论文标题
与最近邻居相互作用的布朗颗粒链的通用断裂定律
Universal break law for chains of Brownian particles with nearest neighbour interaction
论文作者
论文摘要
我们研究了有限的布朗颗粒链的行为，通过成对的潜在$ u $相互作用，链的一端固定，另一端被拉开，以缓慢的拉力速度和小的布朗尼噪声的极限。我们研究链条“断裂”的瞬间和位置，即两个相邻粒子之间的距离大于一定阈值。我们假设$ u $具有吸引力，并且严格传达到休息距离，而连续三倍。我们考虑了这种制度，其中拉力和噪声都显着影响休息时间和断裂位置的分布。事实证明，在这个制度中，有限制数量不取决于$ u $的细节，而仅在休息距离处的曲率。
We investigate the behaviour of a finite chain of Brownian particles, interacting through a pairwise potential $U$, with one end of the chain fixed and the other end pulled away, in the limit of slow pulling speed and small Brownian noise. We study the instant when and the place where the chain "breaks", that is, the distance between two neighbouring particles becomes larger than a certain threshold. We assume $U$ to be attractive and strictly convex up to the break distance, and three times continuously differentiable. We consider the regime, where both the pulling and the noise significantly influence the distribution of the break time and break position. It turns out that in this regime there is a universality of both the break time distribution and the break position distribution, in the sense that the limiting quantities do not depend on the details of $U$, but only on its curvature at the break distance.
