Related papers: An inverse problem from condense matter physics
We study the inverse conductivity problem of how to reconstruct an isotropic electrical conductivity distribution $\gamma$ in an object from static electrical measurements on the boundary of the object. We give an exact reconstruction…
We are concerned with the inverse scattering problem of extracting the geometric structures of an unknown/inaccessible inhomogeneous medium by using the corresponding acoustic far-field measurement. Using the intrinsic geometric properties…
Inverse problems, which are related to Maxwell's equations, in the presence of nonlinear materials is a quite new topic in the literature. The lack of contributions in this area can be ascribed to the significant challenges that such…
This paper addresses the inverse obstacle scattering problem of simultaneously reconstructing the obstacle geometry and boundary conditions from multi-frequency near-field backscattering data. We first establish rigorous high-frequency…
Analog gravity models of black holes and exotic compact objects provide a unique opportunity to study key properties of such systems in controlled laboratory environments. In contrast to astrophysical systems, analog gravity systems can be…
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 present a general framework to study uniqueness, stability and reconstruction for infinite-dimensional inverse problems when only a finite-dimensional approximation of the measurements is available. For a large class of inverse problems…
We introduce a functional framework taylored to investigate the minimality and stability properties of the Ginzburg-Landau vortex of degree one on the whole plane. We prove that a renormalized Ginzburg-Landau energy is well-defined in that…
We present full three-dimensional numerical calculations of single vortex states in rotating dipolar condensates. We consider a Bose-Einstein condensate of 52Cr atoms with dipole-dipole and s-wave contact interactions confined in an axially…
We show that the inference problem of constraining the dipole amplitude with inclusive deep inelastic scattering data can be written into a discrete linear inverse problem, in an analogous manner as can be done for computed tomography. To…
In the context of the Minimal Geometric Deformation method, in this paper we implement the inverse problem in a black hole scenario. In order to deal with an anisotropic polytropic black hole solution of the Einstein field equations with…
We study the inverse problem of reconstructing an incompressible velocity field $\boldsymbol{v}$ from observations of the induced magnetic field $\boldsymbol{b}$. In the presence of a strong, constant background field $\mathbf{F}$, the…
We study the vortex lattices in a Bose-Einstein Condensate in a rotating anisotropic harmonic trap. We first investigate the single particle wavefunctions obtained by the exact solution of the problem and give simple expressions for these…
Vortex reconnections plays an important role in the turbulent flows associated with the superfluids. To understand the dynamics, we examine the reconnections of vortex rings in the superfluids of dilute atomic gases confined in trapping…
We propose an optimisation method for the inverse structural design of self-assembly of anisotropic patchy particles. The anisotropic interaction can be expressed by the spherical harmonics of the surface pattern on a patchy particle, and…
The aim of this paper is to show how the homotopy type of compact metric spaces can be reconstructed by the inverse limit of an inverse sequence of finite approximations of the corresponding space. This recovering allows us to define…
In this paper, a Sturm--Liouville problem with some nonlocal boundary conditions of the Bitsadze-Samarskii type is studied. We show that the coefficients of the problem can be uniquely determined by a dense set of nodal points. Moreover, we…
Recently we have derived a set of mapping relations that enables the reconstruction of the family of Horndeski scalar-tensor theories which reproduce the background dynamics and linear perturbations of a given set of effective field theory…
We study the non-diffusive Westervelt equation in the weakly nonlinear regime. We show that the leading profile equation is of Burgers' type. We show that a compactly supported nonlinearity $\alpha$ can be reconstructed from the tilt of the…
Given a compact manifold with boundary with unknown Riemannian metric. The problem is to reconstruct the metric in a class of conformal metrics from knowledge of lengths of all closed geodesics (kinematic data). An integral inequality is…