论文标题
圆盘周围分形聚合物的拉伸揭示了类似KPZ的统计数据
Stretching of a fractal polymer around a disc reveals KPZ-like statistics
论文作者
论文摘要
虽然聚合物沿平坦表面的拉伸与在自由空间中拉链末端的经典圆锥形问题没有什么不同，但弯曲几何形状在拉伸链的构象统计中的作用是一个令人兴奋的开放问题。在这里，通过缩放分析和计算机模拟，我们检查了在2D（或3D中的圆柱体）半径$ r $的圆盘周围的分形聚合物链的拉伸。令人惊讶的是，我们揭示了聚合物的典型偏移远离表面尺度为$δ\ sim r^β$，而Kardar-Parisi-Zhang（kpz）生长指数$β= 1/3 $，对于链的任何分形维度。此外，我们发现分形链的曲率诱导的相关长度与$ s^* \ sim r^{1/z} $与kpz动态指数$ z = 3/2 $的相关性，这表明从平坦到弯曲聚合物的弯曲几何形状的跨界几何相对于从大型时代到kp kp kp zp kp s s oftractic controvent的弯曲几何形状对应。因此，我们认为，潜在边界的曲率为拉伸的分形路径提供了通用的KPZ样统计量，这进一步提出了与数学物理的多个分支的许多联系。
While stretching of a polymer along a flat surface is hardly different from the classical Pincus problem of pulling chain ends in free space, the role of curved geometry in conformational statistics of the stretched chain is an exciting open question. Here by means of the scaling analyses and computer simulations we examine stretching of a fractal polymer chain around a disc in 2D (or a cylinder in 3D) of radius $R$. Surprisingly, we reveal that the typical excursions of the polymer away from the surface scale as $Δ\sim R^β$, with the Kardar-Parisi-Zhang (KPZ) growth exponent $β=1/3$, for any fractal dimension of the chain. Moreover, we find that the curvature-induced correlation length of a fractal chain behaves as $S^* \sim R^{1/z}$ with the KPZ dynamic exponent $z=3/2$, suggesting that the crossover from flat to curved geometry of a stretched polymer corresponds to the crossover from large to short time scales in the KPZ stochastic growth. Thus, we argue that curvature of an underlying boundary furnishes universal KPZ-like statistics to the stretched fractal paths, which further suggests numerous connections with several branches of mathematical physics.
