一个代表性的颗粒方法凝聚和破碎的灰尘聚集体和液滴
A representative particle approach to coagulation and fragmentation of dust aggregates and fluid droplets
摘要：
内容：越来越需要好的算法来模拟各种天体物理环境中固体颗粒（尘埃颗粒、尘埃聚集体、巨石）的聚集和碎裂，包括原行星盘、行星和亚恒星大气以及致密分子云核。在这里，我们描述了一个新的算法，结合了各种标准方法的优点。目的：目的是开发一种方法，1）可以解决聚集和破碎，2）可以很容易地包括颗粒性质的影响和演变，如致密性，成分等，以及3）可以作为凝结/破碎模块构建到流体动力学模拟中。方法：我们开发了一种Monte-Carlo方法，其中我们遵循有限数量的代表性粒子的“生命”。这些粒子中的每一个都与总尘埃质量的某一部分有关，因此代表了大量的真实粒子，这些粒子都被假定具有与其代表粒子相同的性质。在真实粒子的总数大大超过代表粒子的数目的假设下，一个代表粒子与另一个代表粒子碰撞的机会小得可以忽略，因此我们忽略了这种可能性。现在，这使得有可能采用统计方法来研究代表性粒子的演化。结果如下：该方法再现了已知的简化凝聚核的解析解，并与其他方法对布朗运动的数值结果进行了比较。对于行为良好的内核，即使对于中等数量的群，它也会产生良好的结果。
英文摘要：
Context: There is increasing need for good algorithms for modeling the aggregation and fragmentation of solid particles (dust grains, dust aggregates, boulders) in various astrophysical settings, including protoplanetary disks, planetary- and sub-stellar atmospheres and dense molecular cloud cores. Here we describe a new algorithm that combines advantages of various standard methods into one. Aims: The aim is to develop a method that 1) can solve for aggregation and fragmentation, 2) can easily include the effect and evolution of grain properties such as compactness, composition, etc., and 3) can be built as a coagulation/fragmentation module into a hydrodynamics simulations. Methods: We develop a Monte-Carlo method in which we follow the 'life' of a limited number of representative particles. Each of these particles is associated with a certain fraction of the total dust mass and thereby represents a large number of true particles which all are assumed to have the same properties as their representative particle. Under the assumption that the total number of true particles vastly exceeds the number of representative particles, the chance of a representative particle colliding with another representative particle is negligibly small, and we therefore ignore this possibility. This now makes it possible to employ a statistical approach to the evolution of the representative particles. Results: The method reproduces the known analytic solutions of simplified coagulation kernels, and compares well to numerical results for Brownian motion using other methods. For reasonably well-behaved kernels it produces good results even for moderate number of swarms.
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