摘要翻译：
我们考虑一个由大量小球形颗粒组成的三维系统，这些颗粒分布在一定的大小和高度范围内（在水平方向上分布均匀）。粒子以与尺寸有关的终速垂直运动。它们要么被允许在交叉时合并，要么有一个大小比标准来考虑碰撞效率。在平均场近似下，这种系统可以用带有微分沉降核的Smoluchowski动力学方程来描述，该方程用于研究例如雨的形成和大气中的粒子分布。我们借用弱湍流理论的方法，对动力学方程进行解析求解，得到稳态解和在时间和高度上的自相似解。将解析结果与直接数值模拟(DNS)进行了比较，得到了很好的一致性。
---
英文标题：
《Coalescence of particles by differential sedimentation》
---
作者：
P. Horvai, S. V. Nazarenko, T. H. M. Stein (University of Warwick)
---
最新提交年份：
2007
---
分类信息：

一级分类：Physics        物理学
二级分类：Statistical Mechanics        统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
--

---
英文摘要：
  We consider a three dimensional system consisting of a large number of small spherical particles, distributed in a range of sizes and heights (with uniform distribution in the horizontal direction). Particles move vertically at a size-dependent terminal velocity. They are either allowed to merge whenever they cross or there is a size ratio criterion enforced to account for collision efficiency. Such a system may be described, in mean field approximation, by the Smoluchowski kinetic equation with a differential sedimentation kernel, used to study e.g. rain initiation and particle distributions in the atmosphere. We solve the kinetic equation analytically to obtain steady state and self-similar solutions in time and in height, using methods borrowed from weak turbulence theory. Analytical results are compared with direct numerical simulations (DNS) of moving and merging particles, and a good agreement is found.
---
PDF链接：
https://arxiv.org/pdf/705.2618