Related papers: Global determination for an inverse problem from t…
We consider the problem of reconstructing the features of a weak anisotropic background potential by the trajectories of vortex dipoles in a nonlinear Gross-Pitaevskii equation. At leading order, the dynamics of vortex dipoles are given by…
In this work, we study the inverse problem of analog gravity systems which admit rotation and energy-dependent boundary conditions. By extending two recent results, we provide a recipe that allows one to relate resonant transmission spectra…
This paper concerns an inverse problem for the initial boundary value problem of the two-dimensional Navier-Stokes system defined in a bounded simply connected domain with slip, vorticity boundary conditions, and a global vorticity…
We set up general equations of motion for point vortex systems on closed Riemannian surfaces, allowing for the case that the sum of vorticities is not zero and there hence must be counter-vorticity present. The dynamics of global…
In this work we have found an exact solution for the problem of the movement of a dipole type point vortex in an area of fluid limited by a flat boundary. We also present a solution to the problem of dipole point vortex motion in a right…
The dynamics of a constrained three-vortex problem, a free point vortex pair in the velocity field of a fixed point vortex, is investigated. The underlying dynamical system is simplified using a coordinate transformation and categorized…
We consider the classical dynamics of a particle in a $d=2,3$-dimensional space-periodic potential under the influence of time-periodic external fields with zero mean. We perform a general time-space symmetry analysis and identify…
We consider the inverse problem of the determining the potential in the dynamical Schr\"odinger equation on the interval by the measurement on the whole boundary. Provided that source is \emph{generic} using the Boundary Control method we…
Modelling the vortex structures and then translating them into the corresponding velocity fields are two essential aspects for the vortex-based modelling works in wall-bounded turbulence. This work develops a datadriven method, which allows…
In the context of a dynamical Ginzburg-Landau model it is shown numerically that under the influence of a homogeneous external current J the vortex drifts against the current with velocity $V= -J$ in agreement to earlier analytical…
In this article, we study the one-dimensional inverse problem of determining the memory kernel by the integral overdetermination condition for the direct problem of finding the velocity potential and the displacement of boundary points. A…
We consider a region $M$ in $\mathbb{R}^n$ with boundary $\partial M$ and a metric $g$ on $M$ conformal to the Euclidean metric. We analyze the inverse problem, originally formulated by Dix, of reconstructing $g$ from boundary measurements…
We address the classical inverse problem of recovering the position and shape of obstacles immersed in a planar Stokes flow using boundary measurements. We prove that this problem can be transformed into a shape-from-moments problem to…
We investigate vortex dipoles on surfaces of variable negative curvature, focusing on a catenoid of arbitrary throat radius as a concrete example. We construct the effective dynamical system including mutual and geometric self-interaction…
We consider the inverse dynamic problem for the wave equation with a potential on a real line. The forward initial-boundary value problem is set up with a help of boundary triplets. As an inverse data we use an analog of a response operator…
We consider the self-adjoint Dirac operators on a finite interval with summable matrix-valued potentials and general boundary conditions. For such operators, we study the inverse problem of reconstructing the potential and the boundary…
We study the inverse problem for determining the time-dependent matrix potential appearing in the wave equation. We prove the unique determination of potential from the knowledge of solution measured on a part of the boundary.
We use holography to investigate the dynamics of a vortex-anti-vortex dipole in a strongly coupled superfluid in 2+1 dimensions. The system is evaluated in numerical real-time simulations in order to study the evolution of the vortices as…
The paper deals with some problems related to recovering information about an obstacle in an Euclidean space from certain measurements of lengths of generalized geodesics in the exterior of the obstacle. The main result is that if two…
We present an analytical model to account for the inertial dynamics of a magnetic vortex. The model is based on a deformation of the core profile based on the D\"oring kinetic field, whereby the deformation amplitudes are promoted to…