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Geometry and topology of vortices in random quantum eigenfunctions

Disordered complex 3D scalar wave fields typically contain a dense tangle of nodal lines (quantized vortices), which are important in diverse physical wave systems including turbulent superfluids, optical volume speckle, the quantum eigenfunctions of chaotic 3D cavities, and liquid crystal phases. Based on extensive numerical simulations these nodal tangles are known to have fractal properties on large scales, although more subtle topological quantities such as the probability of knotted or linked vortices are sensitive to the details of the model. We numerically generate many examples of wave chaos in three random systems at fixed energy (3D cube with periodic boundary conditions, 3-sphere and 3D harmonic oscillator), analysing aspects of their statistical geometry and identifying the knot types of the vortex curves which appear. Knots tend to occur with high probability even at comparatively low energies, and the statistics of knot complexity vary significantly amongst the three systems. Furthermore, the different symmetries and boundary conditions of these systems strongly affect the knotted conformations that can occur, and we discuss how this relates to the statistics of knotting with mode count in different systems.

This is a custom-designed set of activities designed to stimulate growth in the space industry and to help position the UK to play a stronger role in programmes of the European Space Agency.

Created in 2011, The National Space Technology Programme aims to develop the growth of the UK Space Sector as embodied in the by funding space technology research and development projects. Proposals are welcome from industry and academia, but they must align with the National Space Technology Strategy and the related technology roadmaps covering the 5 main themes;

• Telecommunications
• Sensing
• Position, Navigation and Timing
• Exploration and Robotics
• Access to Space

The overarching intention of the programme is to develop space technology and capabilities to drive growth in the UK economy as set out in the UK Civil Space Strategy. Space technology is also critical in providing UK citizens and businesses with the public infrastructure and security necessary to underpin societal and economic wellbeing. The key intention is to ensure that future space technologies that may come to underpin the UK economy in the medium and long term are investigated, understood and nurtured.

The Fast Track and Pathfinder calls are now open. Please refer to the necessary documents below.

The Royal Astronomical Society invites applications for its research fellowships. These enable early-career scientists to pursue research in the UK in astronomy, solar-system science, geophysics and closely related branches of these sciences.

Applicants should have obtained a recognised PhD degree or equivalent after 1 October, five years before the start of the fellowship or have taken the viva examination by the application deadline and expect to be awarded a PhD degree by the fellowship start date. Applicants may be of any nationality, but employment will be through the host institution.

The award amount will be between spine points 30 and 36, inclusive, on the UCU single pay spine. If the host university wishes to pay at spine points above 36, the extra expenditure must be found from their own funds. A further £2,000 per year may be claimed for travel and incidental expenses. The RAS accept claims for national insurance at normal rates and the employer pension contribution at 18 per cent of the salary. In addition sums of up to £2,000 per year for travel and incidental expenses will be considered.

This supports scientists who wish to investigate the potential to commercialise an aspect of their research. Eight awards are available worth up to £50,000 each for a duration of up to two years.