Collective behaviour in biological systems presents theoretical challenges beyond the borders of classical statistical physics. The lack of concepts such as scaling and renormalization is particularly problematic, as it forces us to negotiate details whose relevance is often hard to assess. In an attempt to improve this situation, we present here experimental evidence of the emergence of dynamic scaling laws in natural swarms of midges. We find that spatio-temporal correlation functions in different swarms can be rescaled by using a single characteristic time, which grows with the correlation length with a dynamical critical exponent z ≈ 1, a value not found in any other standard statistical model. To check whether out-of-equilibrium effects may be responsible for this anomalous exponent, we run simulations of the simplest model of self-propelled particles and find z ≈ 2, suggesting that natural swarms belong to a novel dynamic universality class. This conclusion is strengthened by experimental evidence of the presence of non-dissipative modes in the relaxation, indicating that previously overlooked inertial effects are needed to describe swarm dynamics. The absence of a purely dissipative regime suggests that natural swarms undergo a near-critical censorship of hydrodynamics.

中文翻译：

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自然群的动态缩放

生物系统中的集体行为提出了超越经典统计物理学领域的理论挑战。缺乏诸如缩放和重新规范化之类的概念特别成问题，因为它迫使我们协商通常难以评估其相关性的细节。为了改善这种情况，我们在此提供实验证据，证明自然mid虫中出现了动态缩放定律。我们发现在不同群的是空间-时间相关的功能可以通过使用单个特征的时间，这与具有动态临界指数相关长度增长被重新缩放ž ≈1，在任何其他标准统计模型中找不到的值。要检查是否影响外的平衡可能是造成这种反常指数，我们跑的最简单的模型进行仿真自行颗粒，找到ž ≈ 2，这表明自然群属于一种新型的动态普适类。通过松弛中存在非耗散模式的实验证据进一步加强了这一结论，表明需要先前被忽略的惯性效应来描述群动力学。缺乏纯粹的耗散机制表明自然群体经历了流体动力学的近乎严格的审查制度。