扭转弹性杆非均匀双螺旋线的形成
Formation of Non-uniform Double Helices for Elastic Rods under Torsion
摘要：
在扭转条件下，纤维自发形成双螺旋是常见的，也是重要的。例如，对DNA超螺旋的研究有助于理解DNA的复制和转录。类似的双螺旋可以出现在聚合物链、碳纳米管纱线、电缆、电话线等中。我们注意到，由于自接触引起的表面摩擦，可以产生不均匀的双螺旋。因此，提出了一个理想的模型来研究双螺旋的形成弹性杆扭矩。利用变分法导出了一个对光滑表面和粗糙表面都适用的一般平衡条件。在此基础上，通过进一步的约束条件，分别对光滑和粗糙表面的情况进行了详细的研究。此外，该模型表明，如何扭曲和松弛杆的具体过程可以确定表面摩擦，从而影响由具有粗糙表面的杆形成的双螺旋的构型。基于这一原理，提出并论证了一种设计构型的双螺旋线加工方法。最后通过实验对模型进行了验证，实验结果与理论分析吻合较好.
英文摘要：
The spontaneous formation of double helices for filaments under torsion is common and significant. For example, the research on the supercoiling of DNA is helpful for understanding the replication and transcription of DNA. Similar double helices can appear in polymer chains, carbon nanotube yarns, cables, telephone wires and so forth. We noticed that non-uniform double helices can be produced due to the surface friction induced by the self-contact. Therefore an ideal model was presented to investigate the formation of double helices for elastic rods under torque. A general equilibrium condition which is valid for both the smooth surface and the rough surface situations is derived by using the variational method. Based on this, by adding further constraints, the smooth and rough surface situations are investigated in detail respectively. Additionally, the model showed that the specific process of how to twist and slack the rod can determine the surface friction and hence influence the configuration of the double helix formed by rods with rough surfaces. Based on this principle, a method of manufacturing double helices with designed configurations was proposed and demonstrated. Finally, experiments were performed to verify the model and the results agreed well with the theory.
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