多个自回避链的有限空间和有效相互作用
Confined space and effective interactions of multiple self-avoiding chains
摘要：
我们研究了三种不同的情况下，自避免聚合物之间的联系：强烈重叠的多个链在稀溶液中，链下的球形限制，和发病的半稀溶液。我们的主要结果是，重叠的$n$链的自由能是链长的\emph{independent}，并以$n^{9/4}$为尺度，随着$n$的增加，慢慢地过渡到$n^3$。对于强约束的聚合物内的球形腔，我们表明，重新安排链不需要额外的自由能。我们的研究结果表明，在细胞周期中，真核细胞染色体的\emph{global}重组在一个大的细胞核可以很容易地实现。
英文摘要：
We study the link between three seeming-disparate cases of self-avoiding polymers: strongly overlapping multiple chains in dilute solution, chains under spherical confinement, and the onset of semi-dilute solutions. Our main result is that the free energy for overlapping $n$ chains is \emph{independent} of chain length and scales as $n^{9/4}$, slowly crossing over to $n^3$, as $n$ increases. For strongly confined polymers inside a spherical cavity, we show that rearranging the chains does not cost an additional free energy. Our results imply that, during cell cycle, \emph{global} reorganization of eukaryotic chromosomes in a large cell nucleus could be readily achieved.
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