论文标题
与温度依赖性Smoluchowski方程的确切解决方案
Exact solutions of temperature-dependent Smoluchowski equations
论文作者
论文摘要
我们报告了许多依赖温度的Smoluchowski方程的精确解决方案。这些方程式量化了弹道聚集，其中不同大小的聚集物的密度演变与此类簇的平均动能（部分温度）的演变纠缠在一起。获得的精确溶液可以用作评估数值方法的准确性和计算效率的基准，这些方法是为了解决温度依赖性的Smoluchowski方程而开发的。此外，它们还可以说明这些系统中可能的进化制度。已经为一系列模型速率系数获得了确切的解决方案，我们证明可能有无限数量的这种模型系数可以进行精确分析。我们将精确解决方案与各种进化制度的数值解决方案进行了比较；数值和精确结果之间的一个很好的一致性证明了被剥削的数值方法的准确性。
We report a number of exact solutions for temperature-dependent Smoluchowski equations. These equations quantify the ballistic agglomeration, where the evolution of densities of agglomerates of different size is entangled with the evolution of the mean kinetic energy (partial temperatures) of such clusters. The obtained exact solutions may be used as a benchmark to assess the accuracy and computational efficiency of the numerical approaches, developed to solve the temperature-dependent Smoluchowski equations. Moreover, they may also illustrate the possible evolution regimes in these systems. The exact solutions have been obtained for a series of model rate coefficients, and we demonstrate that there may be an infinite number of such model coefficient which allow exact analysis. We compare our exact solutions with the numerical solutions for various evolution regimes; an excellent agreement between numerical and exact results proves the accuracy of the exploited numerical method.
