Related papers: A Sampling Theorem for Computational Diffraction
We present a numerical method for the solution of diffusion problems in unbounded planar regions with complex geometries of absorbing and reflecting bodies. Our numerical method applies the Laplace transform to the parabolic problem,…
We study the time-harmonic scattering by a heterogeneous object covered with a thin layer of randomly distributed sound-soft nanoparticles. The size of the particles, their distance between each other and the layer's thickness are all of…
The product of any number of Legendre functions, under a restricted domain, can be expanded by the corresponding Legendre polynomials, with the coefficient being the sinc function. While an analogous expansion can be made for any number of…
The sampling theorem for the offset linear canonical transform (OLCT) of bandlimited functions in polar coordinates is an important signal analysis tool in many fields of signal processing and medical imaging. This study investigates two…
Numerous vector angular spectrum methods have been presented to model the vectorial nature of diffractive electromagnetic field, facilitating optical field engineering in polarization-related and high numerical aperture systems. However,…
We consider the inverse problem of determining the geometry of penetrable objects from scattering data generated by one incident wave at a fixed frequency. We first study an orthogonality sampling type method which is fast, simple to…
Short distance structure of spacetime may show up in the form of high freqency dispersion. Although such dispersion is not locally Lorentz invariant, we show in a scalar field model how it can nevertheless be incorporated into a generally…
We develop embedding formulae for all possible diffraction problems with Dirichlet scatterers on square lattices using the Wiener--Hopf perspective. The embedding formula expresses solutions for arbitrary plane-wave incidence in terms of a…
We consider the numerical solution of time-harmonic acoustic scattering by obstacles with uncertain geometries for Dirichlet, Neumann, impedance and transmission boundary conditions. In particular, we aim to quantify diffracted fields…
The path integral formulation can reproduce the right energy spectrum of the harmonic oscillator potential, but it cannot resolve the Coulomb potential problem. This is because the path integral cannot properly take into account the…
This work is concerned with the inverse source problem of locating multiple multipolar sources from boundary measurements for the Helmholtz equation. We develop simple and effective sampling schemes for location acquisition of the sources…
We consider the inverse problem of fitting atmospheric dispersion parameters based on time-resolved back-scattered differential absorption Lidar (DIAL) measurements. The obvious advantage of light-based remote sensing modalities is their…
In this paper, we consider the obstacle scattering problem for biharmonic equations with a Dirichlet boundary condition in both two and three dimensions. Some basic properties are first derived for the biharmonic scattering solutions, which…
This article is the third and last of a series presenting an alternative method to compute the one-loop scalar integrals. It extends the results of first two articles to the infrared divergent case. This novel method enjoys a couple of…
A new sampling method for inverse scattering problems is proposed to process far field data of one incident wave. As the linear sampling method, the method sets up ill-posed integral equations and uses the (approximate) solutions to…
We consider the inverse problem of reconstructing general solutions to the Helmholtz equation on some domain $\Omega$ from their values at scattered points $x_1,\dots,x_n\subset \Omega$. This problem typically arises when sampling acoustic…
Electromagnetic wave scattering from planar dielectric films deposited on one-dimensional, randomly rough, perfectly conducting substrates is studied by numerical simulations for both p- and s-polarization. The reduced Rayleigh equation,…
For a general formulation of linearised hybrid inverse problems in impedance tomography, the qualitative properties of the solutions are analysed. Using an appropriate scalar pseudo-differential formulation, the problems are shown to permit…
The work is devoted to Dirichlet problem for sub-quintic semi-linear wave equation with damping damping term of the form $(-\Delta)^\alpha\partial_t u$, $\alpha\in(0,\frac{1}{2})$, in bounded smooth domains of $\Bbb R^3$. It appears that to…
A new sampling methodology based on incomplete cosine expansion series is presented as an alternative to the traditional sinc function approach. Numerical integration shows that this methodology is efficient and practical. Applying the…