Related papers: Helicity, polarization, and Riemann-Silberstein vo…
Optical vortices are phase singularities nested in electromagnetic waves that constitute a fascinating source of phenomena in the physics of light and display deep similarities to their close relatives, quantized vortices in superfluids and…
The real Schur form (RSF) of a generic velocity gradient field $\nabla \mathbf{u}$ is exploited to expose the structures of flows, in particular our field decomposition resulting in two vorticities with only mutual linkage as the…
A class of harmonic solutions to the steady Euler equations for incompressible fluids is presented in two dimensions in circular, elliptic and bipolar coordinates. Since the velocity field is solenoidal in this case, it can be written as…
Helicity is a topological invariant that measures the linkage and knottedness of lines, tubes and ribbons. As such, it has found myriads of applications in astrophysics and solar physics, in fluid dynamics, in atmospheric sciences, and in…
Superfluidity is a special state of matter exhibiting macroscopic quantum phenomena and acting like a fluid with zero viscosity. In such a state, superfluid vortices exist as phase singularities of the model equation with unique…
A relativistically invariant expression for the magnetic and electric helicities of free electromagnetic field through the currents, which created those field, are derived. It is demonstrated that for radiative fields (e.g. laser pulses)…
Vortices are pervasive in nature, representing the breakdown of laminar fluid flow and hence playing a key role in turbulence. The fluid rotation associated with a vortex can be parameterized by the circulation $\Gamma=\oint {\rm d}{\bf…
A relativistic helicity has been formulated in the four-dimensional Minkowski space-time. Whereas the relativistic distortion of space-time violates the conservation of the conventional helicity, the newly defined relativistic helicity…
Geometric phase is a far-reaching concept in quantum and classical physics. The first discovered geometric phase, the Pancharatnam-Berry (PB) phase, has profoundly shaped nanophotonics through metasurfaces. However, the PB phase arises from…
A Rossby-Haurwitz (RH) wave is an excitation mode of a fluid on a rotating spherical surface, which propagates westward in the rotating frame of reference. Motivated by the recent realization of the shell-shaped Bose-Einstein condensate in…
We consider Riemann surfaces obtained from nodal curves with infinite cylinders in the place of nodal and marked points, and study the space of finite energy vortices defined on these surfaces. To compactify the space of vortices, we need…
Helicity is a universal quantity describing the internal rotation of an object or a field. Whether it characterizes fundamental properties such as the spin of elementary particles or leads to practical consequences such as the toxicity or…
We consider the existence, stability and dynamics of the nodeless state and fundamental nonlinear excitations, such as vortices, for a quasi-two-dimensional polariton condensate in the presence of pumping and nonlinear damping. We find a…
We study abelian BPS vortices on a surface $S$ with boundary, which satisfy the Neumann boundary condition on the norm of the scalar field, or equivalently, that the current along the boundary vanishes. These vortices have quantised…
In classical hydrodynamics with uniform density, vortices move with the local fluid velocity. This description is rewritten in terms of forces arising from the interaction with other vortices. Two such positive straight vortices experience…
Electromagnetic waves are described by not only polarization ellipses but also cyclically rotating vectors tracing out them. The corresponding fields are respectively directionless steady line fields and directional instantaneous vector…
Appearance of quantized vortices in a superfluid and a Bose-Einstein condensate (BEC) stems from their nontrivial response to broken time-reversal symmetry (TRS). Here we show that breaking of the TRS by, for example, rotation or an…
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…
It is shown that, in the presence of a magnetic field, a quantized vortex line in a superfluid liquid acquires a linear polarization charge, which is localized near the vortex axis over a length on the order of the coherence length. It is…
We describe the linear and nonlinear stability and instability of certain symmetric configurations of point vortices on the sphere forming relative equilibria. These configurations consist of one or two rings, and a ring with one or two…