摘要翻译：
基于并裂旋涡环的动力学，建立了描述超流湍流的理论。由于非常频繁的重新连接，涡旋环（作为一个整体）的寿命不够长，无法进行任何本质的演化，由于确定性的运动。相反，它们迅速合并和分裂，这些随机重组过程压倒其他较慢的动态过程。为了进行定量描述，我们把涡旋环看作是一个布朗结构，它的唯一自由度是环的长度$L$。本文从Boltzmann型动力学方程出发，对长度为$l$的环数的分布函数$n(l)$进行了研究。利用碰撞积分中特殊的ansatz方法，在定常情况下，得到了动力学方程的精确幂函数解。这个解不是（热力学上）平衡，相反，它描述了两个涡旋环的长度（或能量）在空间中的相互通量的状态。通量这个术语只是指由于重新连接而在不同大小的环路之间重新分配长度（或能量）。通过对这个解的分析，我们得到了湍流超流氦中涡旋缠结的结构和动力学的一些结果。特别地，我们评估了曲率的平均半径和重联事件的完全速率。我们还研究了单位体积涡旋环的全长--所谓的涡旋线密度--的演化。结果表明，这种演化符合著名的Vinen方程。从发展的方法的角度讨论了Vinen方程的性质。
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英文标题：
《Kinetics of a Network of Vortex Loops in He II and a Theory of
  Superfluid Turbulence》
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作者：
Sergey K. Nemirovskii
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最新提交年份：
2008
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分类信息：

一级分类：Physics        物理学
二级分类：Statistical Mechanics        统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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英文摘要：
  A theory is developed to describe the superfluid turbulence on the base of kinetics of the merging and splitting vortex loops. Because of very frequent reconnections the vortex loops (as a whole) do not live long enough to perform any essential evolution due to the deterministic motion. On the contrary, they rapidly merge and split, and these random recombination processes prevail over other slower dynamic processes. To develop quantitative description we take the vortex loops to have a Brownian structure with the only degree of freedom, which is the length $l$ of the loop. We perform investigation on the base of the Boltzmann type kinetic equation for the distribution function $n(l)$ of number of loops with length $l$. By use of the special ansatz in the collision integral we have found the exact power-like solution to kinetic equation in the stationary case. This solution is not (thermodynamically) equilibrium, but on the contrary, it describes the state with two mutual fluxes of the length (or energy) in space of sizes of the vortex loops. The term flux means just redistribution of length (or energy) among the loops of different sizes due to reconnections. Analyzing this solution we drew several results on the structure and dynamics of the vortex tangle in the turbulent superfluid helium. In particular, we evaluated the mean radius of the curvature and the full rate of the reconnection events. We also studied the evolution of the full length of vortex loops per unit volume-the so-called vortex line density. It is shown this evolution to obey the famous Vinen equation. The properties of the Vinen equation from the point of view of the developed approach had been discussed.
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PDF链接：
https://arxiv.org/pdf/802.0651