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This document is on considerations and findings on modelling of spinning beams. Spinning has been proposed for stabilizing beams against perturbations notably risen by non-linear space charge forces, see [Y.-L. Cheon et al., Effects of beam…
We study the dynamics of scroll vortices in excitable reaction-diffusion systems analytically and numerically. We demonstrate that intrinsic three-dimensional instability of a straight scroll leads to the formation of helicoidal structures.…
In this fluid dynamics video we study the dynamics of miscible vortex rings falling in ambient strongly (near two-layer) stratified fluid. Experiments and direct numerical simulations using the variable density Navier-Stokes (VARDEN) solver…
Using the Klein-Majda-Damodaran model of nearly-parallel vortex filaments, we construct vortex knots and links on a torus involving periodic boundary conditions and analyze their stability. For a special class of vortex knots -- toroidal…
In bistable systems, the stability of front structures often influences the dynamics of extended patterns. We show how the combined effect of an instability to curvature modulations and proximity to a pitchfork front bifurcation leads to…
The motion of a vortex filament in superfluid 4He is considered by using the Hall-Vinen-Bekarevich-Khalatnikov (HVBK) phenomenological model for the scattering process between the vortex and thermal excitations in liquid 4He. The HVBK…
The motion of a vortex domain wall in a ferromagnetic strip of submicron width under the influence of an external magnetic field exhibits three distinct dynamical regimes. In a viscous regime at low fields the wall moves rigidly with a…
Patterns of vortex ripples form when a sand bed is subjected to an oscillatory fluid flow. Here we describe experiments on the response of regular vortex ripple patterns to sudden changes of the driving amplitude a or frequency f. A…
One of the main questions in planet formation theory is how to cross the metre-scale barrier. In this two-part series, we assess the merits of vortex-based theories by investigating the effect of backreacting dust on vortices. Specifically,…
We study the dynamics and interaction of coaxial vortex rings in the FitzHugh-Nagumo excitable medium. We find that threading vortex rings with a vortex string results in significant qualitative differences in their evolution and…
By utilizing the AdS/CFT correspondence, we explore the dynamics of strongly coupled superfluid vortices in a disk with constant angular velocity. Each vortex in the vortex lattice is quantized with vorticity one from the direct inspection…
Stochastic dynamics of a vortex filament obeying local induced approximation equation plus random agitation is investigated by analytical and numerical methods. The character of a stirring force is supposed to be a white noise with spatial…
Stratified wakes past an isolated conical seamount are simulated at a Froude number of $Fr = 0.15$ and Rossby numbers of $Ro = 0.15$, 0.75, and $\infty$. The wakes exhibit a K{\' a}rm{\' a}n vortex street, unlike their unstratified,…
A superconducting rod with a magnetic moment on top develops vortices obtained here through 3D calculations of the Ginzburg-Landau theory. The inhomogeneity of the applied field brings new properties to the vortex patterns that vary…
Dynamics of magnetic vortex core switching in nanometer-scale permalloy disk, having a single vortex ground state, was investigated by micromagnetic modeling. When an in-plane magnetic field pulse with an appropriate strength and duration…
Disorganized electrical activity in the heart leads to sudden cardiac death. To what extent can this electrical turbulence be viewed as classical fluid turbulence,which is an important central problem in modern physics? We investigate,for…
Recently, a nonlinear stability theory has been developed for wave trains in reaction-diffusion systems relying on pure $L^\infty$-estimates. In the absence of localization of perturbations, it exploits diffusive decay caused by smoothing…
Theories, simulations and experiments on vortex dynamics in quasi-two-dimensional magnetic materials are reviewed. These materials can be modelled by the classical two-dimensional anisotropic Heisenberg model with XY (easy-plane) symmetry.…
Rotating spiral waves are a form of self-organization observed in spatially extended systems of physical, chemical, and biological nature. A small perturbation causes gradual change in spatial location of spiral's rotation center and…
Model description of patterns of atomic displacements in twisted bilayer systems has been proposed. The model is based on the consideration of several dislocation ensembles, employing a language that is widely used for grain boundaries and…