摘要翻译：
本文从质点分布在随机位移场$\bu(\bx)$作用下的两点关联函数的精确单步演化方程出发，推导出了当$\bu(\bx)$迭代建立速度场时的不同动力学状态。首先，我们证明了空间不相关场$\bu(\bx)$导致标准扩散方程和反常扩散方程。当场$\bu(\bx)$空间相关时，每个粒子执行简单的自由布朗运动，但不同粒子的运动轨迹是相互关联的。Bu(\bx)$场的两点统计性质在粒子分布中诱导出两点空间关联，满足一个简单但非平凡的类扩散方程。这些位移-位移相关性导致该系统有三种可能的状态：聚并、简单聚类和两者的结合。通过计算机模拟和一个简单的理论论证，证明了在一维系统中存在这些不同的状态。
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英文标题：
《Diffusion, super-diffusion and coalescence from single step》
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作者：
Andrea Gabrielli and Fabio Cecconi
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最新提交年份：
2007
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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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一级分类：Physics        物理学
二级分类：Disordered Systems and Neural Networks        无序系统与神经网络
分类描述：Glasses and spin glasses; properties of random, aperiodic and quasiperiodic systems; transport in disordered media; localization; phenomena mediated by defects and disorder; neural networks
眼镜和旋转眼镜；随机、非周期和准周期系统的性质；无序介质中的传输；本地化；由缺陷和无序介导的现象；神经网络
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英文摘要：
  From the exact single step evolution equation of the two-point correlation function of a particle distribution subjected to a stochastic displacement field $\bu(\bx)$, we derive different dynamical regimes when $\bu(\bx)$ is iterated to build a velocity field. First we show that spatially uncorrelated fields $\bu(\bx)$ lead to both standard and anomalous diffusion equation. When the field $\bu(\bx)$ is spatially correlated each particle performs a simple free Brownian motion, but the trajectories of different particles result to be mutually correlated. The two-point statistical properties of the field $\bu(\bx)$ induce two-point spatial correlations in the particle distribution satisfying a simple but non-trivial diffusion-like equation. These displacement-displacement correlations lead the system to three possible regimes: coalescence, simple clustering and a combination of the two. The existence of these different regimes, in the one-dimensional system, is shown through computer simulations and a simple theoretical argument.
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PDF链接：
https://arxiv.org/pdf/709.2333