Wave scattering by small particles in a medium

Journal of Mathematical Physics

2007

125

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.

“…It is sufficient to prove that the homogeneous problem 15) has only the trivial solution if conditions (1.14) hold. Taking complex conjugate of (3.13) -(3.15) one gets: …”

Section: Proof Of Lemma 2 Let Us Start With the Equationmentioning

confidence: 99%

Many-body wave scattering by small bodies and applications

Journal of Mathematical Physics

2007

125

“…[8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23] Our presentation and some of the results are novel. These results and methods of their derivation differ much from those in the homogenization theory.…”

Section: In This Case the Scattering Is Also Isotropic And Of The Ormentioning

confidence: 93%

Scattering of scalar waves by many small particles

2011

AIP Advances

Formulas are derived for solutions of many-body wave scattering problems by small particles in the case of acoustically soft, hard, and impedance particles embedded in an inhomogeneous medium. The limiting case is considered, when the size a of small particles tends to zero while their number tends to infinity at a suitable rate. Equations for the limiting effective (self-consistent) field in the medium are derived.

“…where q(x) is defined by formula (13). Applying the operator ∇ 2 + k 2 to (17), one verifies that the function u e (x) solves problem (5)- (6).…”

Section: Problem Rcmentioning

confidence: 96%

Scattering by many small inhomogeneities and applications

2011

Chaos Theory

Many-body quantum-mechanical scattering problem is solved asymptotically when the size of the scatterers (inhomogeneities) tends to zero and their number tends to infinity.A method is given for calculation of the number of small inhomogeneities per unit volume and their intensities such that embedding of these inhomogeneities in a bounded region results in creating a new system, described by a desired potential. The governing equation for this system is a non-relativistic Schrödinger's equation described by a desired potential. Similar ideas were developed by the author for acoustic and electromagnetic (EM) wave scattering problems.