The signal-to-noise ratio scales as \rho ~ -2.7 log(r_p/r_g) + log(\mu/M_sol) + 4.9. For periapses r_p < 10 r_g, EMRBs can be informative, and provide good constraints on both the MBH's mass and spin. Closer orbits provide better constraints, with the best giving accuracies of better than one part in 10^4 for both the mass and spin parameter.Comment: 25 pages, 17 figures, 1 appendix. One more typo fixe

Analysis and test for space shuttle propellant dynamics

This report presents the results of a study to develop an analytical model capable of predicting the dynamic interaction forces on the Shuttle External Tank, due to large amplitude propellant slosh during RTLS separation. The report details low-g drop tower and KC-135 test programs that were conducted to investigate propellant reorientation during RTLS. In addition, the development of a nonlinear finite element slosh model (LAMPS2, two dimensional, and one LAMPS3, three dimensional) is presented. Correlation between the model and test data is presented as a verification of the modeling approach

Analysis and test for space shuttle propellant dynamics (1/10th scale model test results). Volume 1: Technical discussion

Space shuttle propellant dynamics during ET/Orbiter separation in the RTLS (return to launch site) mission abort sequence were investigated in a test program conducted in the NASA KC-135 "Zero G" aircraft using a 1/10th-scale model of the ET LOX Tank. Low-g parabolas were flown from which thirty tests were selected for evaluation. Data on the nature of low-g propellant reorientation in the ET LOX tank, and measurements of the forces exerted on the tank by the moving propellent will provide a basis for correlation with an analytical model of the slosh phenomenon

Statistical Properties of Many Particle Eigenfunctions

Wavefunction correlations and density matrices for few or many particles are derived from the properties of semiclassical energy Green functions. Universal features of fixed energy (microcanonical) random wavefunction correlation functions appear which reflect the emergence of the canonical ensemble as the number of particles approaches infinity. This arises through a little known asymptotic limit of Bessel functions. Constraints due to symmetries, boundaries, and collisions between particles can be included.Comment: 13 pages, 4 figure

Nanoscale magnetometry using a single spin system in diamond

We propose a protocol to estimate magnetic fields using a single nitrogen-vacancy (N-V) center in diamond, where the estimate precision scales inversely with time, ~1/T$, rather than the square-root of time. The method is based on converting the task of magnetometry into phase estimation, performing quantum phase estimation on a single N-V nuclear spin using either adaptive or nonadaptive feedback control, and the recently demonstrated capability to perform single-shot readout within the N-V [P. Neumann et. al., Science 329, 542 (2010)]. We present numerical simulations to show that our method provides an estimate whose precision scales close to ~1/T (T is the total estimation time), and moreover will give an unambiguous estimate of the static magnetic field experienced by the N-V. By combining this protocol with recent proposals for scanning magnetometry using an N-V, our protocol will provide a significant decrease in signal acquisition time while providing an unambiguous spatial map of the magnetic field.Comment: 8 pages and 5 figure

Geometric phases and anholonomy for a class of chaotic classical systems

Berry's phase may be viewed as arising from the parallel transport of a quantal state around a loop in parameter space. In this Letter, the classical limit of this transport is obtained for a particular class of chaotic systems. It is shown that this ``classical parallel transport'' is anholonomic --- transport around a closed curve in parameter space does not bring a point in phase space back to itself --- and is intimately related to the Robbins-Berry classical two-form.Comment: Revtex, 11 pages, no figures

Level spacings and periodic orbits

Starting from a semiclassical quantization condition based on the trace formula, we derive a periodic-orbit formula for the distribution of spacings of eigenvalues with k intermediate levels. Numerical tests verify the validity of this representation for the nearest-neighbor level spacing (k=0). In a second part, we present an asymptotic evaluation for large spacings, where consistency with random matrix theory is achieved for large k. We also discuss the relation with the method of Bogomolny and Keating [Phys. Rev. Lett. 77 (1996) 1472] for two-point correlations.Comment: 4 pages, 2 figures; major revisions in the second part, range of validity of asymptotic evaluation clarifie

The design of digital-adaptive controllers for VTOL aircraft

Design procedures for VTOL automatic control systems have been developed and are presented. Using linear-optimal estimation and control techniques as a starting point, digital-adaptive control laws have been designed for the VALT Research Aircraft, a tandem-rotor helicopter which is equipped for fully automatic flight in terminal area operations. These control laws are designed to interface with velocity-command and attitude-command guidance logic, which could be used in short-haul VTOL operations. Developments reported here include new algorithms for designing non-zero-set-point digital regulators, design procedures for rate-limited systems, and algorithms for dynamic control trim setting