论文标题
通过蒸发和从间隔重置控制粒子电流
Controlling particle currents with evaporation and resetting from an interval
论文作者
论文摘要
我们研究了一个空间维度中颗粒的布朗扩散，并在存在有限区域的情况下，在该区域中颗粒可以蒸发或重置为给定位置。对于开放的边界条件，我们强调了布朗尼但非高斯扩散的外观：长期以来，粒子分布是非高斯，但其方差随着时间的及时线性增长。此外，我们表明，这种系统中颗粒的有效扩散系数从下面的$（1-2/π）$倍$倍其裸露的扩散系数限制。对于周期性的边界条件，即，对于重置的环上的扩散，我们证明了空间粒子分布的“规格不变性”，以在固定和非平稳状态下，以不同的选择重置概率电流。最后，我们将发现应用于转录暂停过程中RNA聚合酶运动的随机生物物理模型，从分析得出裂解的RNA转录物长度的分布以及RNA裂解在回本恢复中的效率。
We investigate the Brownian diffusion of particles in one spatial dimension and in the presence of finite regions within which particles can either evaporate or be reset to a given location. For open boundary conditions, we highlight the appearance of a Brownian yet non-Gaussian diffusion: at long times, the particle distribution is non-Gaussian but its variance grows linearly in time. Moreover, we show that the effective diffusion coefficient of the particles in such systems is bounded from below by $(1-2/π)$ times their bare diffusion coefficient. For periodic boundary conditions, i.e., for diffusion on a ring with resetting, we demonstrate a "gauge invariance" of the spatial particle distribution for different choices of the resetting probability currents, in both stationary and non-stationary regimes. Finally, we apply our findings to a stochastic biophysical model for the motion of RNA polymerases during transcriptional pauses, deriving analytically the distribution of the length of cleaved RNA transcripts and the efficiency of RNA cleavage in backtrack recovery.
