Related papers: An inverse problem from condense matter physics
We consider the problem of reconstructing a background potential from the dynamical behavior of vortex dipole. We prove that under suitable conditions, one can uniquely reconstruct a real-analytic potential by measuring the entrance and…
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 is concerned with the detection of objects immersed in anisotropic media from boundary measurements. We propose an accurate approach based on the Kohn-Vogelius formulation and the topological sensitivity analysis method. The…
We study the dynamics of vortices with arbitrary topological charges in weakly interacting Bose-Einstein condensates using the Adomian Decomposition Method to solve the nonlinear Gross-Pitaevskii equation in polar coordinates. The solutions…
We give uniqueness theorem and reconstruction algorithm for the nonlinearized problem of finding the dielectric anisotropy f of the medium from non-overdetermined polarization tomography data. We assume that the medium has uniform…
We consider an inverse problem for the compressible Euler's equations in polytropic fluid. We show that by taking active measurements near a particle trajectory one can determine the background flow in a set where pressure waves can…
We study the dynamics of vortices in an inhomogeneous Gross-Pitaevskii equation $i \partial_t u = \Delta u + {1\over \varepsilon^2} (p_\varepsilon^2(x) - |u|^2)$. For a unique scaling regime $|p_\varepsilon(x) - 1 | = O(|\log…
We derive the asymptotical dynamical law for Ginzburg-Landau vortices in an inhomogeneous background density under the Schr\"odinger dynamics, when the Ginzburg-Landau parameter goes to zero. New ingredients involve across the cores lower…
Unoriented surface reconstructions based on the Gauss formula have attracted much attention due to their elegant mathematical formulation and excellent performance. However, the isotropic characteristics of the formulation limit their…
This paper is concerned with analysis of electromagnetic wave scattering by an obstacle which is embedded in a two-layered lossy medium separated by an unbounded rough surface. Given a dipole point source, the direct problem is to determine…
We study the motion of a vortex dipole in a Bose-Einstein condensate confined to an anisotropic trap. We focus on a system of ordinary differential equations describing the vortices' motion, which is in turn a reduced model of the…
A novel computational, non-iterative and noise-robust reconstruction method is introduced for the planar anisotropic inverse conductivity problem. The method is based on bypassing the unstable step of the reconstruction of the values of the…
Dissipative vortices are stable two-dimensional localized structures existing due to balance between gain and loss in nonlinear systems far from equilibrium. Being resistant to the dispersion and nonlinear distortions they are considered as…
We study the response of a trapped Bose-Einstein condensate to a sudden turn-on of a rotating drive by solving the two-dimensional Gross-Pitaevskii equation. A weakly anisotropic rotating potential excites a quadrupole shape oscillation and…
We consider vortices in the nonlocal two-dimensional Gross-Pitaevskii equation with the interaction potential having the Lorentz-shaped dependence on the relative momentum. It is shown that in the Fourier series expansion with respect to…
A direct reconstruction algorithm based on Calder\'on's linearization method for the reconstruction of isotropic conductivities is proposed for anisotropic conductivities in two-dimensions. To overcome the non-uniqueness of the anisotropic…
A method for the reconstruction of the primordial density fluctuation field is presented. Various previous approaches to this problem rendered {\it non-unique} solutions. Here, it is demonstrated that the initial positions of dark matter…
Here we study properties of a homogeneous dipolar Bose-Einstein condensate in a weak anisotropic random potential with Lorentzian correlation at zero temperature. To this end we solve perturbatively the Gross-Pitaevskii equation to second…
We present a reconstruction algorithm for recovering both "magnetic-hard" and "magnetic-soft" obstacles in a background domain with known isotropic medium from the boundary impedance map. We use in our algorithm complex geometric optics…
Dix formulated the inverse problem of recovering an elastic body from the measurements of wave fronts of point sources. We geometrize this problem in the context of seismology, leading to the geometrical inverse problem of recovering a…