Download Analysis of Quantised Vortex Tangle by Alexander John Taylor PDF

By Alexander John Taylor

In this thesis, the writer develops numerical innovations for monitoring and characterising the convoluted nodal traces in 3-dimensional house, analysing their geometry at the small scale, in addition to their worldwide fractality and topological complexity---including knotting---on the big scale. The paintings is extremely visible, and illustrated with many appealing diagrams revealing this unanticipated point of the physics of waves. Linear superpositions of waves create interference styles, this means that in a few locations they advance each other, whereas in others they thoroughly cancel one another out. This latter phenomenon happens on 'vortex strains' in 3 dimensions. more often than not wave superpositions modelling e.g. chaotic hollow space modes, those vortex traces shape dense tangles that experience by no means been visualised at the huge scale prior to, and can't be analysed mathematically by way of any identified strategies.

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1. 5 Knotting and Linking as a Statistical Tool 23 Fig. 11 Four examples of knots. Each image represents a curve through three-dimensional space, with a showing the so-called unknot while b–d show geometrically different representations of the so-called trefoil knot. Each curve is coloured with the colour wheel along its length only to visually distinguish the different regions of the curve To give a visual example of knotting, Fig. 11a–d shows images of four loops in three dimensions. Each has been coloured along its length, but this colour has no meaning other than to distinguish different sections of the curve.

7. The first system of our investigation is the 3-torus, geometrically equivalent to a unit cube with periodic boundary conditions along all three of its Cartesian axes. The advantage here is that vortices will not terminate on the boundaries of the unit cell but can be traced through them as they pass through the boundary and enter the opposite face, so each short vortex segment terminating on the boundary can be identified as part of a much longer vortex loop. This makes accessible far longer vortex segments than would be the case in an equivalently sized region of the RWM.

9 that this does not apparently pose a problem, as even relatively small numbers of wavevectors in superposition closely approximate the truly isotropic limit. It may even be the case that the zeros of the field are a better statistical approximation of the isotropic limit than other features such as the maxima of intensity, since the latter may depend more subtly on the normalisation of the power spectrum. 6). Under such a model it is possible to simulate some volume of a chaotic wavefield, to track the vortex lines within it (we discuss this in detail in Chap.

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