Absfracf—A modal analysis of the problems of excitation of the dominant mode in ah optical fiber by incident plane waves and Gaussian beams has been carried out, and the results applied to the effect on transmission of misalignment in fiber junctions due to offsets, tilts, and gaps. The results in cases of matched media confirm the accuracy of previous theoretical treatments using the Born appr...

A rigorous error analysis is presented for the scattering coefficient of biological random continuous media in the Born (or single-scattering) approximation. The analysis is done in two dimensions (2-D) for simplicity of numerical computation. Scattering coefficients of various tissue-like random media are numerically calculated via statistical finite-difference-time-domain analysis. The result...

Because optical diffusion imaging is a highly nonlinear inverse problem, iterative inversion algorithms based on the Born approximation have usually been employed as reconstruction technique, but convergence is slow, especially for high contrast parameter distributions. We show here that the slow convergence of the conventional algorithms is due to the linear integral operator derived by the Bo...

The GISAXS intensity from buried Ge nanodots have been examined both by GISAXS/reflectivity measurements and also simulations with Distorted Wave Born Approximation (DWBA). The validity and the condition of using Born Approximation (BA) are discussed from the simulations based on the layer structures modelled from a reflectivity analysis. As expected in the previous kinematical analysis, use of...

The linearized wave-equation MVA operator can be used for velocity analysis using both Born and Rytov approximations. The distinction arises from the method used to compute the image perturbations. Both approximations suffer from limitations that limit their practicality: the Born approximation is usable only for small anomalies, while the Rytov approximation requires phase unwrapping. Differen...

Quasi-continuum (QC) methods are computational techniques, which reduce the complexity of atomistic simulations in a static setting while keeping information on smallscale structures and effects. The main idea is to couple atomistic and continuum models and thus to obtain quite detailed but still not too expensive numerical simulations. We aim at a mathematically rigorous verification of QC met...

A method for determining the internal structure of a localized scattering potential from field measurements performed outside the scattering volume is developed by using the Rytov approximation. The theory is compared with the inverse-scattering method within the Born and eikonal approximations and found to reduce to these methods in the weak-scattering (Born) and very-short-wavelength (eikonal...

We study the quantum foundations of a theory of large amplitude collective motion for a Hamiltonian expressed in terms of canonical variables. In previous work the separation into slow and fast (collective and non-collective) variables was carried out without the explicit intervention of the Born Oppenheimer approach. The addition of the Born Oppenheimer assumption not only provides support for...

The authors study a validity timescale of the discrete truncated Wigner approximation for several quantum-spin systems with long-range interactions step-function form by using Bogoliubov-Born-Green-Kirkwood-Yvon equation.

The exclusive production of one μ+μ− pair in collisions of two ultra-relativistic nuclei is considered. We present the simple method for calculation of the Born cross section for this process. Then we found that the Coulomb corrections to this cross section (which correspond to multi-photon exchange of the produced μ with nuclei) are small while the unitarity corrections are large. This is in s...