Pattern synthesis from singular solutions in the Debye limit: helical waves and twisted toroidal scroll structures

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Abstract
Applying the Debye limit to a suitable superposition of singular solutions of the linear two-component reaction-diffusion equations in three dimensions leads to helical and twisted toroidal scroll waves of constant concentration. An integral representation of the solutions of the Helmholtz equation in toroidal coordinates establishes a connection between helical and toroidal waves.