论文标题
具有钟形分布的聚合模型的精确渐近溶液
Exact asymptotic solution of an aggregation model with a bell-shaped distribution
论文作者
论文摘要
我们以一种详细的方式介绍了不可逆聚集的比例理论，其特征是反应速率$ k（k，l）= 1/k+1/l $以及其次要的概括。在这种情况下，可以精确评估缩放函数。通过这种情况，我们的意思是将其表示为具有给定边界条件的普通微分方程的独特解。这可以通过数值求解以高精度，从而对缩放行为进行了高度详细的分析。该结果证实了关于III型的所谓反应速率的一般缩放理论的早期工作的更一般结果。另一方面，固定时间的大骨料的行为，即，不在缩放限制中，现在已经在小时限制的近似值中进行了分析，可以在这种情况下更精确地确定，并且显示出与小型近似值显示出细微的差异。
We present in a detailed manner the scaling theory of irreversible aggregation characterized by the set of reaction rates $K(k,l)=1/k+1/l$, as well as a minor generalisation thereof. In this case, it is possible to evaluate the scaling function exactly. By this we mean that it is expressed as the unique solution of an ordinary differential equation with given boundary conditions. This can be solved numerically to high accuracy, making a highly detailed analysis of the scaling behaviour possible. The results confirm the far more general results of earlier work concerning a general scaling theory for so-called reaction rates of Type III. On the other hand, the behaviour of large aggregates at fixed time, that is, not in the scaling limit, which had been up to now analysed in an approximation valid in the limit of small times, can be determined more precisely in this case, and is shown to display subtle differences from the small-time approximation.
