混乱的昆虫群的平均场理论
R González-Albaladejo1, L L Bonilla2
1Departamento de Matemática Aplicada, Universidad Complutense de Madrid, 28040 Madrid, Spain and Gregorio Millán Institute for Fluid Dynamics, Nanoscience and Industrial Mathematics, Universidad Carlos III de Madrid, 28911 Leganés, Spain.
Physical review. E
|July 19, 2023
概括
协调限制的Vicsek模型显示了昆虫群中的无尺度相位过渡. 平均场理论揭示了与兰道理论相匹配的临界指数,发生在零限制和噪声下.
科学领域:
- 物理 物理学 物理
- 复杂的系统复杂的系统.
- 统计力学 统计力学
背景情况:
- 维塞克模型是研究自我推进的粒子和新兴集体行为的基本框架.
- 自然昆虫群体表现出复杂的动态,包括有序和混乱状态之间的相位过渡.
研究的目的:
- 为了开发一个平均场理论的和局限的Vicsek模型.
- 通过分析来确定关键指数,并了解在模拟中观察到的无尺度相位过渡.
主要方法:
- 对于局限的Vicsek模型的平均场理论的分析推导.
- 使用兰道理论和动态关键指数计算关键指数.
- 分析噪声线及其与群体行为及其关系的分析和利亚普诺夫指数.
主要成果:
- 平均场理论预测,在零限制和噪音的情况下,一个无尺度的相位过渡.
- 从分析上得出的关键指数与兰道理论一致,包括最大的利亚普诺夫指数的z=1和φ=0.5.
- 该理论解释了观察到的群体形状和与自然群体相似的关键指数.
结论:
- 平均场理论成功地捕获了有限的Vicsek模型中无尺度相变的基本特征.
- 该理论为理解生物系统中的集体行为提供了一个框架,并预测了群体动态的力量规律.
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