Abstract

The analytical equation of the non-circular elastic rod governed by the low-dimensional and single-variable system was obtained. We reconstructed the Kirchhoff equations with a group of complex vectors and then introduced a novel complex variable solution of the torque. The knowledge of effective bending rigidity was further extended to fit the characteristic of non-circular cross section with periodically varying bending coefficients embodied in the sequence-dependent effects of a DNA molecule. The resulting low-dimensional systems were closely fit for the analytical analysis, so that the numerical simulation turned out to be not an exclusive approach during the analysis of the non-circular cross section Kirchhoff model, such as deriving the asymptotic solutions and microscopic topology of the spatial configuration.

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