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首页> 外文期刊>Proceedings of the National Academy of Sciences of the United States of America >Helices
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Helices

机译：螺旋

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摘要

Helices are among the simplest shapes that are observed in the filamentary and molecular structures of nature. The local mechanical properties of such structures are often modeled by a uniform elastic potential energy dependent on bending and twist, which is what we term a rod model. Our first result is to complete the semi-inverse classification, initiated by Kirchhoff, of all infinite, helical equilibria of inextensible, unshearable uniform rods with elastic energies that are a general quadratic function of the flexures and twist. Specifically, we demonstrate that all uniform helical equilibria can be found by means of an explicit planar construction in terms of the intersections of certain circles and hyperbolas. Second, we demonstrate that the same helical center-lines persist as equilibria in the presence of realistic distributed forces modeling nonlocal interactions as those that arise, for example, for charged linear molecules and for filaments of finite thickness exhibiting self-contact. Third, in the absence of any external loading, we demonstrate how to construct explicitly two helical equilibria, precisely one of each handedness, that are the only local energy minimizers subject to a nonconvex constraint of self-avoidance.
机译：螺旋是在自然的丝状和分子结构中观察到的最简单的形状之一。此类结构的局部机械性能通常通过取决于弯曲和扭曲的均匀弹性势能来建模，这就是我们所说的杆模型。我们的第一个结果是完成基尔霍夫（Kirchhoff）发起的所有具有弹性能量的，不可伸展，不可剪切的均匀杆的所有无限螺旋螺旋平衡的半逆分类，弯曲和扭曲通常是二次函数。具体来说，我们证明了可以通过某些圆与双曲线的交点的显式平面构造来找到所有均匀的螺旋平衡。其次，我们证明，在模拟非局部相互作用的现实分布力的存在下，相同的螺旋中心线仍然保持平衡，例如，对于带电荷的线性分子和有限厚度的细丝，它们表现出自接触。第三，在没有任何外部载荷的情况下，我们演示了如何显式构造两个螺旋平衡，即每个惯用力之一，这是唯一受非回避自约束非局部约束的局部能量最小化器。

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