With the aim to probe the effects of the microscopic details of fractal substrates on the scaling of discrete growth models, the surface structures of the equilibrium restricted curvature （ERC） model on Sierpinski a...With the aim to probe the effects of the microscopic details of fractal substrates on the scaling of discrete growth models, the surface structures of the equilibrium restricted curvature （ERC） model on Sierpinski arrowhead and crab sub- strates are analyzed by means of Monte Carlo simulations. These two fractal substrates have the same fractal dimension dr, but possess different dynamic exponents of random walk Zrw. The results show that the surface structure of the ERC model on fractal substrates are related to not only the fractal dimension df, but also to the microscopic structures of the substrates expressed by the dynamic exponent of random walk Zrw- The ERC model growing on the two substrates follows the well-known Family-Vicsek scaling law and satisfies the scaling relations 2a ~ df ~ z ~ 2Zrw. In addition, the values of the scaline exponents are in ~ood a^reement with the analytical orediction of the fractional Mullins-Herring equation.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
基金Project support by the Fundamental Research Funds for the Central Universities of Ministry of Education of China(Grant No.2013XK04)
文摘With the aim to probe the effects of the microscopic details of fractal substrates on the scaling of discrete growth models, the surface structures of the equilibrium restricted curvature （ERC） model on Sierpinski arrowhead and crab sub- strates are analyzed by means of Monte Carlo simulations. These two fractal substrates have the same fractal dimension dr, but possess different dynamic exponents of random walk Zrw. The results show that the surface structure of the ERC model on fractal substrates are related to not only the fractal dimension df, but also to the microscopic structures of the substrates expressed by the dynamic exponent of random walk Zrw- The ERC model growing on the two substrates follows the well-known Family-Vicsek scaling law and satisfies the scaling relations 2a ~ df ~ z ~ 2Zrw. In addition, the values of the scaline exponents are in ~ood a^reement with the analytical orediction of the fractional Mullins-Herring equation.
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.
