Needs assessment of gossamer structures in communications platform end-of-life disposal

The use of a gossamer structure is considered in application to end-of-life disposal of communications platforms. A wide-ranging survey of end-of-life disposal techniques and strategies is presented for comparison against a gossamer structure prior to a down-selection of viable competing techniques; solar sailing, high and low-thrust propulsion, and electrodynamic tethers. A parametric comparison of the down-selection competing techniques is presented where it was found that exploiting solar radiation pressure on the gossamer structure was of limited value. In general terms, it was found that if a spacecraft propulsion system remains functioning at the end-of-life then this will likely provide the most efficient means of re-orbiting, especially when the propulsion system is only used to lower the orbit to a point where atmospheric drag will cause the orbit to decay within the required timeframe. Atmospheric drag augmentation was found to be of most benefit for end-of-life disposal when an entirely passive means is required, allowing the device to act as a ‘fail-safe’, which if the spacecraft suffers a catastrophic failure would activate. The use of an atmospheric drag augmentation system is applicable to only low and medium mass spacecraft, or spacecraft that are unlikely to survive atmospheric re-entry, hence minimizing risk to human life

Solving eigenvalue problems on curved surfaces using the Closest Point Method

Eigenvalue problems are fundamental to mathematics and science. We present a simple algorithm for determining eigenvalues and eigenfunctions of the Laplace--Beltrami operator on rather general curved surfaces. Our algorithm, which is based on the Closest Point Method, relies on an embedding of the surface in a higher-dimensional space, where standard Cartesian finite difference and interpolation schemes can be easily applied. We show that there is a one-to-one correspondence between a problem defined in the embedding space and the original surface problem. For open surfaces, we present a simple way to impose Dirichlet and Neumann boundary conditions while maintaining second-order accuracy. Convergence studies and a series of examples demonstrate the effectiveness and generality of our approach

Strong Stability Preserving Two-Step Runge-Kutta Methods

We investigate the strong stability preserving (SSP) property of two-step Runge– Kutta (TSRK) methods. We prove that all SSP TSRK methods belong to a particularly simple\ud subclass of TSRK methods, in which stages from the previous step are not used. We derive simple order conditions for this subclass. Whereas explicit SSP Runge–Kutta methods have order at most four, we prove that explicit SSP TSRK methods have order at most eight. We present TSRK methods of up to eighth order that were found by numerical search. These methods have larger SSP coefficients than any known methods of the same order of accuracy, and may be implemented in a form with relatively modest storage requirements. The usefulness of the TSRK methods is demonstrated through numerical examples, including integration of very high order WENO discretizations

A snapshot of young children's mathematical competencies: results from the Longitudinal Study of Australian Children

This article presents a snapshot of the mathematical competencies of children aged four to five years in Australian early childhood education settings, as perceived by their educators. Data are presented from a nationally-representative sample of 6511 children participating in the Longitudinal Study of Australian Children (LSAC). The results reveal that children are seen to possess a number of mathematical competencies at 4-5 years, with the majority of children displaying interest in mathematics. Moreover, differences were noted with respect to the different program types in which the children participated. These results are discussed in relation to previous research, and implications for future research, policy and practice are presented

Solar sail science mission applications and advancement : solar sailing: concepts, technology, missions

Solar sailing has long been envisaged as an enabling or disruptive technology. The promise of open-ended missions allows consideration of radically new trajectories and the delivery of spacecraft to previously unreachable or unsustainable observation outposts. A mission catalogue is presented of an extensive range of potential solar sail applications, allowing identification of the key features of missions which are enabled, or significantly enhance, through solar sail propulsion. Through these considerations a solar sail application-pull technology development roadmap is established, using each mission as a technology stepping-stone to the next. Having identified and developed a solar sail application-pull technology development roadmap, this is incorporated into a new vision for solar sailing. The development of new technologies, especially for space applications, is high-risk. The advancement difficulty of low technology readiness level research is typically underestimated due to a lack of recognition of the advancement degree of difficulty scale. Recognising the currently low technology readiness level of traditional solar sailing concepts, along with their high advancement degree of difficulty and a lack of near-term applications a new vision for solar sailing is presented which increases the technology readiness level and reduces the advancement degree of difficulty of solar sailing. Just as the basic principles of solar sailing are not new, they have also been long proven and utilised in spacecraft as a low-risk, high-return limited-capability propulsion system. It is therefore proposed that this significant heritage be used to enable rapid, near-term solar sail future advancement through coupling currently mature solar sail, and other, technologies with current solar sail technology developments. As such the near-term technology readiness level of traditional solar sailing is increased, while simultaneously reducing the advancement degree of difficulty along the solar sail application-pull technology development roadmap