矿物分形生长的动力学模型与数值模拟

本文通过考虑离子电位、环境温度以及噪声等的影响,建立了一个矿物分形生长的DLA模型.在300×300的正方格子中心处放置一个种子构成生长中心,吸引域设置为菱形,主要考虑了三个参数的影响,其中总体的表面粘附几率为Pg,范围为0~99%,用来消除噪声的影响,模拟矿物的结晶生长速度与矿物结构的关系;吸附距离d变化范围为0~9单元距离,用来模拟离子电位对矿物生长的影响;填充间隔s的变化范围为0.00~5.00单元距离,表现为环境温度对矿物生长体系的影响.进行了三组模拟,分别是固定其中2个参数,改变另一个参数.结果表明,DLA集团的分维值随模拟参数成规律性的变化,分形维数在一定的条件下随着Pg的降低、d和s的增大而增大,矿物的结构也随之从浸染状、星散状或放射状逐渐过渡到团块状.该模型只是对三维分形生长的二维平面模拟,不能完全反映整个矿物在三维受限空间中聚集生长的复杂动力学.

An Numerical Approach for the Dynamic Model ofFractal Growth of Minerals

A modified fractal growth model of minerals is proposed to simulate the influence of ionic potential,temperature and noises.One seed is placed at the center of a square with 300 × 300 lattices as a growth focus and the attraction domain is set to diamond.Three main parameters are considered in this model.One of them is the probability of surface adhesion(Pg)which with the range of 0 to 99% to eliminate the impact of noise.The others are adsorption distance d and filled interval s.The former parameter varies from 0 to 9 units which on behalf of the ionic potential of particles and the latter varied from 0.00 to 5.00 units distance to perform the influence of environmental temperature on minerals growth system.Three model sets are carried out with two fixed parameters and the other variable parameter.The results show that the fractal dimension of DLA groups are increasing with the decrease of Pg and the increases of d and s,as well as the structure of minerals from disseminated,star or radial gradual transition to agglomerate.The model is a two-dimensional simulation for three-dimensional fractal growth and can not fully reflect the complex growth dynamics of mineral aggregate in space.