径向生长团簇的界面涨落统计
Statistics of interfacial fluctuations of radially growing clusters
摘要：
利用生长区域上的随机生长方程，研究了波动径向生长界面的动力学行为。这个框架揭示了表面生长过程中产生的一些动态功能。对于快速增长，稀释，空间重新排序的传入的物质，是负责传输的相关性。它的影响包括擦除关于初始条件的记忆，部分衰减几何起源的不稳定性，以及在临界指数依赖于运动方程的参数的某些特殊情况下恢复普遍性。在这个意义上，稀释使动力学更类似于平面系统的通常动力学。这种快速增长制度的特点也是由空间解相关的接口，这在径向增长的接口的情况下，自然产生快速粗糙化和规模依赖分形，并建议出现一个自相似的分形维数。还研究了生长中的团簇的质心涨落，我们的分析表明，通常的标度可能不适用于径向伊甸园模型的长程表面涨落。事实上，我们的研究指出了这样一个事实，即该模型属于无稀释普适类。
英文摘要：
The dynamics of fluctuating radially growing interfaces is approached using the formalism of stochastic growth equations on growing domains. This framework reveals a number of dynamic features arising during surface growth. For fast growth, dilution, which spatially reorders the incoming matter, is responsible for the transmission of correlations. Its effects include the erasing of memory with respect to the initial condition, a partial attenuation of geometrically originated instabilities, and the restoring of universality in some special cases in which the critical exponents depend on the parameters of the equation of motion. In this sense, dilution rends the dynamics more similar to the usual one of planar systems. This fast growth regime is also characterized by the spatial decorrelation of the interface, which in the case of radially growing interfaces naturally originates rapid roughening and scale dependent fractality, and suggests the advent of a self-similar fractal dimension. The center of mass fluctuations of growing clusters are also studied, and our analysis suggests the possible non-applicability of usual scalings to the long range surface fluctuations of the radial Eden model. In fact, our study points to the fact that this model belongs to a dilution-free universality class.
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