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8 papers · 2 filters
Wave scattering by many small particles embedded in a medium
A. G. Ramm
Theory of scattering by many small bodies is developed under various assumptions concerning the ratio , where is the characteristic dimension of a small body and $…
The Pontrjagin-Hopf invariants for Sobolev maps
Dave Auckly, Lev Kapitanski
Subtle issues arise when extending homotopy invariants to spaces of functions having little regularity, e.g., Sobolev spaces containing discontinuous functions. Sometimes it is not…
A recipe for making materials with negative refraction in acoustics
A. G. Ramm
A recipe is given for making materials with negative refraction in acoustics, i.e., materials in which the group velocity is directed opposite to the phase velocity. The recipe con…
Some Results on Inverse Scattering
A. G. Ramm
A review of some of the author's results in the area of inverse scattering is given. The following topics are discussed: 1) Property and applications, 2) Stable inversion of fi…
Many-body wave scattering by small bodies and applications
A. G. Ramm
A rigorous reduction of the many-body wave scattering problem to solving a linear algebraic system is given bypassing solving the usual system of integral equation. The limiting ca…
Materials with a desired refraction coefficient can be made by embedding small particles
A. G. Ramm
A method is proposed to create materials with a desired refraction coefficient, possibly negative one. The method consists of embedding into a given material small particles. Given…