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There has been a recent tendency to apply Schroedinger's wave equation to macroscopic domains, from Bose-Einstein condensates in neutron stars to planetary orbits. In these applications a hydrodynamical interpretation, involving vortices in…
We study the evolution of turbulent magnetic fields from a topological point of view, invoking commonplace mathematical tools from general topology and dynamical systems theory which connect magnetic field evolution to time reversal…
For a topological flow $(V,\phi)$ - i.e., $V$ is a linearly compact vector space and $\phi$ a continuous endomorphism of $V$ - we gain a deep understanding of the relationship between $(V,\phi)$ and the Bernoulli shift: a topological flow…
Hydrodynamic reformulations of the Schr\"odinger equation suggest an interpretation of quantum mechanics in terms of a fluid flowing on configuration space. In the discrete hydrodynamic view, this fluid is not fundamental but emerges from…
We study perfect fluid cosmological models with a constant equation of state parameter $\gamma$ in which there are two naturally defined time-like congruences, a geometrically defined geodesic congruence and a non-geodesic fluid congruence.…
We point out an interesting connection between fluid dynamics and minimal surface theory: When gluing helicoids into a minimal surface, the limit positions of the helicoids correspond to a "vortex crystal", an equilibrium of point vortices…
Ideas from quantum field theory and topology have proved remarkably fertile in suggesting new phenomena in the quantum physics of condensed matter. Here I'll supply some broad, unifying context, both conceptual and historical, for the…
The theory of point vortex dynamics has existed since Kirchhoff's proposal in 1891 and is still under development with connections to many fields in mathematics. As a strong simplification of the concept of vorticity it excels in…
Two dimensional flows on fixed smooth surfaces have been studied in the point of view of vorticity dynamics. Firstly, the related deformation theory including kinematics and kinetics is developed. Secondly, some primary relations in…
A vortex, a circulating flow around a void, is one of the basic topological phenomena in nature. Here we show that vortices generally emerge in spin wave travelling upon topologically nontrivial magnetic texture, due to the transverse…
Active systems, from bacterial suspensions to cellular monolayers, are continuously driven out of equilibrium by local injection of energy from their constituent elements and exhibit turbulent-like and chaotic patterns. Here we demonstrate…
The basic building blocks of many forms of optical topologies are particle-like singularities in phase and polarisation, giving rise to lines of darkness that weave complex threads in 3D space. Although known for half a century since…
For certain families of fluid flow, a new conserved quantity -- stream-helicity -- has been established.Using examples of linked and knotted streamtubes, it has been shown that stream-helicity does, in certain cases, entertain itself with a…
As an effective theory, relativistic hydrodynamics is fixed by symmetries up to a set of transport coefficients. A lot of effort has been devoted to explicit calculations of these coefficients. Here we propose a shift in perspective: we…
Understanding what happens inside the rippling and dancing surface of a liquid remains one of the great challenges of fluid dynamics. Using molecular dynamics (MD) we can pick apart the interface structure and understand surface tension. In…
Optical vortices as topological objects exist ubiquitously in nature. In this paper, by making use of the $\phi$-mapping topological current theory, we investigate the topology in the closed and knotted optical vortices. The topological…
Superfluid turbulence, often referred to as quantum turbulence, is a fascinating phenomenon for which a satisfactory theoretical framework is lacking. Holographic duality provides a systematic new approach to studying quantum turbulence by…
I point out how coherence vortices, i.e., topological defects in a correlation function, could help explore new physics if they are created in matter waves. Vortex dynamics could be studied in up to six dimensions, and spin topological…
We introduce several new models whose common feature is to take into account effects from topological vorticity. The macroscopic unknown is driven by a dissipative anomalous diffusion (of SQG-type) and is coupled with the orientation of the…
A new method for the creation of 3D solitary topological modes, corresponding to vortical droplets of a two-component dilute superfluid, is presented. We use the recently introduced system of nonlinearly coupled Gross-Pitaevskii equations,…