论文标题
自我避免步行的分形和拓扑
Fractality and Topology of Self-Avoiding Walks
论文作者
论文摘要
我们分析了自我避免步行的几何和拓扑特征。我们介绍了一种新的步行：由染色质与核薄片相互作用的动机的环路填充自避免行走（LDSAW）。计算其关键指数，并发现与普通锯的指数不同。散步作为点云，LDSAW是锯子的子集。我们通过比较贝蒂数的分形维度和生长速率来研究LDSAW和SAW之间的差异。另外，在相同的例程之后，对锯中的触点的空间分布也是SAW的子集。结果表明，Betti数字的接触云具有多性分裂特性和不同的增长率。最后，为了进行比较，我们分析了锯的随机子集，表明它们具有与SAW相同的分形维度。
We have analyzed geometric and topological features of self-avoiding walks. We introduce a new kind of walk: the loop-deleted self-avoiding walk (LDSAW) motivated by the interaction of chromatin with the nuclear lamina. Its critical exponent is calculated and found to be different from that of the ordinary SAW. Taking the walks as point-clouds, the LDSAW is a subset of the SAW. We study the difference between the LDSAW and SAW by comparing their fractal dimensions and growth rates of the Betti number. In addition, the spatial distribution of the contacts inside a SAW, which is also a subset of SAW, is analyzed following the same routine. The results show that the contact-cloud has a multi-fractal property and different growth rates for the Betti number. Finally, for comparison, we have analyzed random subsets of the SAW, showing them to have the same fractal dimension as the SAW.
