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Computer Methods for Field Intensity Predictions
Published in Charles Polk, Elliot Postow, CRC Handbook of Biological Effects of Electromagnetic Fields, 2019
An alternate surface integral equation method for computing the distribution of absorbed electromagnetic energy in realistic models of biological body is the extended boundary condition method.55 This method employs analytic continuation, spherical harmonics, and the equivalence theorem to calculate fields inside the body. Specifically, the fields induced inside the body are replaced by equivalent surface currents. These surface currents are such that they reduce the total fields inside the body to zero. Thus, upon applying the boundary conditions at the surface of the body, an integral equation results which relates the incident field to the surface currents. This equation is then cast in a form suitable for numerical computation by expansion of the various field quantities in vector spherical harmonics.56 It should be noted that the expansion coefficients for the incident field are known; only the coefficients for the surface currents need to be determined. This is accomplished by applying the orthogonality properties of the vector spherical harmonics, giving rise to a set of simultaneous equations that can be solved for the unknown coefficients. The induced fields are then determined in terms of the surface currents through the equivalence theorem.
Enhanced survival fractions of UV-irradiated spores in clusters on a surface in air: Measured and mathematically modeled results at 254-nm
Published in Aerosol Science and Technology, 2023
Steven C. Hill, David C. Doughty, Daniel W. Mackowski, Vipin Rastogi, Jay D. Eversole, Dan McGrady, Frank Handler, Jana Kesavan
In the MSTM (Mackowski and Mishchenko 1996; Mackowski 2008) the electromagnetic fields within each sphere are expressed as a sum of vector spherical harmonics (solutions to Maxell’s equations in spherical coordinates) with unknown coefficients. The fields within the homogeneous planar region are expanded as an angular spectrum of plane waves with unknown coefficients. The spheres and planar region are illuminated by a UV plane wave, which is expressed as a sum of vector spherical harmonics with known coefficients. The unknown coefficients are obtained by enforcing the EM boundary conditions at each interface to obtain a series of equations which are then solved for the unknown coefficients. The method is exact in principle. However, because of computational issues (e.g., finite precision computers, non-convergence issues), no surface can intersect any other surface (other spheres or a planar surface). To avoid computational issues in the work presented here, especially for the larger clusters near the planar surface, typically the surface of no sphere is positioned closer to the planar surface than about 0.1 µm.
Electrodynamic multiple-scattering method for the simulation of optical trapping atop periodic metamaterials
Published in Journal of Modern Optics, 2018
Vassilios Yannopapas, Emmanuel Paspalakis
where () are coefficients to be determined. are the so-called vector spherical harmonics [46] and may be any linear combination of the spherical Bessel function, , and the spherical Hankel function, . The corresponding magnetic induction, , can be readily obtained from using Maxwell’s equations,