Ki DY, Woo KY, Lee SB
Department of Physics, Kyungpook National University, Taegu 702-701, Korea.
Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 2000 Jul;62(1 Pt B):821-7. doi: 10.1103/physreve.62.821.
We study by Monte Carlo simulations the fractal nature of the backbone network for the irreversible kinetic gelation model in both two and three dimensions. The fractal dimension of the backbone network generated at the gel point is measured by various methods, and results are found to be consistent with that of the standard percolation backbone. Our observation is different from the previous work in three dimensions, where a distinctly larger value was observed. We also measure the spectral dimension d(B)(s) and the fractal dimension d(B)(w) of random walks on a backbone, defined by, respectively, the probability of random walks returning to the starting point and the rms displacements after t time steps. Results are also found to be consistent with the corresponding percolation values. We therefore conclude that the backbone network of the kinetic gelation model exhibits the same static and dynamic properties as those of the standard percolation backbone.
我们通过蒙特卡罗模拟研究了二维和三维不可逆动力学凝胶化模型的主链网络的分形性质。在凝胶点生成的主链网络的分形维数通过各种方法进行测量，结果发现与标准渗流主链的分形维数一致。我们的观察结果与之前在三维空间中的工作不同，在之前的工作中观察到了明显更大的值。我们还测量了主链上随机游走的谱维数d(B)(s)和分形维数d(B)(w)，它们分别由随机游走回到起点的概率和t个时间步后的均方根位移定义。结果也发现与相应的渗流值一致。因此，我们得出结论，动力学凝胶化模型的主链网络表现出与标准渗流主链相同的静态和动态性质。
