In this paper the method of renormalization group (RG) [Phys. Rev. E54, 376 (1996)] is related to the well-known approximations of Rytov and Born used in wave propagation in deterministic and random media. Certain problems in linear and nonlinear media are examined from the viewpoint of RG and compared with the literature on Born and Rytov approximations. It is found that the Rytov approximatio...

Higher Born Approximations for Elastic Electron Scattering from Atoms. A theorem analogous to the unitarity relation by Glauber and Schomaker is derived for Born’s approximations. For a given potential (r) —/u (h2/2 m) V ( r) of the scattering atom the n-th approximation f n for the scattering amplitude is defined as the function resulting from the rc-th iterative step of Born’s approximation. ...

The nonlinear Diffuse Optical Tomography (DOT) problem involves the inversion of the associated coefficient-to-measurement operator, which maps the spatially varying optical coefficients of turbid medium to the boundary measurements. The inversion of the coefficient-to-measurement operator is approximated by using the Fréchet derivative of the operator. In this work, we first analyze the Born e...

The Universe's matter inhomogeneity gravitationally affects the propagation of gravitational waves (GWs), causing lensing effect. Particularly, weak GWs has been studied within range Born approximation to constrain small-scale power spectrum. In this work, validity is investigated by accounting for higher-order terms in potential $\mathrm{\ensuremath{\Phi}}$. To do so, we formulate post-Born an...

We discuss three ways of obtaining the Born approximations for Coulomb scattering: The standard way, making use a convergence factor ("screening"), Oppenheimer's way using cylindrical (instead spherical) coordinates, and finally Landau Lifshitz' way. last one although it does require some background from theory generalized functions is nevertheless very instructive important technique deserving...

An approximate scattering theory that utilizes the exact solutions for spherical defects is being developed. A defect of arbitrary shape can be represented by a sphere S and a remainder volume δv. By treating δv as a perturbation, one obtains an approximate solution that contains non-trivial frequency dependence and phase information. The approach is expected to be useful for studying defects w...