一维Levy扩散团簇-团簇凝聚的标度性质
Scaling properties of one-dimensional cluster-cluster aggregation with Levy diffusion
摘要：
我们提出了一个研究团簇聚集与源的单体在静止状态下的粒子的空间传输发生Levy航班的标度特性。我们表明，从平均场统计的波动为主的统计，更普遍认为的情况下，扩散运输，发生的系统的空间维度是通过两个以上的调谐，可以模仿，甚至在一维通过改变特征指数，β，的Levy跳跃长度分布。我们还证明了两质点关联函数是强普适的，它描述了定态下的质量通量，其标度指数由与空间维数无关的平均场值和与β值无关的平均场值给出.最后，我们用数值方法研究了在扩散限制区中描述重粒子耗尽区结构的两点空间关联函数。我们发现，这个关联函数消失的粒子之间的分离的非平凡的分数功率，因为这个分离去零。我们提供了这个指数的值，这是在合理的协议与数值测量的缩放参数。
英文摘要：
We present a study of the scaling properties of cluster-cluster aggregation with a source of monomers in the stationary state when the spatial transport of particles occurs by Levy flights. We show that the transition from mean-field statistics to fluctuation-dominated statistics which, for the more commonly considered case of diffusive transport, occurs as the spatial dimension of the system is tuned through two from above, can be mimicked even in one dimension by varying the characteristic exponent, beta, of the the Levy jump length distribution. We also show that the two-point mass correlation function, responsible for the flux of mass in the stationary state, is strongly universal: its scaling exponent is given by the mean field value independent of the spatial dimension and independent of the value of beta. Finally we study numerically the two point spatial correlation function which characterises the structure of the depletion zone around heavy particles in the diffusion limited regime. We find that this correlation function vanishes with a non-trivial fractional power of the separation between particles as this separation goes to zero. We provide a scaling argument for the value of this exponent which is in reasonable agreement with the numerical measurements.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
