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Stationary power-law distribution in a generalized aggregation system with injection

带注入的广义聚集系统中的平稳幂律分布

基本信息

批准号：
02804022
负责人：
TAKAYASU Hideki
金额：
$ 1.66万
依托单位：
Kobe University
依托单位国家：
日本
项目类别：
Grant-in-Aid for General Scientific Research (C)
财政年份：
1990
资助国家：
日本
起止时间：
1990 至 1991
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-02804022/
关键词：
Aggregation power-low distribution Practals Landform Model 緩和有限サイズ効果

项目摘要

In this research we studied a generalized aggregation process in which charged particles diffuse and coalesce randomly on a lattice. For 1-dimensional and mean-field models, we show that there exists a statistically-invariant steady state when randomly charged particles are constantly injected. The steady state charge distribution obeys a power law with exponent depending both on the type of the injection and the spatial dimension. The response of the system to a perturbation(i. e., relaxation)is characterized by either a power law decay or a compressed exponential decay.As an application of this model we introduced a model of landform created by water erosion. Water flows aggregate making river networks and the earth's surface is eroded as a result. We showed that the landform automatically makes Practal geometry by the effect of erosion.

在这项研究中，我们研究了一个广义的聚集过程中，带电粒子的扩散和合并随机的晶格。对于一维和平均场模型，我们证明了当随机带电粒子不断注入时，存在一个几何不变的稳态。稳态电荷分布服从幂律，其指数取决于注入的类型和空间维度。系统对扰动的响应（即，例如，作为该模型的一个应用，我们介绍了一个水蚀地貌模型。水流汇聚成河流网络，结果地球表面被侵蚀。我们表明，地形自动使实际几何的侵蚀的影响。