在非变量Swift-Hohenberg方程中局部模式的碰撞
Mathi Raja1, Adrian van Kan1, Benjamin Foster1
1Department of Physics, University of California at Berkeley, Berkeley, California 94720, USA.
Physical review. E
|July 19, 2023
概括
这项研究研究了带有折叠对称性的立方-五进制Swift-Hohenberg方程 (SH35),揭示了局部结构 (LSs) 呈现复杂的碰撞动态. 这些相互作用导致了多样化的约束状态,可以通过减少的ODE模型来预测,突出了丰富的时间动态.
科学领域:
- 复杂系统和非线性动力学
- 流体动力学和模式形成
- 计算物理 计算物理
背景情况:
- 立方体-五进制的Swift-Hohenberg方程 (SH35) 建模了具有中平面反射对称性的对流系统,例如二进制流体对流.
- 打破这种对称性引入非变量项,导致不对称的空间局部结构 (LSs).
研究的目的:
- 为了研究非变量立方-五进制Swift-Hohenberg方程 (SH35) 中不对称局部结构 (LSs) 的动态.
- 分析这些结构之间的碰撞场景,了解由此产生的边界状态.
- 为LS相互作用开发和验证一个简化的普通微分方程 (ODE) 模型.
主要方法:
- 使用了数值连续和广泛的直接数值模拟 (DNS).
- 使用非对称分析来预测LSs的漂移速度.
- 通过梯度下降优化,制定了一个简化的ODE模型,并与DNS数据进行验证.
主要成果:
- 非变性SH35支持具有可预测漂移速度的不对称LS.
- LS 之间的碰撞是不弹性的,形成可能比初始结构更长或更短的边界状态.
- 简化的ODE模型准确地捕捉了简单的束状态的动态,但显示波长变化的限制.
结论:
- 约束状态的稳定性,而不是麦克斯韦点,决定了非变量SH35.5中的碰撞结果.
- 复杂的参数空间结构 (孤立) 描述了多脉冲束状态.
- 简化的ODE模型提供了LS相互作用的大量定量描述,揭示了净吸引力或排斥性的行为.
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