不可逆聚集动力学标度理论的严格结果
Rigorous results in the scaling theory of irreversible aggregation kinetics
摘要：
简要回顾了描述不可逆聚集的动力学方程和在大尺度和大时间范围内描述不可逆聚集的标度方法。接下来，考虑一个系统，其中聚集体只能与其自身大小的聚集体反应。然后，在系统总质量守恒的情况下，可以严格地证明动力学方程的标度解的存在性。大量的详细性质的解决方案，以前预测的定性参数，可以严格显示，以及在这个系统。在凝胶化发生的情况下，一些粗略的严格的结果，并提出了一个缩放解决方案的存在的数值证据。这些是第一个明确的例子，典型的缩放行为的系统表现出凝胶化。
英文摘要：
The kinetic equations describing irreversible aggregation and the scaling approach developed to describe them in the limit of large times and large sizes are tersely reviewed. Next, a system is considered in which aggregates can only react with aggregates of their own size. The existence of a scaling solution of the kinetic equations can then be shown rigorously in the case in which the total mass of the system is conserved. A large number of detailed properties of the solution, previously predicted by qualitative arguments, can be shown rigorously as well in this system. In the case in which gelation occurs, some sketchy rigorous results are shown, and numerical evidence for the existence of a scaling solution is presented. These are the first explicit examples of typical scaling behaviour for systems exhibiting gelation.
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