从单个系统大小来看,基于波纹的粗粒度测定了透的临界性
1Department of Statistics, Texas A&M University, College Station, Texas 77843, USA.
Chaos (Woodbury, N.Y.)
|July 7, 2025
概括
本研究介绍了一种基于波形小组的方法,用于分析单一大小的复杂系统中的缩放行为. 这种方法准确地估计了关键点和指数,为透关键性提供了新的视角.
科学领域:
- 复杂的系统复杂的系统.
- 统计物理 统计物理
- 计算科学 计算科学
背景情况:
- 缩放分析对于相位过渡至关重要,但通常需要多个系统大小.
- 现实世界的系统往往存在于一个单一的大小,这给传统分析带来了挑战.
研究的目的:
- 开发一种基于波纹的方法,从单个大小的复杂系统中提取缩放行为.
- 为了使有限大小数据的系统中精确估计关键点和指数.
主要方法:
- 基于波形的粗粒处理应用于二维随机和爆炸性点透.
- 在有效系统大小中计算高频波段系数.
- 定义和分析波束能量 (平方系数) 捕捉集群边界.
主要成果:
- 发现平均波束能量遵循一个缩放规律.
- 精确估计了关键点和指数,与传统方法相一致.
- 波段能量证明了在透系统中可观察到的类似易感性的实用性.
结论:
- 基于波纹的分析允许从单个系统大小识别缩放属性.
- 这种方法为透的关键性提供了一个新的视角.
- 这种方法可能适用于各种现实世界系统,如神经活动和社交网络.
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