28 research outputs found
Scattering of electromagnetic waves by many small perfectly conducting or impedance bodies
A theory of electromagnetic (EM) wave scattering by many small particles of an arbitrary shape is developed. The particles are perfectly conducting or impedance. For a small impedance particle of an arbitrary shape, an explicit analytical formula is derived for the scattering amplitude. The formula holds as a → 0, where a is a characteristic size of the small particle and the wavelength is arbitrary but fixed. The scattering amplitude for a small impedance particle is shown to be proportional to a2−κ, where κ ∈ [0,1) is a parameter which can be chosen by an experimenter
as he/she wants. The boundary impedance of a small particle is assumed to be of the form ζ = ha−κ, where h = const, Reh ≥ 0. The scattering amplitude for a small perfectly conducting particle is proportional to a3, and it is much smaller than that for the small impedance particle. The many-body scattering problem is solved under the physical assumptions a ≪ d ≪ λ, where d is the minimal distance between neighboring particles and λ is the wavelength. The distribution law for the small
impedance particles is N(∆) ∼ 1/a2−κ∆ N(x)dx as a → 0. Here, N(x) ≥ 0 is an
arbitrary continuous function that can be chosen by the experimenter and N(∆)
is the number of particles in an arbitrary sub-domain ∆. It is proved that the EM field in the medium where many small particles, impedance or perfectly conducting, are distributed, has a limit, as a → 0 and a differential equation is derived for the limiting field. On this basis, a recipe is given for creating materials with a desired refraction coefficient by embedding many small impedance particles into a given material. C 2015 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4929965
Charge Fluctuation Forces Between Stiff Polyelectrolytes in Salt Solution: Pairwise Summability Re-examined
We formulate low-frequency charge-fluctuation forces between charged
cylinders - parallel or skewed - in salt solution: forces from dipolar van der
Waals fluctuations and those from the correlated monopolar fluctuations of
mobile ions. At high salt concentrations forces are exponentially screened. In
low-salt solutions dipolar energies go as or ; monopolar
energies vary as or , where is the minimal separation
between cylinders. However, pairwise summability of rod-rod forces is easily
violated in low-salt conditions. Perhaps the most important result is not the
derivation of pair potentials but rather the demonstration that some of these
expressions may not be used for the very problems that originally motivated
their derivation.Comment: 8 pages and 1 fig in ps forma