The Mean First Rotation Time of a Planar Polymer
The Mean First Rotation Time of a Planar Polymer
复制标题
平面聚合物的平均首次旋转时间
DOI：
10.1007/s10955-011-0227-6
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发表时间：
2011
影响因子：
1.6
通讯作者：
D. Holcman
中科院分区：
文献类型：
--
作者：
Stavros Vakeroudis;M. Yor;D. Holcman
我们估计的平均第一次，称为平均旋转时间（MRT），平面随机聚合物绕一个点。该聚合物被建模为n个杆的集合，其中每个杆由布朗角参数化。我们被引导去研究i.i.d.的总和。以一维布朗运动为自变量的虚指数。我们发现，自由端的聚合物满足一个新的随机方程的非线性时间函数。最后，我们得到了一个渐近公式的MRT，其领导阶项依赖于$\sqrt{n}$，有趣的是，弱依赖于平均初始配置。我们的分析结果证实了布朗模拟。
We estimate the mean first time, called the mean rotation time (MRT), for a planar random polymer to wind around a point. This polymer is modeled as a collection of n rods, each of them being parameterized by a Brownian angle. We are led to study the sum of i.i.d. imaginary exponentials with one dimensional Brownian motions as arguments. We find that the free end of the polymer satisfies a novel stochastic equation with a nonlinear time function. Finally, we obtain an asymptotic formula for the MRT, whose leading order term depends on $\sqrt{n}$ and, interestingly, depends weakly on the mean initial configuration. Our analytical results are confirmed by Brownian simulations.