边界信息流入增强群集中的相关性
Boundary information inflow enhances correlation in flocking
摘要：
动物集体行为最显著的特征是高度有序结构的出现。远距离空间相关性的存在，虽然肉眼看不太明显，但也许是自我组织的一个更深刻的标志。三维椋鸟群的实验数据表明，速度关联函数的衰减指数C（r）~ 1/r^γ非常小，γ<< 1。这一结果既不能用平衡场论解释，也不能用非平衡理论和有源系统的模拟来解释。本文通过数值模拟和理论计算，证明了在三维格点上的一组海森伯格自旋的边界上施加一个动力学场，会产生一个消失指数γ，就像在椋鸟群中一样。动态场的作用是产生从边界到体块的信息流入，触发长程自旋波模式，从而产生有害的长程相关。这种现象的生物学起源可以是外源性的-由环境扰动产生的信息从群体的边界传递到群体的主体-或内源性的-群体使自己保持在一个恒定的动态激发状态，这有利于相关性和集体反应。
英文摘要：
The most conspicuous trait of collective animal behaviour is the emergence of highly ordered structures. Less obvious to the eye, but perhaps more profound a signature of self-organization, is the presence of long-range spatial correlations. Experimental data on starling flocks in 3d show that the exponent ruling the decay of the velocity correlation function, C(r) ~ 1/r^γ, is extremely small, γ<< 1. This result can neither be explained by equilibrium field theory, nor by off-equilibrium theories and simulations of active systems. Here, by means of numerical simulations and theoretical calculations, we show that a dynamical field applied to the boundary of a set of Heisemberg spins on a 3d lattice, gives rise to a vanishing exponent γ, as in starling flocks. The effect of the dynamical field is to create an information inflow from border to bulk that triggers long range spin wave modes, thus giving rise to an anomalously long-ranged correlation. The biological origin of this phenomenon can be either exogenous - information produced by environmental perturbations is transferred from boundary to bulk of the flock - or endogenous - the flock keeps itself in a constant state of dynamical excitation that is beneficial to correlation and collective response.
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