Orbit period modulation for relative motion using continuous low thrust in the two-body and restricted three-body problems

This paper presents rich new families of relative orbits for spacecraft formation flight generated through the application of continuous thrust with only minimal intervention into the dynamics of the problem. Such simplicity facilitates implementation for small, low-cost spacecraft with only position state feedback, and yet permits interesting and novel relative orbits in both two- and three-body systems with potential future applications in space-based interferometry, hyperspectral sensing, and on-orbit inspection. Position feedback is used to modify the natural frequencies of the linearised relative dynamics through direct manipulation of the system eigenvalues, producing new families of stable relative orbits. Specifically, in the Hill–Clohessy–Wiltshire frame, simple adaptations of the linearised dynamics are used to produce a circular relative orbit, frequency-modulated out-of-plane motion, and a novel doubly periodic cylindrical relative trajectory for the purposes of on-orbit inspection. Within the circular restricted three-body problem, a similar minimal approach with position feedback is used to generate new families of stable, frequency-modulated relative orbits in the vicinity of a Lagrange point, culminating in the derivation of the gain requirements for synchronisation of the in-plane and out-of-plane frequencies to yield a singly periodic tilted elliptical relative orbit with potential use as a Lunar far-side communications relay. The Δv requirements for the cylindrical relative orbit and singly periodic Lagrange point orbit are analysed, and it is shown that these requirements are modest and feasible for existing low-thrust propulsion technology

Baxter operator formalism for Macdonald polynomials

We develop basic constructions of the Baxter operator formalism for the Macdonald polynomials associated with root systems of type A. Precisely we construct a dual pair of mutually commuting Baxter operators such that the Macdonald polynomials are their common eigenfunctions. The dual pair of Baxter operators is closely related to the dual pair of recursive operators for Macdonald polynomials leading to various families of their integral representations. We also construct the Baxter operator formalism for the q-deformed gl(l+1)-Whittaker functions and the Jack polynomials obtained by degenerations of the Macdonald polynomials associated with the type A_l root system. This note provides a generalization of our previous results on the Baxter operator formalism for the Whittaker functions. It was demonstrated previously that Baxter operator formalism for the Whittaker functions has deep connections with representation theory. In particular the Baxter operators should be considered as elements of appropriate spherical Hecke algebras and their eigenvalues are identified with local Archimedean L-factors associated with admissible representations of reductive groups over R. We expect that the Baxter operator formalism for the Macdonald polynomials has an interpretation in representation theory of higher-dimensional arithmetic fields.Comment: 22 pages, typos are fixe

E151 (sym15), A Pleiotropic Mutant of Pea (Pisum sativum L.), Displays Low Nodule Number, Enhanced Mycorrhizae, Delayed Lateral Root Emergence, and High Root Cytokinin Levels

In legumes, the formation of rhizobial and mycorrhizal root symbioses is a highly regulated process which requires close communication between plant and microorganism. Plant mutants that have difficulties establishing symbioses are valuable tools for unravelling the mechanisms by which these symbioses are formed and regulated. Here E151, a mutant of Pisum sativum cv. Sparkle, was examined to characterize its root growth and symbiotic defects. The symbioses in terms of colonization intensity, functionality of micro-symbionts, and organ dominance were compared between the mutant and wild type. The endogenous cytokinin (CK) and abscisic acid (ABA) levels and the effect of the exogenous application of these two hormones were determined. E151 was found to be a low and delayed nodulator, exhibiting defects in both the epidermal and cortical programmes though a few mature and functional nodules develop. Mycorrhizal colonization of E151 was intensified, although the fungal functionality was impaired. Furthermore, E151 displayed an altered lateral root (LR) phenotype compared with that of the wild type whereby LR emergence is initially delayed but eventually overcome. No differences in ABA levels were found between the mutant and the wild type, but non-inoculated E151 exhibited significantly high CK levels. It is hypothesized that CK plays an essential role in differentially mediating the entry of the two micro-symbionts into the cortex; whereas it would inhibit the entry of the rhizobia in that tissue, it would promote that of the fungus. E151 is a developmental mutant which may prove to be a useful tool in further understanding the role of hormones in the regulation of beneficial root symbioses

Collective Modes in a Symmetry-Broken Phase: Antiferromagnetically Correlated Quantum Wells

We investigate the intersubband spin-density-excitation spectrum of a double quantum well in a low-density symmetry-broken phase with interwell antiferromagnetic correlations. This spectrum is related to the intensity measured in depolarized inelastic light scattering (ILS) experiments and therefore provides a means of empirically identifying the antiferromagnetic phase. Our computations reveal the existence of two collective modes, a damped Nambu-Goldstone (NG) mode arising from the broken spin symmetry and an undamped optical mode. Since the NG mode contains most of the spectral weight, ILS experiments will need to examine the low-frequency response for signatures of the antiferromagnetic phase.Comment: 4 pages, REVTEX with psfig macro, 4 figure

Minority carrier lifetime in silicon photovoltaics : the effect of oxygen precipitation

Single-crystal Czochralski silicon used for photovoltaics is typically supersaturated with interstitial oxygen at temperatures just below the melting point. Oxide precipitates therefore can form during ingot cooling and cell processing, and nucleation sites are typically vacancy-rich regions. Oxygen precipitation gives rise to recombination centres, which can reduce cell efficiencies by as much as 4% (absolute). We have studied the recombination behaviour in p-type and n-type monocrystalline silicon with a range of doping levels intentionally processed to contain oxide precipitates with a range of densities, sizes and morphologies. We analyse injection-dependent minority carrier lifetime measurements to give a full parameterisation of the recombination activity in terms of Shockley–Read–Hall statistics. We intentionally contaminate specimens with iron, and show recombination activity arises from iron segregated to oxide precipitates and surrounding defects. We find that phosphorus diffusion gettering reduces the recombination activity of the precipitates to some extent. We also find that bulk iron is preferentially gettered to the phosphorus diffused layer rather than to oxide precipitates

General moments of the inverse real Wishart distribution and orthogonal Weingarten functions

Let $W$ be a random positive definite symmetric matrix distributed according to a real Wishart distribution and let $W^{-1}=(W^{ij})_{i,j}$ be its inverse matrix. We compute general moments $\mathbb{E} [W^{k_1 k_2} W^{k_3 k_4} ... W^{k_{2n-1}k_{2n}}]$ explicitly. To do so, we employ the orthogonal Weingarten function, which was recently introduced in the study for Haar-distributed orthogonal matrices. As applications, we give formulas for moments of traces of a Wishart matrix and its inverse.Comment: 29 pages. The last version differs from the published version, but it includes Appendi

ADVANCED TECHNOLOGIES FOR STRIPPER GAS WELL ENHANCEMENT

As part of Task 1 in the Advanced Technologies for Stripper Gas Well Enhancement, Schlumberger--Holditch Reservoir Technologies (H-RT) has partnered with two Appalachian Basin producers, Great Lakes Energy (formerly Range Resources) and Belden and Blake Corporation, to develop methodologies for the identification and enhancement of stripper wells with economic upside potential. These industry partners have provided data for over 700 wells in northwestern Pennsylvania. Phase 1 goals of this project are to develop and validate methodologies that can quickly and cost-effectively identify wells with enhancement potential. We are currently in the final stages of developing and testing our new Access/Excel based software and processing this well data to generate a list of potential candidate wells that can be used in Phase 2 to validate these methodologies

Orbital and spin contributions to the gg-tensors in metal nanoparticles

We present a theoretical study of the mesoscopic fluctuations of $g$-tensors in a metal nanoparticle. The calculations were performed using a semi-realistic tight-binding model, which contains both spin and orbital contributions to the $g$-tensors. The results depend on the product of the spin-orbit scattering time $\tau_{\textrm{\small so}}$ and the mean-level spacing $\delta$, but are otherwise weakly affected by the specific shape of a {\it generic} nanoparticle. We find that the spin contribution to the $g$-tensors agrees with Random Matrix Theory (RMT) predictions. On the other hand, in the strong spin-orbit coupling limit $\delta \tau_{\textrm{\small so}}/\hbar \to 0$, the orbital contribution depends crucially on the space character of the quasi-particle wavefunctions: it levels off at a small value for states of $d$ character but is strongly enhanced for states of $sp$ character. Our numerical results demonstrate that when orbital coupling to the field is included, RMT predictions overestimate the typical $g$-factor of orbitals that have dominant $d$-character. This finding points to a possible source of the puzzling discrepancy between theory and experiment.Comment: 21 pages, 6 figures; accepted for publication in Physical Review

Colour analysis and verification of CCTV images under different lighting conditions

Colour information is not faithfully maintained by a CCTV imaging chain. Since colour can play an important role in identifying objects it is beneficial to be able to account accurately for changes to colour introduced by components in the chain. With this information it will be possible for law enforcement agencies and others to work back along the imaging chain to extract accurate colour information from CCTV recordings. A typical CCTV system has an imaging chain that may consist of scene, camera, compression, recording media and display. The response of each of these stages to colour scene information was characterised by measuring its response to a known input. The main variables that affect colour within a scene are illumination and the colour, orientation and texture of objects. The effects of illumination on the appearance of colour of a variety of test targets were tested using laboratory-based lighting, street lighting, car headlights and artificial daylight. A range of typical cameras used in CCTV applications, common compression schemes and representative displays were also characterised