平面情况下闭合双链DNA总能量的一阶和二阶变分
The First and Second Variation of the Total Energy of Closed Duplex DNA in Planar Case
摘要：
DNA的形状主要取决于它的总能量$F$。用经典的变分法：取第一能量变分$δ^{(1)}F=0$，得到相应的平衡形状方程。这里我们不仅给出了平面情形下的第一种变式$δ^{(1)}F$，而且给出了第二种变式$δ^{(2)}F$。同时，得到了DNA的一般形状方程，纠正了[Zhang，\emph{et al} . { \it Phys. Rev. E} { \bf 70} 051902（2004）]中指出。
英文摘要：
DNA's shape mostly lies on its total energy $F$. Its corresponding equilibrium shape equations can be got by classical variation method: letting the first energy variation $δ^{(1)}F=0$. Here we not only provide the first variation $δ^{(1)}F$ but also give the second variation $δ^{(2)}F$ in planar case. Moreover, the general shape equations of DNA are obtained and a mistake in [Zhang, \emph{et al}. {\it Phys. Rev. E} {\bf 70} 051902 (2004)] is pointed out.
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