非均匀杆的圆平衡解和螺旋平衡解
Circular and helical equilibrium solutions of inhomogeneous rods
摘要：
真正的细丝并不是完全均匀的。它们大多数具有不同的材料组成和形状，使得它们的刚度沿弧长不是恒定的。在Kirchhoff模型的框架内，我们研究了具有不同弯曲和扭转刚度的固有直杆的圆形和螺旋形平衡解的存在性。平面环平衡解只存在于具有给定形式的弯曲刚度变化的杆中。我们表明，众所周知的圆形螺旋线是不是一个平衡的解决方案的静态基尔霍夫方程组的杆与非常数弯曲刚度。我们的研究结果可以解释在浸入含Zn^{2+}溶液中的小的封闭DNA以及包裹在核小体周围的DNA中所观察到的曲率变化。
英文摘要：
Real filaments are not perfectly homogeneous. Most of them have various materials composition and shapes making their stiffnesses not constant along the arclength. We investigate the existence of circular and helical equilibrium solutions of an intrinsically straight rod with varying bending and twisting stiffnesses, within the framework of the Kirchhoff model. The planar ring equilibrium solution only exists for a rod with a given form of variation of the bending stiffness. We show that the well known circular helix is not an equilibrium solution of the static Kirchhoff equations for a rod with non constant bending stiffness. Our results may provide an explanation for the variation of the curvature seen in small closed DNAs immersed in a solution containing Zn^{2+}, and in the DNA wrapped around a nucleosome.
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