Related papers: On a Frequency-Stabilized Single Current Inverse S…
Single quantum dots are solid-state emitters which mimic two-level atoms but with a highly enhanced spontaneous emission rate. A single quantum dot is the basis for a potentially excellent single photon source. One outstanding problem is…
This work introduces a Hamiltonian approach to regularization and linearization of central-force particle dynamics through a new canonical extension of the so-called "projective decomposition". The regularization scheme is formulated within…
This paper addresses the direct and inverse source problems for the stochastic acoustic, biharmonic, electromagnetic, and elastic wave equations in a unified framework. The driven source is assumed to be a centered generalized microlocally…
Source conditions are a key tool in regularisation theory that are needed to derive error estimates and convergence rates for ill-posed inverse problems. In this paper, we provide a recipe to practically compute source condition elements as…
We study the inverse boundary value problem for the Helmholtz equation using the Dirichlet-to-Neumann map at selected frequencies as the data. A conditional Lipschitz stability estimate for the inverse problem holds in the case of…
An unstable magnetron RF source for driving an accelerator cavity at high power is stabilized using ferroelectric fast reactive tuning. The magnetron output is converted to a selected reference frequency with negligible insertion loss. The…
We consider an inverse scattering problem and its near-field approximation at high frequencies. We first prove, for both problems, Lipschitz stability results for determining the low-frequency component of the potential. Then we show that,…
In this investigation we use a simple model of the dynamics of an inviscid vortex sheet given by the Birkhoff-Rott equation to obtain fundamental insights about the potential for stabilization of shear layers using feedback control. As…
The Kelvin--Helmholtz (KH) and tearing instabilities are likely to be important for the process of fast magnetic reconnection that is believed to explain the observed explosive energy release in solar flares. Theoretical studies of the…
We consider an inverse source problem for the Helmholtz equation in a bounded domain. The problem is to reconstruct the shape of the support of a source term from the Cauchy data on the boundary of the solution of the governing equation. We…
For an ill-posed inverse problem, particularly with incomplete and limited measurement data, regularization is an essential tool for stabilizing the inverse problem. Among various forms of regularization, the lp penalty term provides a…
We consider two formally determined inverse problems for the wave equation in more than one space dimension. Motivated by the fixed angle inverse scattering problem, we show that a compactly supported potential is uniquely determined by the…
We develop a novel method of virtual sources to formulate boundary integral equations for exterior wave propagation problems. However, by contrast to classical boundary integral formulations, we displace the singularity of the Green's…
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…
The present manuscript consists of inverse problems for a coupled system of wave equations with potential in $\mathbb{R}^3$. By establishing the fundamental solution to the aforementioned operator, we study the uniqueness aspects of the…
In this paper, we study the inverse source problem for the biharmonic wave equation. Mathematically, we characterize the radiating sources and non-radiating sources at a fixed wavenumber. We show that a general source can be decomposed into…
In this paper, we consider the prediction of the helium concentrations as function of a spatially variable source term perturbed by fractional Brownian motion. For the direct problem, we show that it is well-posed and has a unique mild…
In this paper, we present an inverse problem of identifying the reaction coefficient for time fractional diffusion equations in two dimensional spaces by using boundary Neumann data. It is proved that the forward operator is continuous with…
We show that on a simple Riemannian manifold, the electric potential and the solenoidal part of the magnetic potential appearing in the magnetic Schr\"odinger operator can be recovered H\"older stably from the boundary spectral data. This…
In this work, we consider an inverse problem of determining a source term for a structural acoustic partial differentia equation (PDE) model, comprised of a two or three-dimensional interior acoustic wave equation coupled to a Kirchoff…