Related papers: Interaction of a dipole point vortex with flat bou…
Some approach to the solution of boundary value problems for finding functions, which are analytical in a wedge, is proposed. If the ratio of the angle at the wedge vertex to a number \pi is rational, then the boundary value problem is…
We consider a stochastic version of the point vortex system, in which the fluid velocity advects single vortices intermittently for small random times. Such system converges to the deterministic point vortex dynamics as the rate at which…
We consider a two-dimensional, two-layer, incompressible, steady flow, with vorticity which is constant in each layer, in an infinite channel with rigid walls. The velocity is continuous across the interface, there is no surface tension or…
We investigate the propagation of infinitesimal harmonic mechanical waves emitted from a boundary with variable velocity and arriving at a stationary observer. In the classical Doppler effect, $X_\mathrm{s}(t) = vt$ is the location of the…
Using the time-dependent Ginzburg Landau equations we study vortex motion driven by an applied current in two dimensional superconductors in the presence of a physical boundary. At smaller sourced currents the vortex lattice moves as a…
We provide a rigorous mathematical study of an asymptotic model describing Darcy flow with free boundary in a low amplitude/large wavelength approximation. In particular, we prove several well-posedness results in critical spaces.…
As a model for vortex-wall interactions, we consider the two-dimensional incompressible Navier--Stokes equations in the half-plane $R^2_+$ with no-slip boundary condition and point vortices as initial data. We focus on the paradigmatic…
We show that a vortex matter, that is a dense assembly of vortices in an incompressible two-dimensional flow, such as a fast rotating superfluid or turbulent flows with sign-like eddies, exhibits (i) a boundary layer of vorticity (vorticity…
The velocity field within a steady toroidal vortex is found for arbitrary mean core radius and section ellipticity. The problem is solved by transforming to coordinates that define invariant sets. The method allows the properties of the…
We study the orientational and translational dynamics of spherical microswimmers trapped at fluid interfaces, in terms of the force dipole and source dipole components of their flow field. Using numerical simulations and analytical…
We have calculated components of torque and the interaction energy of small rotating particle with a permanent dipole moment in the case where the rotation axis is perpendicular to the surface and the dipole axis is inclined to it. The…
In this paper, we prove that in bounded planar domains with $C^{2,\alpha}$ boundary, for almost every initial condition in the sense of the Lebesgue measure, the point vortex system has a global solution, meaning that there is no collision…
We study the motion of a superfluid vortex in condensates having different background density profiles, ranging from parabolic to uniform. The resulting effective point-vortex model for a generic power-law potential $\propto r^k$ can be…
We analyze the force on a point charge moving at relativistic speeds parallel to the surface of a uniaxial dielectric. Two cases are examined: a lossless dielectric with no dispersion and a dielectric with a plasma type response. The…
We construct a model to explore the hydrodynamic interactions of active inclusions in curved biological membranes. The curved membrane is modelled as a two dimensional layer of highly viscous fluid, surrounded by external solvents of…
We investigate a steady planar flow of an ideal fluid in a bounded simple connected domain and focus on the vortex patch problem with prescribed vorticity strength. There are two methods to deal with the existence of solutions for this…
Vortex-antivortex pairs are localized excitations and have been found to be spontaneously created in magnetic elements. In the case that the vortex and the antivortex have opposite polarities the pair has a nonzero topological charge, and…
The present research is devoted to the problem of stability of the fluid flow moving in a channel with flexible walls and interacting with the walls, which are subject to traveling waves. Experimental data shows that the energy of the…
The conventional no-slip boundary condition leads to a non-integrable stress singularity at a contact line. This is a main challenge in numerical simulations of two-phase flows with moving contact lines. We derive a two-dimensional…
When considering flows in biological membranes, they are usually treated as flat, though more often than not, they are curved surfaces, even extremely curved, as in the case of the endoplasmic reticulum. Here, we study the topological…