在一个维度的静态多孔-中等方程.
Maximilien Bernard1,2, Andrei A Fedorenko3, Pierre Le Doussal1
1l'Ecole Normale Supérieure, Laboratoire de Physique de , CNRS, ENS and PSL Université, Sorbonne Université, Université Paris Cité, 24 rue Lhomond, 75005 Paris, France.
Physical review. E
|November 18, 2025
概括
我们研究了带有白噪声的多孔介质方程 (PME),使用功能性重规范化组预测增长指数. 模拟显示了异常的缩放和多缩放,由贝塞尔过程随机步行模型解释.
科学领域:
- 随机局部微分方程 随机局部微分方程
- 统计物理 统计物理
- 接口增长现象 接口增长现象
背景情况:
- 孔隙介质方程 (PME) 模拟了各种物理现象,包括流体流动和热传递.
- 了解噪声存在的接口动力学对于材料科学和流体动力学至关重要.
- 随机增长模型对于描述自然界的随机过程至关重要.
研究的目的:
- 为了研究一个维的多孔介质方程 (PME) 与添加的非保守的白噪声.
- 将 PME 解释为接口高度场的随机增长方程.
- 预测和分析增长指数 (α和β) 和缩放行为.
主要方法:
- 运用功能重规范化组 (FRG) 预测增长指数.
- 广泛的数值模拟以验证理论预测和探索缩放性质.
- 使用与贝塞尔过程相关的随机步行模型对静止测量的分析.
主要成果:
- 功能性重规范化组成功预测了增长指数α和β.
- 数字模拟证实了预测的指数,但也揭示了局部指数α_{loc}的异常缩放.
- 观察到多尺度的证据,源于局部高度差异的广泛分布.
- 随机PME的静态测量被准确地描述了与贝塞尔过程相关的随机步行模型.
结论:
- 该研究提供了对一个维度的随机多孔介质方程的全面分析.
- 功能重规范化组是预测随机增长模型中的指数的强大工具.
- 异常缩放和多缩放现象是该系统的重要特征,需要先进的建模.
- 贝塞尔过程随机步行模型为随机 PME 的多尺度性质提供了有价值的见解.
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