Numerical solution of many-body wave scattering problem for small particles and creating materials with desired refraction coefficient

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dc.contributor.author Andriychuk, M. I.
dc.contributor.author Ramm, Alexander G.
dc.contributor.editor Awrejcewicz, Jan
dc.date.accessioned 2012-08-07T13:58:27Z
dc.date.available 2012-08-07T13:58:27Z
dc.date.issued 2011-09-26
dc.identifier.uri http://hdl.handle.net/2097/14130
dc.description.abstract Theory of wave scattering by small particles of arbitrary shapes was developed by A. G. Ramm in papers (Ramm, 2005; 2007;a;b; 2008;a; 2009; 2010;a;b) for acoustic and electromagnetic (EM) waves. He derived analytical formulas for the S-matrix for wave scattering by a small body of arbitrary shape, and developed an approach for creating materials with a desired spatial dispersion. One can create a desired refraction coefficient n 2 (x, ω) with a desired x, ω-dependence, where ω is the wave frequency. In particular, one can create materials with negative refraction, i.e., material in which phase velocity is directed opposite to the group velocity. Such materials are of interest in applications, see, e.g., (Hansen, 2008; von Rhein et al., 2007). The theory, described in this Chapter, can be used in many practical problems. Some results on EM wave scattering problems one can find in (Tatseiba & Matsuoka, 2005), where random distribution of particles was considered. A number of numerical methods for light scattering are presented in (Barber & Hill, 1990). An asymptotically exact solution of the many body acoustic wave scattering problem was developed in (Ramm, 2007) under the assumptions ka << 1, d = O(a 1/3), M = O(1/a), where a is the characteristic size of the particles, k = 2π/λ is the wave number, d is the distance between neighboring particles, and M is the total number of the particles embedded in a bounded domain D ⊂ R 3 . It was not assumed in (Ramm, 2007) that the particles were distributed uniformly in the space, or that there was any periodic structure in their distribution. In this Chapter, a uniform distribution of particles in D for the computational modeling is assumed (see Figure 1). An impedance boundary condition on the boundary Sm of the m-th particle Dm was assumed, 1 ≤ m ≤ M. In (Ramm, 2008a) the above assumptions were generalized as follows:
dc.publisher InTech en_US
dc.relation.uri https://doi.org/10.5772/24495 en_US
dc.rights This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).
dc.rights.uri http://rightsstatements.org/vocab/InC/1.0/
dc.subject Many-body wave scattering en_US
dc.subject Small particles en_US
dc.subject Refraction coefficient en_US
dc.subject Numerical solution en_US
dc.title Numerical solution of many-body wave scattering problem for small particles and creating materials with desired refraction coefficient en_US
dc.type Book chapter (publisher version) en_US
dc.date.published 2011 en_US
dc.citation.doi 10.5772/24495
dc.citation.epage 28 en_US
dc.citation.isbn 978-953-307-620-1 en_US
dc.citation.spage 1 en_US
dc.citation.btitle Numerical Simulations of Physical and Engineering Processes en_US
dc.contributor.authoreid ramm en_US


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