Distribution of particles creating wave-focusing materials

A.G. Ramm

Mathematics Department, Kansas State University,

Manhattan, KS 66506-2602, USA

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Abstract

A method is given for calculation of a distribution of small (in comparison with the wavelength) acoustically soft particles, embedded in a medium with known properties, so that the resulting new medium would have a desired radiation pattern. The method is based on the author's theory of wave scattering by small particles of arbitrary shapes and on the author's solution of the 3-D inverse scattering problem of non-relativistic quantum mechanics with fixed-energy scattering data. The problem of finding the distribution of small particles in a medium in a bounded region in such a way that for a fixed wavenumber and a fixed direction of the incident wave the resulting medium will have a radiation pattern arbitrarily close to an a priori given function on the unit sphere is posed and solved. It is of practical interest that the relative volume of the embedded particles per unit volume of the original medium is negligible. Therefore the injection of the small particles into the medium can be considered as "dusting". Electromagnetic (EM) wave scattering by many small particles is mentioned.

REFERENCES:

1) A.G.Ramm, Iterative methods for calculating static fields and wave scattering by small bodies, Springer Verlag, New York, 1982.

2) A.G.Ramm, Scattering by obstacles, D.Reidel, Dordrecht, 1986.

3) A.G.Ramm, Equations for the self-consistent field in random medium, Phys.Lett. A, 312, N3-4, (2003), 256-261.

4) A.G.Ramm, Finding small inhomogeneities from surface scattering data, Jour. of Inverse and Ill-Posed Problems, 8, N2, (2000), 205-210.

5) A.G.Ramm, Wave scattering by small bodies of arbitrary shapes, World Sci. Publishers, Singapore, 2005.

6) A.G.Ramm, Inverse problems, Springer, New York, 2005.

7) A.G.Ramm, Distribution of particles which produces a desired radiation pattern, Physica B, (2007) (to appear)

8) A.G.Ramm, Completeness of the set of scattering amplitudes, Phys.Lett. A, 360, (2006), 22-25.

9) A.G.Ramm, Distribution of particles which produces a "smart" material, J. Stat. Phys., (2007) (to appear)

10) A.G.Ramm, Electromagnetic wave scattering by many small particles, Phys. Lett. A360, (2007), 735-741.

11) A.G.Ramm, Many-body wave scattering by small bodies, J. Math. Phys., 48, 1 (2007).

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About the Speaker:

A.G. Ramm

Professor, Mathematics Department,

Kansas State University,

Manhattan, KS 66506-2602,

USA

EDITORIAL WORK:

Associate Editor of the Journals: Math. Inequalities and Applications, Jour. of
Functional Analysis and Approximation

Theory (JFAAT), Advances in Nonlinear Analysis and Applications (ANAA),
PanAmerican Math. Journal,

Math. Sci. Research Journal, Internat. Journ. of Appl. Math., Internat. Journ.
of Diff. Equations and Applications,

Jour. of Inequalities in Pure and Appl. Math. (JIPAM), Nonlinear Functional
Analysis and Applications

(NFAA), Cubo a Math. Journal, Australian Jour. of Math Anal and Appl (AJMAA),
Intern. J. Comp. Sci and

Math (IJCSM), Journ. of Egypt. Math. Soc., Jour. of Inverse and Ill-Posed Probl.

Editor: Intern. J. of Appl. Math. Sci., International J. of Tomography and
Statistics.

HONORARY AND PROFESSIONAL SOCIETIES:

New York Academy of Science, Electromagnetic Academy MIT, International Society
for Analysis, Applications and

Computing, American Mathematical Society, International Assoc. of Math. Physics.

MONOGRAPHS and BOOKS:

1. Theory and applications of some new classes of integral equations. Springer
Verlag, New York, 1980, pp.1-356;

isbn 0-387-90540-5.

2. Iterative methods for calculating the static fields and wave scattering by
small bodies. Springer Verlag, New York,

1982, pp.1-130;

isbn 0-387-90682-7

3. Scattering by obstacles. Reidel, Dordrecht, 1986, pp.1-442;

isbn 90-277-2103-3

4. Random fields estimation theory. Longman Scientific & Wiley, New York,
1990, pp.1-281;

isbn 0-582-03768-9

5. Random fields estimation theory, Expanded Russian edition, Mir, Moscow, 1996,
pp. 1-352;

isbn 5-03-003031-X

6. Multidimensional inverse scattering problems, Longman Scientific & Wiley,
New York. 1992, pp.1-385;

isbn 0-582-05665-9;

7. Multidimensional inverse scattering problems, Expanded Russian edition, Mir,
Moscow, 1994,pp.1-496;

isbn 5-03-002939-7

8. The Radon transform and local tomography. CRC Press, Boca Raton, 1996,
pp.1-503 (with A.Katsevich);

isbn 0-8493-9492-9.

9. Spectral and scattering theory, Plenum publishers, New York, 1998 (editor
A.G. Ramm)

isbn 0-306-45829-2

10. Inverse problems, tomography and image processing, Plenum publishers, New
York, 1998 (editor A.G. Ramm)

isbn 0-306-45828-4

11. Operator Theory and Applications, Amer. Math. Soc., Fields Institute
Communications, Providence RI, 2000

(editors A.G.Ramm, P.N.Shivakumar, A.V.Strauss).

isbn 0-8218-1990-9

12. Inverse problems, Springer, New York, 2005. isbn 0-387-23195-1

13. Wave scattering by small bodies of arbitrary shapes, World Sci. Publishers,
Singapore, 2005.

isbn 981-256-186-2

14. Random fields estimation, World Sci. Publishers, Singapore, 2005.

isbn 981-256-536-1

15. Dynamical Systems Method for solving operator equations, Elsevier,
Amsterdam, 2006.

isbn 0-444-52795-8

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