出生、死亡和水平飞行:马尔萨斯羊群的三维简易平面

John Toner
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引用次数: 0

摘要

我提出了三维 "马尔萨斯羊群 "理论--即在运动过程中 "出生 "和 "死亡 "的自我推进实体(如生物)的连贯运动集合--其组成成分都倾向于让它们的速度矢量平行于同一个二维平面。我精确地确定了表征这类系统的通用缩放指数,发现动力学指数$z=3/2$,"各向异性 "指数$\zeta=3/4$,以及 "粗糙度 "指数$\chi=-1/2$。我还给出了这些指数所隐含的缩放定律。
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Birth, Death, and Horizontal Flight: Malthusian flocks with an easy plane in three dimensions
I formulate the theory of three dimensional "Malthusian flocks" -- i.e., coherently moving collections of self-propelled entities (such as living creatures) which are being "born" and "dying" during their motion -- whose constituents all have a preference for having their velocity vectors lie parallel to the same two-dimensional plane. I determine the universal scaling exponents characterizing such systems exactly, finding that the dynamical exponent $z=3/2$, the "anisotropy" exponent $\zeta=3/4$, and the "roughness" exponent $\chi=-1/2$. I also give the scaling laws implied by these exponents.
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