Related papers: Resonances in axially symmetric dielectric objects
Formulas are derived for solutions of many-body wave scattering problems by small particles in the case of acoustically soft, hard, and impedance particles embedded in an inhomogeneous medium. The limiting case is considered, when the size…
The problem of imaging extended targets (sources or scatterers) is formulated in the framework of compressed sensing with emphasis on subwavelength resolution. The proposed formulation of the problems of inverse source/scattering is…
Fourier imaging is an indirect imaging method which records the diffraction pattern of the object scene coherently in the focal plane of the imaging system and reconstructs the image using computational resources. The spatial resolution,…
This work is devoted to the stability/resolution analysis of several imaging functionals in complex environments. We consider both linear functionals in the wavefield as well as quadratic functionals based on wavefield correlations. Using…
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…
We develop the complex scaling method for the Dirichlet Laplacian in a domain with asymptotically cylindrical end. We define resonances as discrete eigenvalues of non-selfadjoint operators, obtained as deformations of the selfadjoint…
We describe an exact and highly efficient numerical algorithm for solving a special but important class of convection-diffusion equations. These equations occur in many problems in physics, chemistry, or biology, and they are usually hard…
This paper addresses the electromagnetic inverse scattering problem of determining the location and shape of anisotropic objects from near-field data. We investigate both cases involving the Helmholtz equation and Maxwell's equations for…
In this article we discuss density of products of biharmonic functions vanishing on an arbitrarily small part of the boundary. We prove that one can use three or more such biharmonic functions to construct a dense subset of smooth symmetric…
This work is concerned with an inverse problem of identifying the current source distribution of the time-harmonic Maxwell's equations from multi-frequency measurements. Motivated by the Fourier method for the scalar Helmholtz equation and…
We consider the problem of determining the boundary perturbations of an object from far-field electric or acoustic measurements. Assuming that the unknown object boundary is a small perturbation of a circle, we develop a linearized relation…
Precise knowledge of resonator dispersion, from both geometric and material contributions, is essential for reliable high-performance nonlinear integrated photonics devices, such as optical parametric oscillators, frequency doublers, and…
Higher dimensional super symmetry has been analyzed in terms of quaternion variables and the theory of quaternion harmonic oscillator has been analyzed. Supersymmertization of quaternion Dirac equation has been developed for…
This is the third article in a series of three papers on the resonance energy levels of anharmonic oscillators. Whereas the first two papers mainly dealt with double-well potentials and modifications thereof [see J. Zinn-Justin and U. D.…
Subwavelength resonators are small scaled objects that exhibit contrasting medium properties (eigher in intensity or sign) while compared to the ones of a uniform background. Such contrasts allow them to resonate at specific frequencies.…
We consider radial complex scaling/perfectly matched layer methods for scalar resonance problems in homogeneous exterior domains. We introduce a new abstract framework to analyze the convergence of domain truncations and discretizations.…
We develop a polynomial basis to be used in numerical calculations of light-front Fock-space wave functions. Such wave functions typically depend on longitudinal momentum fractions that sum to unity. For three particles, this constraint…
This paper focuses on stability estimates of the inverse random source problems for the polyharmonic, electromagnetic, and elastic wave equations. The source is represented as a microlocally isotropic Gaussian random field, which is defined…
We study generalized (1+1)-dimensional Dirac oscillator in nonuniform electric field. It is shown that in the case of specially chosen electric field the eigenvalue equation can be casted in the form of supersymmetric quantum mechanics. It…
We consider time-harmonic scalar transmission problems between dielectric and dispersive materials with generalized Lorentz frequency laws. For certain frequency ranges such equations involve a sign-change in their principle part. Due to…