Abstract

In relation to the problem of accumulation of dust particles, which are the main structure-forming element of planetesimals in a protoplanetary cloud, we propose a parametric method of moments for solving the Smoluchowski integro-differential equation that describes dispersed coagulation of disk matter. We consider a parametric approach to finding the size distribution function of protoplanetary bodies based on the Pearson diagram, with the aid of which the corresponding distributions are quite satisfactorily found by their first four moments. This approach is especially effective when it is necessary to know only the general properties of the volume distribution functions of coagulating bodies and their temporal evolution. Since the kinetics of the processes of aggregation of protoplanetary bodies substantially depends on the specific type of coagulation kernels, a fairly general method for their approximation is proposed in the study, which allows one to obtain simplified expressions. As a practical application, the parametric method of moments is demonstrated by a number of examples of the growth of protoplanetary bodies. The results provide a new productive approach to solving the key problem of stellar-planetary cosmogony associated with an explanation of the process of growth of interstellar dust particles to large planetesimals.

中文翻译：

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行星尘埃堆积理论中求解Smoluchowski凝聚方程的参数矩法。

摘要

关于粉尘颗粒的堆积问题，粉尘颗粒是原行星云中小行星的主要结构形成元素，我们提出了一种矩量参数方法，用于求解描述圆盘物质分散凝结的Smoluchowski积分微分方程。我们考虑一种基于皮尔森图的参数方法来寻找原行星体的尺寸分布函数，借助该方法，在前四个时刻就可以令人满意地找到相应的分布。当仅需要了解凝血体的体积分布函数的一般属性及其时间演变时，此方法特别有效。由于原行星体聚集过程的动力学基本取决于凝结颗粒的具体类型，因此在研究中提出了一种近似的近似方法，可以简化表达式。作为实际应用，力矩的参数化方法通过原行星体生长的许多例子得到了证明。研究结果提供了一种新的生产方法，可以解决恒星-行星世界的关键问题，该问题与星际尘埃颗粒向大行星的增长过程有关。参数矩量方法由原行星生长的许多例子证明。研究结果提供了一种新的生产方法，可以解决恒星-行星世界的关键问题，该问题与星际尘埃颗粒向大行星的增长过程有关。参数矩量方法由原行星生长的许多例子证明。研究结果提供了一种新的生产方法，可以解决恒星-行星世界的关键问题，该问题与星际尘埃颗粒向大行星的增长过程有关。