Abstract
Transformation from the three-dimensional hypercomplex X(x,y,z) frame to another which has infinite dimensions but has the symmetry properties of an array built in allows the Laplace equation to be solved in structures for which it is nonseparable. The power and practicality of this technique is demonstrated on pairs and chains of spheres of arbitrary complex permittivity in a quasiconstant electric field. New results include strong absorption enhancement at long wavelengths in high density chains due to structurally induced resonances.
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