相关论文: Imaging of nonlinear materials via the Monotonicit…

We apply the method of inverse iteration to the Laplace eigenvalue problem with Robin and mixed Dirichlet-Neumann boundary conditions, respectively. For each problem, we prove convergence of the iterates to a non-trivial principal…

In this paper we take a quasi-Newton approach to nonlinear eigenvalue problems (NEPs) of the type $M(\lambda)v=0$, where $M:\mathbb{C}\rightarrow\mathbb{C}^{n\times n}$ is a holomorphic function. We investigate which types of approximations…

In this article we consider an inverse boundary value problem for the time-harmonic Maxwell equations. We show that the electromagnetic material parameters are determined by boundary measurements where part of the boundary data is measured…

The class of topological insulator materials is one of the frontier topics of condensed matter physics. The great success of this field is due to the conceptual breakthroughs in theories for topological electronic states and is strongly…

We study a transmission problem for the time harmonic Maxwell's equations between a classical positive material and a so-called negative index material in which both the permittivity $\varepsilon$ and the permeability $\mu$ take negative…

In this paper, we study the inverse medium scattering problem to reconstruct unknown inhomogeneous medium from far field patterns of scattered waves. In the first part of our work, the linear inverse scattering problem was discussed, while…

Topological materials are quantum materials with nontrivial ground-state entanglement that are irremovable so long as certain rules, like invariance under symmetries and the existence of an energy gap, are respected. They showcase…

We consider boundary measurements for the wave equation on a bounded domain $M \subset \R^2$ or on a compact Riemannian surface, and introduce a method to locate a discontinuity in the wave speed. Assuming that the wave speed consist of an…

In this paper, we prove the local uniqueness of an inverse problem arising in the nonstationary flow of a nonhomogeneous incompressible asymmetric fluid in a bounded domain with smooth boundary. The direct problem is an initial-boundary…

We investigate inverse boundary problems associated with a time-dependent semilinear hyperbolic equation, where both nonlinearity and sources (including initial displacement and initial velocity) are unknown. We establish in several generic…

In the past few years, deep learning-based methods have demonstrated enormous success for solving inverse problems in medical imaging. In this work, we address the following question:\textit{Given a set of measurements obtained from real…

Recently, with the significant developments in deep learning techniques, solving underdetermined inverse problems has become one of the major concerns in the medical imaging domain. Typical examples include undersampled magnetic resonance…

We derive an efficient stochastic algorithm for inverse problems that present an unknown linear forcing term and a set of nonlinear parameters to be recovered. It is assumed that the data is noisy and that the linear part of the problem is…

The paper extends and enhances in several ways the recently proposed homogenization theory of metamaterials [J. Opt. Soc. Am. B 28, 577 (2011)]. The theory is based on a direct analysis of fields in the lattice cells rather than on an…

In this paper, we introduce two parabolic target-space interior-point algorithms for solving monotone linear complementarity problems. The first algorithm is based on a universal tangent direction, which has been recently proposed for…

In this paper we prove uniqueness in the inverse boundary value problem for quasilinear elliptic equations whose linear part is the Laplacian and nonlinear part is the divergence of a function analytic in the gradient of the solution. The…

We investigate cloaking property of negative-index metamaterials in the time-harmonic electromagnetic setting for the so-called doubly complementary media. These are media consisting of negative-index metamaterials in a shell (plasmonic…

We consider an inverse problem for a Westervelt type nonlinear wave equation with fractional damping. This equation arises in nonlinear acoustic imaging, and we show the forward problem is locally well-posed. We prove that the smooth…

The inverse reflector problem arises in geometrical nonimaging optics: Given a light source and a target, the question is how to design a reflecting free-form surface such that a desired light density distribution is generated on the…

We develop a new, mathematically precise framework for treating the effects of nonlinear phenomena occurring on small scales in general relativity. Our approach is an adaptation of Burnett's formulation of the "shortwave approximation",…