Spatial Coagulation and Gelation

在这个项目中，我们希望在分析空间随机粒子系统进行凝聚和凝胶化相变，与大偏差技术的帮助下，并分析由此产生的Smoluchowski方程的严重创新的步骤。在第一个资助阶段，我们一直在流体动力学环境中工作，并通过推导固定时间粒子配置分布的显式公式和大型系统极限中配置微观部分的大偏差原理奠定了基础。在第二个资助阶段，我们希望将这些公式扩展到宏观部分，并使用它们来更详细地了解空间在模型中的作用。特别是，我们将采用和扩展一些策略，显示凝胶化的发生广泛的一类空间凝固内核。此外，我们还想了解在具有某种随机运动的凝固模型中的迁移率诱导凝胶化现象。最后，我们想在热力学设置中做一些重要的步骤。

In this project we want to make serious innovative steps in the analysis of spatial random-particle systems undergoing coagulation and of the gelation phase transition, with the help of large deviation techniques and the analysis of the resulting Smoluchowski equation. In the first funding phase, we have been working in the hydrodynamic setting and laid foundations by deriving explicit formulas for the distribution of the particle configuration at a fixed time and large-deviation principles for the microscopic part of the configuration in the limit of a large system. In the second funding phase, we would like to extend these formulas to the macroscopic part and use them to gain a more detailed understanding of the role of space in the model. In particular, we will employ and extend a number of strategies for showing the occurrence of gelation for a wide class of spatial coagulation kernels. Additionally, we want to understand the phenomenon of mobility-induced gelation in a certain coagulation model with some random motion. Finally, we would like to make some non-trivial steps in the thermodynamic setting.