Related papers: Cusp Formation in Vortex Patches
We construct infinitely many admissible weak solutions to the 2D incompressible Euler equations for vortex sheet initial data. Our initial datum has vorticity concentrated on a simple closed curve in a suitable H\"older space and the…
Kibble and Zurek have provided a unifying causal picture for the appearance of topological defects like cosmic strings or vortices at the onset of phase transitions in relativistic QFT and condensed matter systems respectively. There is no…
There has been growing speculation that a pair density wave state is a key component of the phenomenology of the pseudogap phase in the cuprates. Recently, direct evidence for such a state has emerged from an analysis of scanning tunneling…
Vortices can form when finite quantal systems are set to rotate. In the limit of small particle numbers the vortex formation in a harmonically trapped fermion system, with repulsively interacting particles, shows similarities to the…
A round up of the present status of the conjecture that n alpha nuclei form an alpha-particle condensate in excited states close to the n alpha threshold is given. Experiments which could demonstrate the condensate character are proposed.…
We explore the possibility that, at zero temperature, vortices can be created spontaneously in a condensate of cold Fermi atoms, whose scattering is controlled by a narrow Feshbach resonance, by rapid magnetic tuning from the BEC to BCS…
This work investigates the universality of cusp formation in the shadows of compact objects. The emergence of cusps is accompanied by three interrelated phenomena: a topological charge transition, an equal-area law governing the…
We observe stable propagation of spatially localized single- and double-charge optical vortices in a self-focusing nonlinear medium. The vortices are created by self-trapping of partially incoherent light carrying a phase dislocation, and…
A class of exact solutions of Hele-Shaw flows without surface tension in a rotating cell is reported. We show that the interplay between injection and rotation modifies drastically the scenario of formation of finite-time cusp…
A vortex molecule is predicted in rotating two-component Bose-Einstein condensates whose internal hyperfine states are coupled coherently by an external field. A vortex in one component and that in the other are connected by a domain wall…
Optical vortices have been observed in a wide variety of optical systems. They can be observed directly in the wavefront of optical beams, or in the correlations between pairs of entangled photons. We present a novel optical vortex which…
We prove the existence of embedded closed constant curvature curves on convex surfaces.
In a numerical experiment based on Gross-Pitaevskii formalism, we demonstrate unique topological quantum coherence in optically trapped Bose-Einstein condensates (BECs). Exploring the fact that vortices in rotating BEC can be pinned by a…
We study vortex patches for the 2D incompressible Euler equations. Prior works on this problem take the support of the vorticity (i.e., the vortex patch) to be a bounded region. We instead consider the horizontally periodic setting. This…
The shape of a liquid surface bounded by an acute or obtuse planar angular sector is considered by using classical analysis methods. For acute angular sectors the two principal curvatures are of the order of the (fixed) mean curvature. But…
Explicit bases for the spaces of holomorphic cusp forms of all even positive weights and all orders are constructed. The dimensions of these spaces are computed.
Azimuthally asymmetric structures have been discovered in millimeter continuum emission from many protoplanetary disks. One hypothesis is that they are vortices produced by the Rossby wave instability, for example at edges of planet-opened…
We demonstrate that a single reconnection of two quantum vortices can lead to creation of a cascade of vortex rings. Our analysis, motivated by the analytical solution in LIA, involves high-resolution Biot-Savart and Gross-Pitaevskii…
We show that the water waves system is locally wellposed in weighted Sobolev spaces which allow for interfaces with corners. No symmetry assumptions are required. These singular points are not rigid: if the initial interface exhibits a…
We investigate the shape of a tin sheet formed from a droplet struck by a nanosecond laser pulse. Specifically, we examine the dynamics of the process as a function of laser beam properties, focusing on the outstanding riddle of curvature…