一维冷气体中的飞溅现象
A splash in a one-dimensional cold gas
AI总结：
本文研究一维交替质量硬点气体中左端粒子受激后产生的动力学级联，发现主体中形成亚弹道激波前沿并可用欧拉流体力学自相似解描述，同时存在完全非流体动力学的弹道飞溅区域，并提出两个关于其长时间动力学的猜想。
摘要：
我们考虑一组硬点粒子，它们以指定密度均匀分布在正半轴上，且初始时全部静止。粒子质量在两个值 $m$ 和 $M$ 之间交替变化。粒子通过能量守恒和动量守恒的碰撞相互作用。我们研究了当最左侧粒子被赋予正速度后所引发的活动级联。在长时间尺度下，我们发现这导致了观测动力学中的两个引人注目的特征。首先，在气体主体中，形成了一个激波前沿，将冷气体与热化区域分隔开来。激波前沿以亚弹道方式传播，主体部分由欧拉流体力学的自相似解描述。其次，存在一个由反弹粒子形成的飞溅区域，这些粒子以负速度作弹道运动。飞溅区域完全是非流体动力学的，我们针对该区域中长时间粒子动力学提出了两个猜想。我们对这些共存的动力学区域提供了详细的解析理解，并得到了分子动力学模拟结果的支持。
英文摘要：
We consider a set of hard point particles distributed uniformly with a specified density on the positive half-line and all initially at rest. The particle masses alternate between two values, $m$ and $M$. The particles interact via collisions that conserve energy and momentum. We study the cascade of activity that results when the left-most particle is given a positive velocity. At long times we find that this leads to two fascinating features in the observed dynamics. First, in the bulk of the gas, a shock front develops separating the cold gas from a thermalized region. The shock-front travels sub-ballistically, with the bulk described by self-similar solutions of Euler hydrodynamics. Second, there is a splash region formed by the recoiled particles which move ballistically with negative velocities. The splash region is completely non-hydrodynamic and we propose two conjectures for the long time particle dynamics in this region. We provide a detailed analytic understanding of these coexisting regimes. These are supported by the results of molecular dynamics simulations.
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