Related papers: On Singular Vortex Patches, II: Long-time dynamics
We investigate theoretically the creation, persistence and detection of quantized vortices in nonequilibrium polariton condensates within a stochastic classical field model. The life time of the quantized vortices is shown to increase with…
In these notes we summarise some recent developments on the existence and uniqueness theory for Vlasov-type equations, both on the torus and on the whole space.
Solitons in the fractional space, supported by lattice potentials, have recently attracted much interest. We consider the limit of deep one- and two-dimensional (1D and 2D) lattices in this system, featuring finite bandgaps separated by…
This work is a companion to [EJE1] and its purpose is threefold: first, we will establish local well-posedness for the axi-symmetric $3D$ Euler equation in the domains $\{(x_1,x_2,x_3) \in \mathbb{R}^3 : x_3^2 \le \mathfrak{c}(x_1^2 +…
In this paper we study the singularity formation for the geometric flow of complex curves $$z_t = -z_{xxx} + \frac{3}{2}\o z_{x} z_{xx}^2,$$ that was derived [R. E. Goldstein and D. M. Petrich, {\em Phys. Rev. Lett.}, 69 (1992), pp.…
This papers presents a formalism describing the dynamics of a quantum particle in a one-dimensional tilted time-dependent lattice. The description uses the Wannier-Stark states, which are localized in each site of the lattice and provides a…
Inertial particles (IPs) in vortical fluid flow cluster strongly, forming singular structures termed caustics for their resemblance to focal surfaces in optics. Here we show that such extreme aggregation onto low-dimensional submanifolds…
We study spatio-temporal bursting in a three-scale reaction diffusion equation organized by the winged cusp singularity. For large time-scale separation the model exhibits traveling bursts, whereas for large space-scale separation the model…
We study the dynamics of quantized superfluid vortices on axisymmetric compact surfaces with no holes, where the total vortex charge must vanish and the condition of irrotational flow forbids distributed vorticity. A conformal…
In this paper, we study the point-vortex dynamics with positive intensities. We show that in the half-plane and in a disk, collapses of point vortices with the boundary in finite time are impossible, hence the solution of the dynamics is…
Several progresses have been done very recently on models for the dynamics of one or more vortex filaments in three-dimensional fluids. In this article we survey the recent and previous results in this topic. We also present some new…
We present for the first time solutions in the gauged $U(1)\times U(1)$ model of Witten describing vortons -- spinning flux loops stabilized against contraction by the centrifugal force. Vortons were heuristically described many years ago,…
Using group theory arguments and numerical simulations, we demonstrate the possibility of changing the vorticity or topological charge of an individual vortex by means of the action of a system possessing a discrete rotational symmetry of…
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…
This paper is concerned with the analysis of a typical singularity of piecewise smooth vector fields on $R^3$ composed by two zones. In our object of study, the cusp-fold singularity, we consider the simultaneous occurrence of a cusp…
In this paper we construct a family of steady symmetric vortex patches for the incompressible Euler equations in an open disk. The result is obtained by studying a variational problem in which the kinetic energy of the fluid is maximized…
In this paper, we investigate the well-posedness theory and exponential stability for the inhomogeneous incompressible Navier-Stokes equation with only horizontal dissipative structure. Due to the lack of the vertical dissipative term and…
The electric field distributions and space-time singularity curves are computed for ultrashort pulsed Laguerre-Gaussian laser beams having spatial chirp. Due to the breaking of cylindrical symmetry by the spatial chirp, the singularities…
Analogous to the various states of condensed matter exhibiting crystalline, amorphous, liquid and spatially inhomogeneous phases, such structures are likewise observed in superconducting vortex matter.
We present an study of the dynamics and decay pattern of phase singularities due to the action of a system with a discrete rotational symmetry of finite order. A topological charge conservation rule is identified. The role played by the…