Related papers: Non-singular field-only surface integral equations…
${}^3$He beam spin-echo experiments have been used to study surface morphology, molecular and atomic surface diffusion, phonon dispersions, phason dispersions and phase transitions of ionic liquids. However, the interactions between…
In this paper, we extend and simplify the methods in [13] to improve the results on uniqueness of the boundary determination for the Maxwell equation. In particular, we show that the electromagnetic parameters are uniquely determined to…
A new development of the ``monodromy transform'' method for analysis of hyperbolic as well as elliptic integrable reductions of Einstein equations is presented. Compatibility conditions for some alternative representations of the…
Meromorphic continuation of the scattering operator leads to scattering poles (resonances) in the complex plane. Despite their significance, numerical investigation of scattering poles remains limited. In this paper, we propose and analyze…
Our main result is the analysis of singularities of integrands of integrals representing matrix elements of scattering matrix and inclusive scattering matrix in perturbation theory. These results are proven for any quantum field theory in…
The electromagnetic (EM) radiation force-per-length exerted on a pair of electrically-conducting cylindrical particles of circular and non-circular cross-sections is examined using a formal semi-analytical method based on boundary matching…
We developed a fast numerical algorithm for solving the three dimensional vectorial Helmholtz equation that arises in electromagnetic scattering problems. The algorithm is based on electric field integral equations and is essentially a…
In this work, a recently developed novel solution of the famous "Sommerfeld Radiation Problem" is revisited. The solution is based on an analysis performed entirely in the spectral domain, through which a compact asymptotic formula…
Electromagnetic fields with complex spatial variation routinely arise in Nature. We study the response of a small molecule to monochromatic fields of arbitrary three-dimensional geometry. First, we consider the allowed configurations of the…
This paper presents a general non-linear computational formulation for rotation-free thin shells based on isogeometric finite elements. It is a displacement-based formulation that admits general material models. The formulation allows for a…
A numerical method using implicit surface representations is proposed to solve the linearized Poisson-Boltzmann equations that arise in mathematical models for the electrostatics of molecules in solvent. The proposed method used an implicit…
We propose a novel scheme to normalize scattering modes of the electromagnetic field. By relying on analytical solutions for Maxwell's equations in the homogenous medium outside the scatterer, we derive normalization conditions that only…
In this article, we propose p and hp least-squares spectral element methods for one-dimensional elliptic boundary layer problems. Stability estimates are derived and we design numerical schemes based on minimizing the residuals in the sense…
The concept of geometric phase was applied to initiate the geometric-phase portrayal of electromagnetic scattering by a three-dimensional object in free space. Whereas the incident electromagnetic field is that of an arbitrarily polarized…
In this work, we are concerned with the mathematical modeling of the electromagnetic (EM) scattering by arbitrarily shaped non-magnetic nanoparticles with high refractive indices. When illuminated by visible light, such particles can…
Controlling single-electron states becomes increasingly important due to the wide-ranging advances in electron quantum optics. Single-electron control enables coherent manipulation of individual electrons and the ability to exploit the wave…
We propose a discussion on the synthesis and scattering analysis of nonlinear metasurfaces. For simplicity, we investigate the case of a second-order nonlinear isotropic metasurface possessing both electric and magnetic linear and nonlinear…
Let $H(\hbar)=-\hbar^2d^2/dx^2+V(x)$ be a Schr\"odinger operator on the real line, $W(x)$ be a bounded observable depending only on the coordinate and $k$ be a fixed integer. Suppose that an energy level $E$ intersects the potential $V(x)$…
The propagation of electromagnetic surface waves guided by the planar interface of two isotropic chiral materials, namely materials $\calA$ and $\calB$, was investigated by numerically solving the associated canonical boundary-value…
In the context of Born-Infeld electrodynamics, the electromagnetic fields interact with each other via their non-linear couplings. A calculation will be performed where an incoming electromagnetic plane wave scatters off a Coulomb Field in…