We derive the hydrodynamic equations with fluctuating currents for the density, momentum, and energy fields for an active system in the dilute limit. In our model, nonoverdamped self-propelled particles (such as grains or birds) move on a lattice, interacting by means of aligning dissipative forces and excluded volume repulsion. Our macroscopic equations, in a specific case, reproduce a transition line from a disordered phase to a swarming phase and a linear dispersion law accounting for underdamped wave propagation. Numerical simulations up to a packing fraction $\sim 10\%$ are in fair agreement with the theory, including the macroscopic noise amplitudes. At a higher packing fraction, a dense-diluted coexistence emerges. We underline the analogies with the granular kinetic theories, elucidating the relation between the active swarming phase and granular shear instability.

中文翻译：

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推导具有惯性的活性颗粒的波动流体动力学的格子模型

我们得出了一个在稀疏极限下具有波动电流的有源系统的密度，动量和能量场的流体动力学方程。在我们的模型中，未过度阻尼的自推进颗粒（例如谷物或鸟类）在晶格上移动，通过对齐耗散力并排除体积排斥来相互作用。在特定情况下，我们的宏观方程再现了从无序相到群相的过渡线以及解释了衰减不足波传播的线性色散定律。数值模拟，直至填充分数$〜10％$与理论（包括宏观噪声幅度）完全吻合。在较高的包装分数下，会出现密集稀释的共存。我们强调了与颗粒动力学理论的类比，阐明了活跃的蜂群相与颗粒剪切不稳定性之间的关系。