Asymptotic analysis of displaced lunar orbits

The design of spacecraft trajectories is a crucial task in space mission design. Solar sail technology appears as a promising form of advanced spacecraft propulsion which can enable exciting new space science mission concepts such as solar system exploration and deep space observation. Although solar sailing has been considered as a practical means of spacecraft propulsion only relatively recently, the fundamental ideas are by no means new (see McInnes1 for a detailed description). A solar sail is propelled by reflecting solar photons and therefore can transform the momentum of the photons into a propulsive force. Solar sails can also be utilised for highly non-Keplerian orbits, such as orbits displaced high above the ecliptic plane (see Waters and McInnes2). Solar sails are especially suited for such non-Keplerian orbits, since they can apply a propulsive force continuously. In such trajectories, a sail can be used as a communication satellite for high latitudes. For example, the orbital plane of the sail can be displaced above the orbital plane of the Earth, so that the sail can stay fixed above the Earth at some distance, if the orbital periods are equal (see Forward3). Orbits around the collinear points of the Earth-Moon system are also of great interest because their unique positions are advantageous for several important applications in space mission design (see e.g. Szebehely4, Roy,5 Vonbun,6 Thurman et al.,7 Gomez et al.8, 9). Several authors have tried to determine more accurate approximations (quasi-Halo orbits) of such equilibrium orbits10. These orbits were first studied by Farquhar11, Farquhar and Kamel10, Breakwell and Brown12, Richardson13, Howell14, 15.If an orbit maintains visibility from Earth, a spacecraft on it (near the L2 point) can be used to provide communications between the equatorial regions of the Earth and the lunar poles. The establishment of a bridge for radio communications is crucial for forthcoming space missions, which plan to use the lunar poles.McInnes16 investigated a new family of displaced solar sail orbits near the Earth-Moon libration points.Displaced orbits have more recently been developed by Ozimek et al.17 using collocation methods. In Baoyin and McInnes18, 19, 20 and McInnes16, 21, the authors describe new orbits which are associated with artificial Lagrange points in the Earth-Sun system. These artificial equilibria have potential applications for future space physics and Earth observation missions. In McInnes and Simmons22, the authors investigate large new families of solar sail orbits, such as Sun-centered halo-type trajectories, with the sail executing a circular orbit of a chosen period above the ecliptic plane. We have recently investigated displaced periodic orbits at linear order in the Earth-Moon restricted three-body system, where the third massless body is a solar sail (see Simo and McInnes23). These highly non-Keplerian orbits are achieved using an extremely small sail acceleration. It was found that for a given displacement distance above/below the Earth-Moon plane it is easier by a factor of order 3.19 to do so at L4=L5 compared to L1=L2 - ie. for a fixed sail acceleration the displacement distance at L4=L5 is greater than that at L1=L2. In addition, displaced L4=L5 orbits are passively stable, making them more forgiving to sail pointing errors than highly unstable orbits at L1=L2.The drawback of the new family of orbits is the increased telecommunications path-length, particularly the Moon-L4 distance compared to the Moon-L2 distance

Structure-function relationships of glucansucrase and fructansucrase enzymes from lactic acid bacteria

Lactic acid bacteria (LAB) employ sucrase-type enzymes to convert sucrose into homopolysaccharides consisting of either glucosyl units (glucans) or fructosyl units (fructans). The enzymes involved are labeled glucansucrases (GS) and fructansucrases (FS), respectively. The available molecular, biochemical, and structural information on sucrase genes and enzymes from various LAB and their fructan and α-glucan products is reviewed. The GS and FS enzymes are both glycoside hydrolase enzymes that act on the same substrate (sucrose) and catalyze (retaining) transglycosylation reactions that result in polysaccharide formation, but they possess completely different protein structures. GS enzymes (family GH70) are large multidomain proteins that occur exclusively in LAB. Their catalytic domain displays clear secondary-structure similarity with α-amylase enzymes (family GH13), with a predicted permuted (β/α)8 barrel structure for which detailed structural and mechanistic information is available. Emphasis now is on identification of residues and regions important for GS enzyme activity and product specificity (synthesis of α-glucans differing in glycosidic linkage type, degree and type of branching, glucan molecular mass, and solubility). FS enzymes (family GH68) occur in both gram-negative and gram-positive bacteria and synthesize β-fructan polymers with either β-(2→6) (inulin) or β-(2→1) (levan) glycosidic bonds. Recently, the first high-resolution three-dimensional structures have become available for FS (levansucrase) proteins, revealing a rare five-bladed β-propeller structure with a deep, negatively charged central pocket. Although these structures have provided detailed mechanistic insights, the structural features in FS enzymes dictating the synthesis of either β-(2→6) or β-(2→1) linkages, degree and type of branching, and fructan molecular mass remain to be identified

Основні закономірності зародження і росту втомних тріщин в алюмінієвих пластинах із зміцненими отворами

The method of modeling stress-strain state for holes burnishing using FEM has been analyzed. A series of fatigue tests were carried out using plates containing plain holes and cold expanded holes in aluminium For various diameters of holes and cold expansion degree there exists a certain correlation between the stress range or maximum stress on the edge of hole on the entrance face of plate and lifetime of fatigue crack initiation

Strontium optical lattice clocks for practical realization of the metre and secondary representation of the second

We present a system of two independent strontium optical lattice standards probed with a single shared ultra-narrow laser. The absolute frequency of the clocks can be verified by the use of Er:fiber optical frequency comb with the GPS-disciplined Rb frequency standard. We report hertz-level spectroscopy of the clock line and measurements of frequency stability of the two strontium optical lattice clocks.Comment: This is an author-created, un-copyedited version of an article accepted for publication in Meas. Sci. Technol. The publisher is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at doi:10.1088/0957-0233/26/7/07520

Line shape measurements of rubidium 5S-7S two-photon transition

We report the use of a digital lock to measure the line profile and center frequency of rubidium 5S-7S two-photon transitions with a cw laser referenced to an optical frequency comb. The narrow, two-photon transition, 5S-7S (760 nm), insensitive to first-order in a magnetic field, is a promising candidate for frequency reference

Cs Fountain Clocks for Commercial Realizations—An Improved and Robust Design

We report on the design, assembly, testing, and delivery of a series of new cesium fountain primary frequency standards built through commercial and scientific collaboration with international users. The new design, based on proven National Physical Laboratory solutions, improves reliability, simplicity of operation, and transportability. The complete system consists of a novel physics package, a specially developed optical package, and dedicated electronics for system control. We present results showing that despite their simplified and more compact design, the new fountains have state-of-the-art performance in terms of signal-to-noise ratio and robust long-term operation. With a sufficiently low-noise local oscillator, they are capable of reaching a short-term stability below $3\times 10^{-14}$ (1 s) and have potential accuracy in the low $10^{-16}$ range, similar to the best cesium fountains currently in operation. This cost-effective solution could be used to increase the availability of accurate frequency references and timescales and provide redundancy in critical locations

Case study on the efficacy of a lanthanum-enriched clay (Phoslock®) in controlling eutrophication in Lake Het Groene Eiland (The Netherlands)

Lake Het Groene Eiland was created in the beginning of 2008 by construction of dikes for isolating it from the surrounding 220-ha water body. This so-called claustrum of 5 ha was treated using lanthanum-modified clay (Phoslock®) to control eutrophication and mitigate cyanobacterial nuisance. Cyanobacteria chlorophyll-a were significantly lower in the claustrum than those in the reference water body, where a massive bloom developed in summer, 2008. However, PO4-P and TP did not statistically differ in these two waters. TN and NO3-N were significantly lower in the claustrum, where dense submerged macrophytes beds developed. Lanthanum concentrations were elevated after the applications of the modified clay in the claustrum, but filterable lanthanum dropped rapidly below the Dutch standard of 10.1 μg l−1. During winter, dozens of Canada geese resided at the claustrum. Geese droppings contained an average of 2 mg PO4-P g−1 dry weight and 12 mg NH3-N g−1 dry weight and might present a growing source of nutrients to the water. Constructing the claustrum enabled unrestricted bathing in subsequent three summers, as no swimming bans had to be issued due to cyanobacteria blooms. However, the role of the modified clay in this positive outcome remains unclear, and longevity of the measures questionable.

An acceptor-substrate binding site determining glycosyl transfer emerges from mutant analysis of a plant vacuolar invertase and a fructosyltransferase

Glycoside hydrolase family 32 (GH32) harbors hydrolyzing and transglycosylating enzymes that are highly homologous in their primary structure. Eight amino acids dispersed along the sequence correlated with either hydrolase or glycosyltransferase activity. These were mutated in onion vacuolar invertase (acINV) according to the residue in festuca sucrose:sucrose 1-fructosyltransferase (saSST) and vice versa. acINV(W440Y) doubles transferase capacity. Reciprocally, saSST(C223N) and saSST(F362Y) double hydrolysis. SaSST(N425S) shows a hydrolyzing activity three to four times its transferase activity. Interestingly, modeling acINV and saSST according to the 3D structure of crystallized GH32 enzymes indicates that mutations saSST(N425S), acINV(W440Y), and the previously reported acINV(W161Y) reside very close together at the surface in the entrance of the active-site pocket. Residues in- and outside the sucrose-binding box determine hydrolase and transferase capabilities of GH32 enzymes. Modeling suggests that residues dispersed along the sequence identify a location for acceptor-substrate binding in the 3D structure of fructosyltransferases