论文标题
避免自我避免步行的流体动力半径的高精度估计值
High-precision estimate of the hydrodynamic radius for self-avoiding walks
论文作者
论文摘要
高分辨率的蒙特卡洛模拟估算了回转半径与自避免步道的流体动力学半径之间的通用渐近幅度比。通过研究最大长度的链条= 2^{25} \大约34 \ times 10^6 $单体，我们发现该比率为$ r _ {\ Mathrm {g}}/r _ {\ Mathrm {\ Mathrm {\ Mathrm {h}} = 1.5803940（45）$，以前的几个列表，该列表的元素是元素的，该列表的数量是元素的。这是通过相当一般的采样方案来促进的，该方案可以有效地估算大型可观察物的平均值。显然可以辨别出流体动力半径的比例缩放的竞争校正。我们还发现了测量链维数的其他通用性能的改进估计。特别是，一种消除了对缩放缩放的主要校正的分析方法，导致对$ν= 0.58759700（40）$的弗洛里指数的高度准确估计。
The universal asymptotic amplitude ratio between the gyration radius and the hydrodynamic radius of self-avoiding walks is estimated by high-resolution Monte Carlo simulations. By studying chains of length of up to $N = 2^{25} \approx 34 \times 10^6$ monomers, we find that the ratio takes the value $R_{\mathrm{G}}/R_{\mathrm{H}} = 1.5803940(45)$, which is several orders of magnitude more accurate than the previous state of the art. This is facilitated by a sampling scheme which is quite general, and which allows for the efficient estimation of averages of a large class of observables. The competing corrections to scaling for the hydrodynamic radius are clearly discernible. We also find improved estimates for other universal properties that measure the chain dimension. In particular, a method of analysis which eliminates the leading correction to scaling results in a highly accurate estimate for the Flory exponent of $ν= 0.58759700(40)$.
