19 research outputs found
Phase recovery from phaseless scattering data for discrete Schr\"{o}dinger operators
We consider scattering for the discrete Schr\"{o}dinger operator on the
square lattice , , with compactly supported potential.
We give formulas for finding the phased scattering amplitude from phaseless
near-field scattering data.Comment: Keywords: Discrete Schr\"{o}dinger operators, monochromatic
scattering data, phase retrieval, phaseless inverse scatterin
Scattering on a square lattice from a crack with a damage zone
A semi-infinite crack in infinite square lattice is subjected to a wave
coming from infinity, thereby leading to its scattering by the crack surfaces.
A partially damaged zone ahead of the crack-tip is modeled by an arbitrarily
distributed stiffness of the damaged links. While the open crack, with an
atomically sharp crack-tip, in the lattice has been solved in closed form with
help of {the} scalar Wiener-Hopf formulation (SIAM Journal on Applied
Mathematics, 75, 1171--1192; 1915--1940), the problem considered here becomes
very intricate depending on the nature of damaged links. For instance, in the
case of partially bridged finite zone it involves a matrix kernel of
formidable class. But using an original technique, the problem, including the
general case of arbitrarily damaged links, is reduced to a scalar one with the
exception that it involves solving an auxiliary linear system of
equations where defines the length of the damage zone. The proposed method
does allow, effectively, the construction of an exact solution. Numerical
examples and the asymptotic approximation of the scattered field far away from
the crack-tip are also presented