Electromagnetic wave scattering by many small particles

Ramm, Alexander G.

doi:10.1016/j.physleta.2006.09.007

Cited by 14 publications

(15 citation statements)

References 10 publications

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“…We look for the solution to problem (1.5) -(1.7) of the form 10) where σ m should be found from the boundary conditions (1.7). For any σ m the function (1.10) solves equation (1.5) and satisfies condition (1.6):…”

Section: 4)mentioning

confidence: 99%

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Many-body wave scattering by small bodies and applications

Ramm

2007

Journal of Mathematical Physics

125

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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 case of infinitely many small particles embedded into a medium is considered and the limiting equation for the field in the medium is derived. The impedance boundary conditions are imposed on the boundaries of small bodies. The case of Neumann boundary conditions (acoustically hard particles) is also considered. Applications to creating materials with a desired refraction coefficient are given. It is proved that by embedding suitable number of small particles per unit volume of the original material with suitable boundary impedances one can create a new material with any desired refraction coefficient. The governing equation is a scalar Helmholtz equation, which one obtains by Fourier transforming the wave equation.

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Section: 4)mentioning

confidence: 99%

“…From (2.8) and (1.7) one gets: 10) where u eN (s) is the normal derivative of u e at the point s ∈ S j . One can rewrite this equation as:…”

Section: Proof Of Theoremmentioning

confidence: 99%

Many-body wave scattering by small bodies and applications

Ramm

2007

Journal of Mathematical Physics

125

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“…In recent works [19]- [34] the author has developed an asymptotically exact theory of wave scattering by many small bodies (particles) embedded in an inhomogeneous medium. The medium can be dielectric and conducting.…”

Section: Introductionmentioning

confidence: 99%

Electromagnetic wave scattering by many small perfectly conducting particles of an arbitrary shape

Ramm

2012

Optics Communications

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In this paper the author's invited plenary talk at the 7-th PACOM (PanAfrican Congress of Mathematicians), is presented.Asymptotic solution to many-body wave scattering problem is given in the case of many small scatterers. The small scatterers can be particles whose physical properties are described by the boundary impedances, or they can be small inhomogeneities, whose physical properties are described by their refraction coefficients. Equations for the effective field in the limiting medium are derived. The limit is considered as the size a of the particles or inhomogeneities tends to zero while their number M (a) tends to infinity. These results are applied to the problem of creating materials with a desired refraction coefficient. For example, the refraction coefficient may have wave-focusing property, or it may have negative refraction, i.e., the group velocity may be directed opposite to the phase velocity. This paper is a review of the author's results presented in

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“…We generalize the approach developed in [4], [5], [6], [7]. Earlier works are [1], [10], [11], to mention a few.…”

Section: Introductionmentioning

confidence: 99%

“…Our basic result is a formula for the wave field in the medium in which small particles are embedded. This field solves equation (4)- (6) and satisfies the radiation condition at infinity:…”

Section: Introductionmentioning

confidence: 99%