Robust Neighboring Optimal Guidance for the Advanced Launch System

In recent years, optimization has become an engineering tool through the availability of numerous successful nonlinear programming codes. Optimal control problems are converted into parameter optimization (nonlinear programming) problems by assuming the control to be piecewise linear, making the unknowns the nodes or junction points of the linear control segments. Once the optimal piecewise linear control (suboptimal) control is known, a guidance law for operating near the suboptimal path is the neighboring optimal piecewise linear control (neighboring suboptimal control). Research conducted under this grant has been directed toward the investigation of neighboring suboptimal control as a guidance scheme for an advanced launch system

Neighboring suboptimal control for vehicle guidance

The neighboring optimal feedback control law is developed for systems with a piecewise linear control for the case where the optimal control is obtained by nonlinear programming techniques. To develop the control perturbation for a given deviation from the nominal path, the second variation is minimized subject to the constraint that the final conditions be satisfied (neighboring suboptimal control). This process leads to a feedback relationship between the control perturbation and the measured deviation from the nominal state. Neighboring suboptimal control is applied to the lunar launch problem. Two approaches, single optimization and multiple optimization for calculating the gains are used, and the gains are tested in a guidance simulation with a mismatch in the acceleration of gravity. Both approaches give acceptable results, but multiple optimization keeps the perturbed path closer to the nominal path

Advanced launch system trajectory optimization using suboptimal control

The maximum-final mass trajectory of a proposed configuration of the Advanced Launch System is presented. A model for the two-stage rocket is given; the optimal control problem is formulated as a parameter optimization problem; and the optimal trajectory is computed using a nonlinear programming code called VF02AD. Numerical results are presented for the controls (angle of attack and velocity roll angle) and the states. After the initial rotation, the angle of attack goes to a positive value to keep the trajectory as high as possible, returns to near zero to pass through the transonic regime and satisfy the dynamic pressure constraint, returns to a positive value to keep the trajectory high and to take advantage of minimum drag at positive angle of attack due to aerodynamic shading of the booster, and then rolls off to negative values to satisfy the constraints. Because the engines cannot be throttled, the maximum dynamic pressure occurs at a single point; there is no maximum dynamic pressure subarc. To test approximations for obtaining analytical solutions for guidance, two additional optimal trajectories are computed: one using untrimmed aerodynamics and one using no atmospheric effects except for the dynamic pressure constraint. It is concluded that untrimmed aerodynamics has a negligible effect on the optimal trajectory and that approximate optimal controls should be able to be obtained by treating atmospheric effects as perturbations

Response and Recovery of the Comanche Carbonate Platform Surrounding Multiple Cretaceous Oceanic Anoxic Events, Northern Gulf of Mexico

The ubiquity of carbonate platforms throughout the Cretaceous Period is recognized as a product of high eustatic sea-level and a distinct climatic optimum induced by rapid sea-floor spreading and elevated levels of atmospheric carbon-dioxide. Notably, a series of global oceanic anoxic events (OAEs) punctuate this time-interval and mark periods of significantly reduced free oxygen in the world's oceans. The best records of these events are often from one-dimensional shelf or basin sections where only abrupt shifts between oxygenated carbonates and anoxic shales are recorded. The Comanche Platform of central Texas provides a unique opportunity to study these events within a well-constrained stratigraphic framework in which their up-dip and down-dip sedimentologic effects can be observed and the recovery of the platform to equilibrium states can be timed and understood. Stable isotope data from whole cores in middle Hauterivian through lower Campanian mixed carbonate-siliciclastic strata are used to construct a 52-myr carbon isotope reference profile for the northern Gulf of Mexico. Correlation of this composite curve to numerous global reference profiles permits identification of several anoxic events and allows their impact on platform architecture and fades distribution to be documented. Oceanic anoxic events la, 1b, 1d, and 2 occurred immediately before, after, or during shale deposition in the Pine Island Member, Bexar Member, Del Rio Formation, and Eagle Ford Group, respectively. Oceanic anoxic event 3 corresponds to deposition of the Austin Chalk Group. Platform drowning on three occasions more closely coincided with globally recognized anoxic sub-events such as the Fallot, Albian-Cenomanian, and Mid-Cenomanian events. This illustrates that the specific anoxic event most affecting a given carbonate platform varied globally as a function of regional oceanographic circumstances. Using chemo- and sequence-stratigraphic observations, a four-stage model is proposed to describe the changing fades patterns, fauna, sedimentation accumulation rates, platform architectures, and relative sea-level trends of transgressive-regressive composite sequences that developed in response to global carbon-cycle perturbations. The four phases of platform evolution include the equilibrium, crisis, anoxic, and recovery stages. The equilibrium stage is characterized by progradational shelf geometries and coralrudist phototrophic faunal assemblages. Similar phototrophic fauna typify the crisis stage; however, incipient biocalcification crises of this phase led to retrogradational shelf morphologies, transgressive facies patterns, and increased clay mineral proportions. Anoxic stages of the Comanche Platform were coincident with back-ground deposition of organic-rich shale on drowned shelves and heterotrophic fauna dominated by oysters or coccolithophorids. Eustatic peaks of this stage were of moderate amplitude (similar to 30 m), yet relative sea-level rises were greatly enhanced by reduced sedimentation rates. In the recovery stage, heterotrophic carbonate factories re-established at the shoreline as progradational ramp systems and sediment accumulation rates slowly increased as dysoxia diminished. Full recovery to equilibrium conditions may or may not have followed. Geochemical and stratigraphic trends present in the four stages are consistent with increased volcanism along mid-ocean ridges and in large-igneous provinces as primary drivers of Cretaceous OAEs and the resulting transgressive-regressive composite sequences. (C) 2014 Elsevier Ltd. All rights reserved.BHP-BillitonReservoir Characterization Research Laboratory, the Bureau of Economic GeologyJackson School of Geosciences at the University of Texas at AustinBureau of Economic Geolog

Primary Beam Shape Calibration from Mosaicked, Interferometric Observations

Image quality in mosaicked observations from interferometric radio telescopes is strongly dependent on the accuracy with which the antenna primary beam is calibrated. The next generation of radio telescope arrays such as the Allen Telescope Array (ATA) and the Square Kilometer Array (SKA) have key science goals that involve making large mosaicked observations filled with bright point sources. We present a new method for calibrating the shape of the telescope's mean primary beam that uses the multiple redundant observations of these bright sources in the mosaic. The method has an analytical solution for simple Gaussian beam shapes but can also be applied to more complex beam shapes through $\chi^2$ minimization. One major benefit of this simple, conceptually clean method is that it makes use of the science data for calibration purposes, thus saving telescope time and improving accuracy through simultaneous calibration and observation. We apply the method both to 1.43 GHz data taken during the ATA Twenty Centimeter Survey (ATATS) and to 3.14 GHz data taken during the ATA's Pi Gigahertz Sky Survey (PiGSS). We find that the beam's calculated full width at half maximum (FWHM) values are consistent with the theoretical values, the values measured by several independent methods, and the values from the simulation we use to demonstrate the effectiveness of our method on data from future telescopes such as the expanded ATA and the SKA. These results are preliminary, and can be expanded upon by fitting more complex beam shapes. We also investigate, by way of a simulation, the dependence of the accuracy of the telescope's FWHM on antenna number. We find that the uncertainty returned by our fitting method is inversely proportional to the number of antennas in the array.Comment: Accepted by PASP. 8 pages, 8 figure

Generalized Geometry and M theory

We reformulate the Hamiltonian form of bosonic eleven dimensional supergravity in terms of an object that unifies the three-form and the metric. For the case of four spatial dimensions, the duality group is manifest and the metric and C-field are on an equal footing even though no dimensional reduction is required for our results to hold. One may also describe our results using the generalized geometry that emerges from membrane duality. The relationship between the twisted Courant algebra and the gauge symmetries of eleven dimensional supergravity are described in detail.Comment: 29 pages of Latex, v2 References added, typos fixed, v3 corrected kinetic term and references adde

A Trapped Field of 17.6 T in Melt-Processed, Bulk Gd-Ba-Cu-O Reinforced with Shrink-Fit Steel

The ability of large grain, REBa$_{2}$Cu$_{3}$O$_{7-\delta}$ [(RE)BCO; RE = rare earth] bulk superconductors to trap magnetic field is determined by their critical current. With high trapped fields, however, bulk samples are subject to a relatively large Lorentz force, and their performance is limited primarily by their tensile strength. Consequently, sample reinforcement is the key to performance improvement in these technologically important materials. In this work, we report a trapped field of 17.6 T, the largest reported to date, in a stack of two, silver-doped GdBCO superconducting bulk samples, each of diameter 25 mm, fabricated by top-seeded melt growth (TSMG) and reinforced with shrink-fit stainless steel. This sample preparation technique has the advantage of being relatively straightforward and inexpensive to implement and offers the prospect of easy access to portable, high magnetic fields without any requirement for a sustaining current source.Comment: Updated submission to reflect licence change to CC-BY. This is the "author accepted manuscript" and is identical in content to the published versio

Duality Invariant M-theory: Gauged supergravities and Scherk-Schwarz reductions

We consider the reduction of the duality invariant approach to M-theory by a U-duality group valued Scherk-Schwarz twist. The result is to produce potentials for gauged supergravities that are normally associated with non-geometric compactifications. The local symmetry reduces to gauge transformations with the gaugings exactly matching those of the embedding tensor approach to gauged supergravity. Importantly, this approach now includes a nontrivial dependence of the fields on the extra coordinates of the extended space.Comment: 22 pages Latex; v2: typos corrected and references adde

Zero Modes for the D=11 Membrane and Five-Brane

There exist extremal p-brane solutions of $D\!=\!11$ supergravity for p=2~and~5. In this paper we investigate the zero modes of the membrane and the five-brane solutions as a first step toward understanding the full quantum theory of these objects. It is found that both solutions possess the correct number of normalizable zero modes dictated by supersymmetry.Comment: Minor typos corrected, one reference added, agrees with published version. 9 RevTeX pages, 1 figure include