Resonant helical deformations in nonhomogeneous Kirchhoff filaments

We study the three-dimensional static configurations of nonhomogeneous Kirchhoff filaments with periodically varying Young's modulus. We analyze the effects of the Young's modulus frequency and amplitude of variation in terms of stroboscopic maps, and in the regular (non chaotic) spatial configurations of the filaments. Our analysis shows that the tridimensional conformations of long filaments may depend critically on the Young's modulus frequency in case of resonance with other natural frequencies of the filament. As expected, far from resonance the shape of the solutions remain very close to that of the homogeneous case. In the case of biomolecules, although various other elements, besides sequence-dependent effects, combine to determine their conformation, our results show that sequence-dependent effects alone may have a significant influence on the shape of these molecules, including DNA.