单边布朗初速度的弹道集结
Ballistic aggregation for one-sided Brownian initial velocity
摘要：
我们研究了一维弹道聚集过程在连续极限下的单边布朗初速度（即粒子在碰撞时合并并在碰撞之间自由运动，在连续极限下右侧的初速度是从原点$x=0$开始的布朗运动）.我们考虑左侧在$t=0$处于静止或空的情况。我们推导出显式表达式的速度分布和平均密度和电流剖面由这个平衡系统。我们发现，在右侧的平均密度保持不变，而平均电流是均匀的，并随时间线性增长。所有的量在最左边都显示出指数衰减。我们还获得了向左移动的最左边的集群的属性。我们发现，在这两种情况下，相关的长度和质量的规模为$t^2$和演化是自相似的。
英文摘要：
We study the one-dimensional ballistic aggregation process in the continuum limit for one-sided Brownian initial velocity (i.e. particles merge when they collide and move freely between collisions, and in the continuum limit the initial velocity on the right side is a Brownian motion that starts from the origin $x=0$). We consider the cases where the left side is either at rest or empty at $t=0$. We derive explicit expressions for the velocity distribution and the mean density and current profiles built by this out-of-equilibrium system. We find that on the right side the mean density remains constant whereas the mean current is uniform and grows linearly with time. All quantities show an exponential decay on the far left. We also obtain the properties of the leftmost cluster that travels towards the left. We find that in both cases relevant lengths and masses scale as $t^2$ and the evolution is self-similar.
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