Related papers: On Direct and Indirect Scattering Approaches for H…
The discrete-dipole approximation (DDA) is a flexible technique for computing scattering and absorption by targets of arbitrary geometry. In this paper we perform systematic study of various non-stationary iterative (conjugate gradient)…
The homogenization of a metamaterial made of a collection of scatterers periodically disposed is studied from three different points of view. Specifically tools for multiple scattering theory, functional analysis, differential geometry and…
The aim of this paper is to analyze from a mathematical perspective some existing schemes to partition a molecular density into several atomic contributions, with a specific focus on Iterative Stockholder Atom (ISA) methods. We provide a…
The Sudden Approximation (SA) for scattering of atoms from surfaces is generalized to allow for double collision events and scattering from time-dependent quantum liquid surfaces. The resulting new schemes retain the simplicity of the…
Direct imaging methods recover the presence, position, and shape of the unknown obstacles in time-harmonic inverse scattering without a priori knowledge of either the physical properties or the number of disconnected components of the…
We study theoretically the concept of homogenization in optics using an ensemble of randomly distributed resonant stationary atoms with density $\rho$. The ensemble is dense enough for the usual condition for homogenization, viz.…
The homogenization of one-dimensional acoustic or elastic structures of finite extent is considered. A new homogenization method based on transfer matrices is derived. The new homogenization method may account for variable cross sectional…
The static diffraction intensity distribution from large material system conceived as perfectly homogeneous system made inhomogeneous, though substitution of groups of atoms, small particles, by other groups of atoms, is explicitly…
We present a review of the discrete dipole approximation (DDA), which is a general method to simulate light scattering by arbitrarily shaped particles. We put the method in historical context and discuss recent developments, taking the…
A standard approach to solving the S$_N$ transport equations is to use source iteration with diffusion synthetic acceleration (DSA). Although this approach is widely used and effective on many problems, there remain some practical issues…
We present a generalization of the coupled dipole method to the scattering of light by arbitrary periodic structures. This new formulation of the coupled dipole method relies on the same direct-space discretization scheme that is widely…
The discrete-dipole approximation (DDA) is a powerful method for calculating absorption and scattering by targets that have sizes smaller than or comparable to the wavelength of the incident radiation. The DDA can be extended to targets…
The direct sampling method (DSM) has been introduced for non-iterative imaging of small inhomogeneities and is known to be fast, robust, and effective for inverse scattering problems. However, to the best of our knowledge, a full analysis…
Photon transport through a diffusing slab can be described by the radiative transfer equation (RTE). When the slab is highly scattering and weakly absorbing, the RTE simplifies to the diffusion equation. In this paper, an inverse diffusion…
The real-space renormalization group technique is introduced to evaluate the effective diffusion constant for diffusion in inhomogeneous media, which has been obtained by singular perturbation methods. Our method is formulated on a…
A practical method is developed to deal with the second quantization of the many-body system containing the composite particles. In our treatment, the modes associated with composite particles are regarded approximately as independent ones…
In this chapter we describe a selection of mathematical techniques and results that suggest interesting links between the theory of gratings and the theory of homogenization, including a brief introduction to the latter. By no means do we…
This paper presents a fast high-order method for the solution of two-dimensional problems of scattering by penetrable inhomogeneous media, with application to high-frequency configurations containing (possibly) discontinuous refractivities.…
We adapt and study a variance reduction approach for the homogenization of elliptic equations in divergence form. The approach, borrowed from atomistic simulations and solid-state science [von Pezold et al, Physical Review B 2010; Wei et…
In this paper, we study numerical homogenization methods based on integral equations. Our work is motivated by materials such as concrete, modeled as composites structured as randomly distributed inclusions imbedded in a matrix. We…