二维和三维中受拉力的聚合物拉链化有向行走模型的精确解
Exact solutions of directed walk models of polymeric zipping with pulling in two and three dimensions
AI总结：
本研究利用有向格点路径得到二维、三维下聚合物拉链化转变模型的精确解，分析相变配分函数标度，并扩展模型纳入与单体吸引作用竞争的端拉力。
摘要：
我们利用成对的有向格点路径，给出了二维和三维下两类结合聚合物（如DNA/RNA中存在的）拉链化转变的若干简单模型变体的精确解。三维情形下的解以完全椭圆积分的形式表述。我们分析了各模型对应的相变，给出了配分函数的标度关系。我们还对模型进行了扩展，纳入了路径对一端之间的拉力，该拉力与聚合物间的单体-单体吸引相互作用存在竞争关系。
英文摘要：
We provide the exact solution of several variants of simple models of the zipping transition of two bound polymers, such as occurs in DNA/RNA, in two and three dimensions using pairs of directed lattice paths. In three dimensions the solutions are written in terms of complete elliptic integrals. We analyse the phase transition associated with each model giving the scaling of the partition function. We also extend the models to include a pulling force between one end of the pair of paths, which competes with the attractive monomer-monomer interactions between the polymers.
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