具有扩散边界的布朗运动的分裂概率：在聚合物易位中的应用
Splitting probabilities for Brownian motion with diffusing boundaries: Application to polymer translocation
AI总结：
本研究针对两端聚合-解聚导致链长随机波动的聚合物纳米孔易位过程，通过映射为含扩散汇的布朗运动模型，精确计算了分裂概率、易位时间与链长分布，验证了幂律尾部特性，还给出分数布朗运动下的数值结果。
AI中文摘要：
我们研究了聚合物链通过纳米孔的易位过程，其中链长由于链两端的聚合-解聚过程而随机波动。我们将该过程映射为等效表示：在纳米孔两侧存在两个扩散汇（扩散常数分别为$D_1$和$D_3$）的情况下，纳米孔在一条线上执行类似随机游走的随机过程；当纳米孔击中两侧任一扩散汇时，易位过程终止。在纳米孔自身为扩散运动（扩散常数为$D_2$）的情况下，我们精确计算了纳米孔击中左侧（右侧）汇先于击中右侧（左侧）汇的分裂概率。我们表明，与固定汇的经典情况（对应链长固定的情况）相比，存在移动汇时的分裂概率相当复杂。此外，我们还精确计算了易位时间的概率分布，以及易位完成时链长的概率分布，结果显示两种分布均具有幂律尾部，其指数连续依赖于扩散常数$D_1$、$D_2$和$D_3$。我们通过数值模拟验证了这些分析预测，随后给出了当纳米孔执行具有Hurst指数$0<H<1$的分数布朗运动、而汇仍为扩散运动时的数值结果。
英文摘要：
We study the translocation of a polymer chain through a nanopore where the chain length fluctuates stochastically due to the polymerization-depolymerization processes at the chain ends. We map this process to an equivalent representation where the pore performs a stochastic random-walk-like process on a line in the presence of two diffusing sinks on either side of it with diffusion constants $D_1$ and $D_3$ respectively. The translocation process terminates when the pore hits either of the two outer diffusing sinks. In the case where the pore motion itself is diffusive with diffusion constant $D_2$, we compute exactly the splitting probability that the pore hits the left (right) sink before hitting the right (left) sink. We show that the splitting probability in the presence of mobile sinks is rather nontrivial compared to the classical case of immobile sinks (the latter corresponds to the case when the chain length is fixed). Furthermore, we also compute exactly the probability distribution of the translocation time and that of the chain length at the completion time of the translocation. We show that both distributions have power law tails with exponents that depend continuously on the diffusion constants $D_1$, $D_2$ and $D_3$. We validate our analytical predictions via numerical simulations. We then present numerical results for the case when the pore performs a fractional Brownian motion with Hurst exponent $0<H<1$, while the sinks are still diffusive.
