Trajectory optimization by a direct descent process

The problem considered is that of trajectory optimization using step-by-step descent to minimum cost along the direction of the cost gradient with respect to the control. Using a hybrid computer, the gradient is computed di rectly as the response to nearly impulsive control perturba tions. A method is presented for computing the gradient when several terminal constraints are enforced. Examples of application of the method are presented. It is concluded that the direct gradient computation method has some significant advantages over other methods.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/68738/2/10.1177_003754976801100308.pd

155-day Periodicity in Solar Cycles 3 and 4

The near 155 days solar periodicity, so called Rieger periodicity, was first detected in solar flares data and later confirmed with other important solar indices. Unfortunately, a comprehensive analysis on the occurrence of this periodicity during previous centuries can be further complicated due to the poor quality of the sunspot number time-series. We try to detect the Rieger periodicity during the solar cycles 3 and 4 using information on aurorae observed at mid and low latitudes. We use two recently discovered aurora datasets, observed in the last quarter of the 18th century from UK and Spain. Besides simple histograms of time between consecutive events we analyse monthly series of number of aurorae observed using different spectral analysis (MTM and Wavelets). The histograms show the probable presence of Rieger periodicity during cycles 3 and 4. However different spectral analysis applied has only confirmed undoubtedly this hypothesis for solar cycle 3.Comment: 13 pages, 6 figures, to appear in New Astronom

Dynamic-error analysis of digital and combined analog-digital computer systems

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/68553/2/10.1177_003754976600600408.pd

Span morphing using the GNATSpar wing

Rigid wings usually fly at sub-optimal conditions generating unnecessary aerodynamic loses represented in flight time, fuel consumption, and unfavourable operational characteristics. High aspect ratio wings have good range and fuel efficiency, but lack manoeuvrability. On the other hand, low aspect ratio wings fly faster and are more manoeuvrable, but have poor aerodynamic performance. Span morphing technology allows integrating both features in a single wing design and allows continuously adjusting the wingspan to match the instantaneous flight conditions and mission objectives. This paper develops, a novel span morphing concept, the Gear driveN Autonomous Twin Spar (GNATSpar) for a mini-UAV. The GNATSpar can be used to achieve span extensions up to 100% but for demonstration purposes it is used here to achieve span extensions up to 20% to reduce induced drag and increase flight endurance. The GNATSpar is superior to conventional telescopic and articulated structures as it uses the space available in the opposite sides of the wing instead of relying on overlapping structures and bearings. In addition, it has a self-locking actuation mechanism due to the low lead angle of the driving worm gear. Following the preliminary aero-structural sizing of the concept, a physical prototype is developed and tested in the 7?×5? wind-tunnel at the University of Southampton. Finally, benefits and drawbacks of the design are highlighted and analysed

Modal scattering at an impedance transition in a lined flow duct

An explicit Wiener-Hopf solution is derived to describe the scattering of duct modes at a hard-soft wall impedance transition in a circular duct with uniform mean flow. Specifically, we have a circular duct r = 1,-8 <x <8 with mean flow Mach number M > 0 and a hard wall along x <0 and a wall of impedance Z along x > 0. A minimum edge condition at x = 0 requires a continuous wall streamline r = 1 + h(x, t ), no more singular than h = O(x1/2) for x ¿ 0. A mode, incident from x <0, scatters at x = 0 into a series of reflected modes and a series of transmitted modes. Of particular interest is the role of a possible instability along the lined wall in combination with the edge singularity. If one of the "upstream" running modes is to be interpreted as a downstream-running instability, we have an extra degree of freedom in the Wiener-Hopf analysis that can be resolved by application of some form of Kutta condition at x = 0, for example a more stringent edge condition where h = O(x3/2) at the downstream side. The question of the instability requires an investigation of the modes in the complex frequency plane and therefore depends on the chosen impedance model, since Z = Z(¿) is essentially frequency dependent. The usual causality condition by Briggs and Bers appears to be not applicable here because it requires a temporal growth rate bounded for all real axial wave numbers. The alternative Crighton-Leppington criterion, however, is applicable and confirms that the suspected mode is usually unstable. In general, the effect of this Kutta condition is significant, but it is particularly large for the plane wave at low frequencies and should therefore be easily measurable. For ¿ ¿ 0, the modulus tends to |R001| ¿ (1 + M)/(1 - M) without and to 1 with Kutta condition, while the end correction tends to8without and to a finite value with Kutta condition. This is exactly the same behaviour as found for reflection at a pipe exit with flow, irrespective if this is uniform or jet flow

Feigin-Frenkel center in types B, C and D

For each simple Lie algebra g consider the corresponding affine vertex algebra V_{crit}(g) at the critical level. The center of this vertex algebra is a commutative associative algebra whose structure was described by a remarkable theorem of Feigin and Frenkel about two decades ago. However, only recently simple formulas for the generators of the center were found for the Lie algebras of type A following Talalaev's discovery of explicit higher Gaudin Hamiltonians. We give explicit formulas for generators of the centers of the affine vertex algebras V_{crit}(g) associated with the simple Lie algebras g of types B, C and D. The construction relies on the Schur-Weyl duality involving the Brauer algebra, and the generators are expressed as weighted traces over tensor spaces and, equivalently, as traces over the spaces of singular vectors for the action of the Lie algebra sl_2 in the context of Howe duality. This leads to explicit constructions of commutative subalgebras of the universal enveloping algebras U(g[t]) and U(g), and to higher order Hamiltonians in the Gaudin model associated with each Lie algebra g. We also introduce analogues of the Bethe subalgebras of the Yangians Y(g) and show that their graded images coincide with the respective commutative subalgebras of U(g[t]).Comment: 29 pages, constructions of Pfaffian-type Sugawara operators and commutative subalgebras in universal enveloping algebras are adde

Chemistry of Chern-Simons Supergravity: reduction to a BPS kink, oxidation to M-theory and thermodynamical aspects

We construct a supersymmetric extension of the two dimensional Kaluza-Klein-reduced gravitational Chern-Simons term, and globally study its solutions, labelled by mass and U(1) charge c. The kink solution is BPS, and in an appropriate conformal frame all solutions asymptotically approach AdS. The thermodynamics of the Hawking effect yields interesting behavior for the specific heat and hints at a Hawking-Page-like transition at T_{critical} \sim c^{3/2}. We address implications for higher dimensions ("oxidation"), in particular D=3,4 and 11, and comment briefly on AdS/CFT aspects of the kink.Comment: 39 pages, 2 figures. v2: reference added, minor changes, typo

Example of function optimization via hybrid computation

Iterative techniques for function optimization have been considered extensivezy for use in all-digital computation. Relatively little has been done to take advantage of the much higher integration speed of hybrid computation systems. This paper demonstrates application of one simple procedure in a hybrid envi ronment and compares the results to those obtained by an efficient digital procedure. Even though a much more efficient procedure was used on the digital, time-saving factors between 8 and 2 were obtained via the simpler hybrid implementation. Since the dollar cost of the hybrid is much less than that of the digital, the hybrid has a large advantage per solution.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/68324/2/10.1177_003754977302100204.pd

Zero-Branes, Quantum Mechanics and the Cosmological Constant

We analyse some dynamical issues in a modified type IIA supergravity, recently proposed as an extension of M-theory that admits de Sitter space. In particular we find that this theory has multiple zero-brane solutions. This suggests a microscopic quantum mechanical matrix description which yields a massive deformation of the usual M(atrix) formulation of M-theory and type IIA string theory.Comment: 15 pages LaTeX, added reference

Glyphosate, Other Herbicides, And Transformation Products In Midwestern Streams, 2002

The use of glyphosate has increased rapidly, and there is limited understanding of its environmental fate. The objective of this study was to document the occurrence of glyphosate and the transformation product aminomethylphosphonic acid (AMPA) in Midwestern streams and to compare their occurrence with that of more commonly measured herbicides such as acetochlor, atrazine, and metolachlor. Water samples were collected at sites on 51 streams in nine Midwestern states in 2002 during three runoff events: after the application of pre-emergence herbicides, after the application of post-emergence herbicides, and during harvest season. All samples were analyzed for glyphosate and 20 other herbicides using gas chromatography/mass spectrometry or high performance liquid chromatography/mass spectrometry. The frequency of glyphosate and AMPA detection, range of concentrations in runoff samples, and ratios of AMPA to glyphosate concentrations did not vary throughout the growing season as substantially as for other herbicides like atrazine, probably because of different seasonal use patterns. Glyphosate was detected at or above 0.1 μg/l in 35 percent of pre-emergence, 40 percent of post-emergence, and 31 percent of harvest season samples, with a maximum concentration of 8.7 μg/l. AMPA was detected at or above 0.1 μg/l in 53 percent of pre-emergence, 83 percent of post-emergence, and 73 percent of harvest season samples, with a maximum concentration of 3.6 μg/l. Glyphosate was not detected at a concentration at or above the U.S. Environmental Protection Agency’s maximum contamination level (MCL) of 700 μg/l in any sample. Atrazine was detected at or above 0.1 μg/l in 94 percent of pre-emergence, 96 percent of postemergence, and 57 percent of harvest season samples, with a maximum concentration of 55 μg/l. Atrazine was detected at or above its MCL (3 μg/l) in 57 percent of pre-emergence and 33 percent of postemergence samples