论文标题
蜂群：压力的流体动力对准
Swarming: hydrodynamic alignment with pressure
论文作者
论文摘要
我们研究流体动力比对的蜂群。对准反映了指向加权平均标题的方向。我们考虑以$ 2P $ -laplacians的价格考虑所谓的$ p $ agemignment流体动力学，并由一般的对称通信内核家族进行加权。这里的主要新方面是一类一般压力张量的长时间出现行为而没有封闭假设，超出了它们形成能量耗散过程的要求。我们指的是“熵”等压力定律，并证明了$ p $对齐的流体动力学的植入，这是由带有一般熵压力张量的奇异核驱动的。这些结果表明，尽管缺乏热力学闭合，但仍在驱动长期植入行为方面对齐的刚性。
We study the swarming behavior of hydrodynamic alignment. Alignment reflects steering towards a weighted average heading. We consider the class of so-called $p$-alignment hydrodynamics, based on $2p$-Laplacians, and weighted by a general family of symmetric communication kernels. The main new aspect here is the long time emergence behavior for a general class of pressure tensors without a closure assumption, beyond the mere requirement that they form an energy dissipative process. We refer to such pressure laws as `entropic', and prove the flocking of $p$-alignment hydrodynamics, driven by singular kernels with general class of entropic pressure tensors. These results indicate the rigidity of alignment in driving long-time flocking behavior despite the lack of thermodynamic closure.
