相关论文: Refractor surfaces determined by near-field data

We consider a stochastic model for the directed motion of a solid object due to the rectification of asymmetric surface vibrations with Poissonian shot-noise statistics. The friction between the object and the surface is given by a…

We study convex solutions to the Monge-Amp\`ere obstacle problem \[ \operatorname{det} D^2 v=g v^q\chi_{\{v>0\}}, \quad v \geq 0, \] where $q \in [0,n)$ is a constant and $g$ is a bounded positive function. This problem emerges from the…

We propose a novel iterative numerical method to solve the three-dimensional inverse obstacle scattering problem of recovering the shape of the obstacle from far-field measurements. To address the inherent ill-posed nature of the inverse…

The inverse source problem for the radiative transfer equation is considered, with partial data. Here it is shown that under certain smoothness conditions on the scattering and absorption coefficients, one can recover sources supported in a…

This work continues the development of the raytracing method of [1] for computing the scattered fields from metasurfaces characterized by locally periodic reflection and transmission coefficients. In this work, instead of describing the…

In this work, near-field imaging by two strongly coupled arrays of split ring resonators is analyzed. A simple theoretical model is developed to obtain the transfer function of the lens. This model shows that magnetoinductive surface waves…

We present a technique for proving convergence to the Aleksandrov solution of the Monge-Ampere equation of a stable and consistent finite difference scheme. We also require a notion of discrete convexity with a stability property and a…

We study the recovery of a spatially dependent source in a one-dimensional space-time fractional wave equation using boundary measurement data collected at a single endpoint. The main challenge arises from the fact that the eigenfunctions…

This paper is concerned with the inverse problem of determining an obstacle and the corresponding incident point sources in the Helmholtz equation from near-field scattering data. An optimization method is proposed to simultaneously recover…

We establish regularity and, under suitable assumptions, convergence to stationary states for weak solutions of a parabolic equation with a non-linear non-local drift term; this equation was derived from a model of active Brownian particles…

This paper studies the near field refraction problem with loss of energy in negative refractive index material. Based on the relative refractive index $\kappa$, the analysis is categorized into two cases, namely $\kappa < -1$ and $-1 <…

We present two novel additions to the semi-analytic solution of Lyman $\alpha$ (Ly$\alpha$) radiative transfer in spherical geometry: (1) implementation of the correct boundary condition for a steady source, and (2) solution of the…

Fix an arbitrary compact orientable surface with a boundary and consider a uniform bipartite random quadrangulation of this surface with $n$ faces and boundary component lengths of order $\sqrt n$ or of lower order. Endow this…

In this paper we present a hybrid approach to numerically solve two-dimensional electromagnetic inverse scattering problems, whereby the unknown scatterer is hosted by a possibly inhomogeneous background. The approach is `hybrid' in that it…

In this paper we analyse the selection problem for weak solutions of the transport equation with rough vector field. We answer in the negative the question whether solutions of the equation with a regularized vector field converge to a…

We prove an Alexandrov type theorem for a quotient space of $\mathbb H^2\times \mathbb R$. More precisely we classify the compact embedded surfaces with constant mean curvature in the quotient of $\mathbb H^2\times \mathbb R$ by a subgroup…

This paper concerns the inverse spectral problem for analytic simple surfaces of revolution. By `simple' is meant that there is precisely one critical distance from the axis of revolution. Such surfaces have completely integrable geodesic…

We study the inverse problem of locating point sources from far-field data under plane wave incidence. A direct computational method is developed based on multiple scattering theory, using a novel indicator function to avoid iterative…

This paper is devoted to the inverse problem of recovering the unknown distributed flux on an inaccessible part of boundary using measurement data on the accessible part. We establish and verify a variational source condition for this…

We present an inverse method for transforming a given parallel light emittance to two light distributions at different parallel target planes using two freeform reflectors. The reflectors control both the spatial and directional target…