Related papers: On Singular Vortex Patches, I: Well-posedness Issu…
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…
Topological singularities are ubiquitous in many areas of physics. Polarization singularities are locations at which an aspect of the polarization ellipse of light becomes undetermined or degenerate. At C points the orientation of the…
In this paper, we obtain uniformly rotating vorticity with sufficiently large angular velocity in the unit disk. The solution consists of either a small nearly-ellipse vortex patch which is highly concentrated near the origin or a $2+1$…
We consider the vortex patch problem for both the 2-D and 3-D incompressible Euler equations. In 2-D, we prove that for vortex patches with $H^{k-0.5}$ Sobolev-class contour regularity, $k \ge 4$, the velocity field on both sides of the…
A system of three point vortices in an unbounded plane has a special family of self-similarly contracting or expanding solutions: during the motion, vortex triangle remains similar to the original one, while its area decreases (grows) at a…
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…
In this paper, we consider the three-dimensional full compressible viscous non-resistive MHD system. Global well-posedness is proved for an initial-boundary value problem around a strong background magnetic field. It is also shown that the…
The collective behavior of self-propelled particles (SPPs) under the combined effects of a circularly patterned substrate and circular confinement is investigated through coarse-grained molecular dynamics simulations of polarized and…
A point particle approximation to the classical dynamics of well separated vortices of the abelian Higgs model is developed. A static vortex is asymptotically identical to a solution of the linearized field theory (a Klein-Gordon/Proca…
This paper presents a comprehensive analysis of two-dimensional water waves characterized by a significant adverse constant vorticity over flows without stagnation points. Surprisingly, we discover qualitative distinctions between this…
Well posedness is established for a family of equations modelling particle populations undergoing delocalised coagulation, advection, inflow and outflow in a externally specified velocity field. Very general particle types are allowed while…
We have investigated the confinement of 3-D vortices in specific cases of Type-II ($\kappa = 2$) nano-superconducting devices. The emergent pattern of vortices greatly depends on the orientation of an applied magnetic field (transverse or…
We present local distributed, stochastic algorithms for \emph{alignment} in self-organizing particle systems (SOPS) on two-dimensional lattices, where particles occupy unique sites on the lattice, and particles can make spatial moves to…
Vortex, the winding of a vector field in two dimensions, has its core the field singularity and its topological charge defined by the quantized winding angle of the vector field. Vortices are one of the most fundamental topological…
There is currently a strong interest in the collective behavior of chiral active particles that can propel and rotate themselves. In the presence of alignment interactions for many chiral particles, chiral self-propulsion can induce vortex…
We prove that finite area isolated singularities of surfaces with constant positive curvature in R^3 are removable singularities, branch points or immersed conical singularities. We describe the space of immersed conical singularities of…
We show that particle trajectories for positive vorticity solutions to the 2D Euler equations on fairly general bounded simply connected domains cannot reach the boundary in finite time. This includes domains with possibly nowhere $C^1$…
An inverse turbulent cascade in a periodic square box produces a coherent system-sized vortex dipole. We study the statistics of its motion by carrying out direct numerical simulations performed for various bottom friction $\alpha$, pumping…
Parabolic geometric flows are smoothing for short time however, over long time, singularities are typically unavoidable, can be very nasty and may be impossible to classify. The idea of [CM6] and here is that, by bringing in the dynamical…
Ensembles of particles rotating in a two-dimensional fluid can exhibit chaotic dynamics yet develop signatures of hidden order. Such "rotors" are found in the natural world spanning vastly disparate length scales - from the rotor proteins…