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The 2016 Physics Nobel Prize honors a variety of discoveries related to topological phases and phase transitions. Here we sketch two exciting facets: the groundbreaking works by John Kosterlitz and David Thouless on phase transitions of…
Salient features of vortex dynamics in super media are summarized. Recent examples are: the demonstration of prominent role of topology in vortex dynamics; the solution to the Hall anomaly which once bothered Bardeen, de Gennes and many…
With the excitement generated by this year's Nobel Prize in physics, here I give a brief critical review of current vortex dynamics research activity, using a recent book as the background material. Two directions in which major progresses…
Topological techniques are used to study the motions of systems of point vortices in the infinite plane, in singly-periodic arrays, and in doubly-periodic lattices. The reduction of each system using its symmetries is described in detail.…
We consider changes of the topological charge of vortices in quantum mechanics by investigating analytical examples where the creation or annihilation of vortices occurs. In classical hydrodynamics of non-viscous fluids the Helmholtz-Kelvin…
We develop a neutral vortex fluid theory on closed surfaces with zero genus. The theory describes collective dynamics of many well-separated quantum vortices in a superfluid confined on a closed surface. Comparing to the case on a plane,…
Neutron scattering played an important role in the experimental exploration of the theoretical ideas of Thouless, Haldane, and Kosterlitz, who won the Nobel Prize in Physics in 2016. This article reviews the signatures of Haldane's…
We present a combined experimental and theoretical investigation of the formation and decay kinetics of vortices in two dimensional, compressible quantum turbulence. We follow the temporal evolution of a quantum fluid of exciton polaritons,…
When considering flows in biological membranes, they are usually treated as flat, though more often than not, they are curved surfaces, even extremely curved, as in the case of the endoplasmic reticulum. Here, we study the topological…
We formulate the equations of fluid dynamics as an intersection-theoretic problem on an infinite-dimensional symplectic manifold naturally associated with spacetime. This perspective separates the structures determined by the equation of…
Toroidal vortices in fluid and gas dynamics underpin a broad spectrum of scientific and technological fields, from elementary particle physics to condensed matter systems, and have recently garnered significant attention in optics because…
As symbolized by the Nobel Prize in Physics 2016, "topology" has been recognized as an essential standpoint to understand and control the physics of condensed matter. This concept may be spreading even into application areas such as novel…
We introduce new classes of hydrodynamic theories inspired by the recently discovered fracton phases of quantum matter. Fracton phases are characterized by elementary excitations (fractons) with restricted mobility. The hydrodynamic…
The motion of noncircular two-dimensional vortices is shown to depend on a form of coupling between vortex ellipticity and the gradient of fluid density. The approach is based on the perspective that an elliptic vortex can be described as…
The requirement of diffeomorphism symmetry for the target space can lead to anomalous commutators for the energy-momentum tensor for sigma models and for fluid dynamics, if certain topological terms are added to the action. We analyze…
Geometric Hydrodynamics has flourished ever since the celebrated 1966 paper of V. Arnold. In this paper we present a collection of open problems along with several new constructions in fluid dynamics and a concise survey of recent…
The title of the paper coincides with the title of a paragraph in the famous book by U. Frisch (1995)on classical turbulence. In this paragraph the author discussed the role of statistical dynamics of vortex filaments in the theory of…
Fluid mixtures, such as the cellular cytoplasm and synthetic DNA nanostars, can spontaneously compartmentalize into many coexisting phases through liquid-liquid phase separation. Despite the diversity of fluid structures that emerge from…
The idea that the knottedness (hydrodynamic Helicity) of a fluid flow is conserved has a long history in fluid mechanics. The quintessential example of a knotted flow is a knotted vortex filament, however, owing to experimental…
A non-relativistic scalar field coupled minimally to electromagnetism supports in the presence of a homogeneous background electric charge density the existence of smooth, finite-energy topologically stable flux vortices. The static…