论文标题
经典Toda晶格的高低压力域壁
High-low pressure domain wall for the classical Toda lattice
论文作者
论文摘要
我们研究了具有域壁初始条件的经典TODA晶格，左右半晶格处于热平衡状态，但具有不同的压力，平均速度和温度的参数。在流体动力学方面，各自的时空轮廓弹道尺度。感兴趣的特殊情况是从均匀温度下的低压到零平均速度的跳跃。因此，平均拉伸的缩放函数（也是自由音量）被迫更改符号。通过直接检查，TODA晶状体的流体动力方程在零伸展下似乎是单数的。在我们的贡献中，我们报告了数值解决方案，并令人信服地确定自相似溶液表现出平稳的行为。
We study the classical Toda lattice with domain wall initial conditions, for which left and right half lattice are in thermal equilibrium but with distinct parameters of pressure, mean velocity, and temperature. In the hydrodynamic regime the respective space-time profiles scale ballisticly. The particular case of interest is a jump from low to high pressure at uniform temperature and zero mean velocity. Thereby the scaling function for the average stretch (also free volume) is forced to change sign. By direct inspection, the hydrodynamic equations for the Toda lattice seem to be singular at zero stretch. In our contribution we report on numerical solutions and convincingly establish that nevertheless the self-similar solution exhibits smooth behavior.
