对于具有转换和旋转动力学的系统的水力动力学方程
Akira Yoshimori1, Shankar P Das2
1Niigata University, Department of Physics, Niigata 950-2181, Japan.
Physical review. E
|November 18, 2025
概括
这项研究开发了波动的非线性水力动力学,用于具有翻译和旋转运动的系统. 它为集体密度推导了新的方程,结合了旋转动力学,并产生了自由能量函数.
科学领域:
- 统计力学 统计力学
- 流体动力学 流体动力学
- 非线性动力学是一种非线性动力学.
背景情况:
- 多粒子系统表现出复杂的动态,包括翻译和旋转.
- 现有的水力动力学模型经常简化或忽略旋转自由度.
- 对于各种物理现象来说,了解这些合动态是至关重要的.
研究的目的:
- 导出波动非线性水力动力学 (FNH) 方程,用于连接转移和旋转运动的系统.
- 研究方向动态对集体密度演变的影响.
- 为这些复杂的流体建立一个自由能量函数.
主要方法:
- 使用导向变量"u"来制定方向动态的朗格温方程.
- 通过布朗和福克-普朗克的位置和动量的方法考虑微观动力学.
- 使用局部平衡分布平均化微观方程,以获得粗粒度随机局部微分方程.
- 分析概率分布的静态解,以导出一个自由能量函数.
主要成果:
- 从微观动力学中获得的集体密度 {ψ̂} 的时间演变的准确表示.
- 粗粒度密度 {ψ} 的随机局部微分方程通过平均化得到.
- 基于乘数噪声解释的集体数密度方程的不同形式的识别 (伊托与斯特拉托诺维奇).
- 从概率分布的静止解中推导一个自由能量函数F[ψ].
结论:
- 开发的FNH框架准确地捕捉了多粒子系统中转化和旋转动态的相互作用.
- 导出的自由能量函数提供了对这些复杂流体的热力学特性的洞察.
- 这项工作为研究方向顺序影响流体行为的现象提供了基础.
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