用反控制对达西·贝纳德对流的线性和弱非线性稳定性分析
P G Siddheshwar1, Vinit Vinod Revankar2, M S Jagadeesh Kumar3
1Centre for Mathematical Needs, CHRIST University, Bengaluru, 560029, India.
Scientific reports
|October 22, 2025
概括
反控制稳定了牛顿流体中的达西-贝纳德对流. 增加控制器增益会延迟混乱并扩大捕获区域,而更高的生物体数量会促进周期性运动而不是混乱的行为.
科学领域:
- 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.
- 热传递是一种热传递.
背景情况:
- 达西-贝纳德对流 (Darcy-Bénard convection) 描述了由浮力驱动的流体运动,这种运动发生在一个有孔的介质或从下方加热的流体层中.
- 了解对流开始对于地质物理学,化学工程和材料科学中的应用至关重要.
- 反控制提供了一种影响和稳定流体不稳定的方法.
研究的目的:
- 从理论上研究反控制对达西-贝纳德对流的开始的影响.
- 分析控制器增益和BIOT数对系统稳定性和混乱行为的影响.
- 构建和分析用于弱非线性稳定性分析的瓦达斯·洛伦茨模型.
主要方法:
- 使用单项加勒金方法,麦克劳林序列扩展和牛顿-拉普森方法的组合进行线性稳定性分析.
- 微弱非线性稳定性分析采用构建的瓦达斯·洛伦茨模型.
- 确定Hopf-Rayleigh数来预测混乱的开始.
主要成果:
- 发现控制器增益参数能够稳定系统并延迟混乱的发生.
- 生物数的增加被证明可以促进长期的周期运动,而不是混乱的行为.
- 瓦达斯·洛伦兹模型表现出与标准洛伦兹模型相似的特性,捕获区域以圆形的形式.
结论:
- 反控制是稳定达西-贝纳德对流和延迟混乱动态的有效策略.
- 控制器增益和BIOT数都在确定系统的稳定性和向混乱过渡方面发挥着重要作用.
- 瓦达斯·洛伦茨模型为理解对流系统的复杂动态提供了一个有价值的框架.
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