格拉斯曼流在凝聚系统中的应用
Applications of Grassmannian flows to coagulation systems
AI总结：
本文证明多类Smoluchowski型凝聚模型（含常核、加性核与乘性核情形）可实现为格拉斯曼流，从而获得可线性化与可积性，涵盖Gallay--Mielke粗化模型、Derrida--Retaux脱钉转变模型及多重合并凝聚模型。
摘要：
我们展示了多类Smoluchowski型凝聚模型如何能够实现为乘法格拉斯曼流，从而可线性化，并在此意义下可积。首先，我们证明一个具有常频率核的一般Smoluchowski型方程（涵盖一大类此类模型）可实现为乘法格拉斯曼流。其次，我们确立其他几个相关的常核模型也可如此实现，包括：Gallay--Mielke粗化模型、Derrida--Retaux脱钉转变模型以及一个一般的多重合并凝聚模型。第三，我们展示了加性和乘性频率核情形如何实现为秩一解析格拉斯曼流。
英文摘要：
We demonstrate how many classes of Smoluchowski-type coagulation models can be realised as multiplicative Grassmannian flows and are therefore linearisable, and thus integrable in this sense. First, we prove that a general Smoluchowski-type equation with a constant frequency kernel, that encompasses a large class of such models, is realisable as a multiplicative Grassmannian flow. Second, we establish that several other related constant kernel models can also be realised as such. These include: the Gallay--Mielke coarsening model; the Derrida--Retaux depinning transition model and a general mutliple merger coagulation model. Third, we show how the additive and multiplicative frequency kernel cases can be realised as rank-one analytic Grassmannian flows.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
