为探讨分形基底结构对生长表面标度行为的影响,本文采用Kinetic Monte Carlo(KMC)方法模拟了刻蚀模型(etching model)在谢尔宾斯基箭头和蟹状分形基底上刻蚀表面的动力学行为.研究表明,在两种分形基底上的刻蚀模型都表现出很好的动力学...为探讨分形基底结构对生长表面标度行为的影响,本文采用Kinetic Monte Carlo(KMC)方法模拟了刻蚀模型(etching model)在谢尔宾斯基箭头和蟹状分形基底上刻蚀表面的动力学行为.研究表明,在两种分形基底上的刻蚀模型都表现出很好的动力学标度行为,并且满足Family-Vicsek标度规律.虽然谢尔宾斯基箭头和蟹状分形基底的分形维数相同,但模拟得到的标度指数却不同,并且粗糙度指数α与动力学指数z也不满足在欧几里得基底上成立的标度关系α+z=2.由此可以看出,标度指数不仅与基底的分形维数有关,而且和分形基底的具体结构有关.展开更多
We propose a novel two-species aggregation-annihilation model, in which irreversible aggregation reactions occur between any two aggregates of the same species and biased annihilations occur simultaneously between two...We propose a novel two-species aggregation-annihilation model, in which irreversible aggregation reactions occur between any two aggregates of the same species and biased annihilations occur simultaneously between two different species. The kinetic scaling behavior of the model is then analytically investigated by means of the mean-field rate equation. For the system without the seff-aggregation of the un-annihilated species, the aggregate size distribution of the annihilated species always approaches a modified scaling form and vanishes finally; while for the system with the self-aggregation of the un-annihilated species, its scaling behavior depends crucially on the details of the rate kernels. Moreover, the results also exhibit that both species are conserved together in some cases, while only the un-annihilated species survives finally in other cases.展开更多
The Etching model on various fractal substrates embedded in two dimensions was investigated by means of kinetic Mento Carlo method in order to determine the relationship between dynamic scaling exponents and fractal p...The Etching model on various fractal substrates embedded in two dimensions was investigated by means of kinetic Mento Carlo method in order to determine the relationship between dynamic scaling exponents and fractal parameters. The fractal dimensions are from 1.465 to 1.893, and the random walk exponents are from 2.101 to 2.578.It is found that the dynamic behaviors on fractal lattices are more complex than those on integer dimensions. The roughness exponent increases with the increasing of the random walk exponent on the fractal substrates but shows a non-monotonic relation with respect to the fractal dimension. No monotonic change is observed in the growth exponent.展开更多
文摘为探讨分形基底结构对生长表面标度行为的影响,本文采用Kinetic Monte Carlo(KMC)方法模拟了刻蚀模型(etching model)在谢尔宾斯基箭头和蟹状分形基底上刻蚀表面的动力学行为.研究表明,在两种分形基底上的刻蚀模型都表现出很好的动力学标度行为,并且满足Family-Vicsek标度规律.虽然谢尔宾斯基箭头和蟹状分形基底的分形维数相同,但模拟得到的标度指数却不同,并且粗糙度指数α与动力学指数z也不满足在欧几里得基底上成立的标度关系α+z=2.由此可以看出,标度指数不仅与基底的分形维数有关,而且和分形基底的具体结构有关.
基金The project supported by National Natural Science Foundation of China under Grant No. 10305009 and the Natural Science Foundation of Zhejiang Province of China under Grant No. 102067
文摘We propose a novel two-species aggregation-annihilation model, in which irreversible aggregation reactions occur between any two aggregates of the same species and biased annihilations occur simultaneously between two different species. The kinetic scaling behavior of the model is then analytically investigated by means of the mean-field rate equation. For the system without the seff-aggregation of the un-annihilated species, the aggregate size distribution of the annihilated species always approaches a modified scaling form and vanishes finally; while for the system with the self-aggregation of the un-annihilated species, its scaling behavior depends crucially on the details of the rate kernels. Moreover, the results also exhibit that both species are conserved together in some cases, while only the un-annihilated species survives finally in other cases.
基金Supported by the Fundamental Research Funds for the Central Universities under Grant No.2015XKMS074-CUMT
文摘The Etching model on various fractal substrates embedded in two dimensions was investigated by means of kinetic Mento Carlo method in order to determine the relationship between dynamic scaling exponents and fractal parameters. The fractal dimensions are from 1.465 to 1.893, and the random walk exponents are from 2.101 to 2.578.It is found that the dynamic behaviors on fractal lattices are more complex than those on integer dimensions. The roughness exponent increases with the increasing of the random walk exponent on the fractal substrates but shows a non-monotonic relation with respect to the fractal dimension. No monotonic change is observed in the growth exponent.
