Random growth of interfaces: Statistical analysis of single columns and detection of critical events.
Description: The dynamics of growth and formation of surfaces and interfaces is becoming very important for the understanding of the origin and the behavior of a wide range of natural and industrial dynamical processes. The first part of the paper is focused on the interesting field of the random growth of surfaces and interfaces, which finds application in physics, geology, biology, economics, and engineering among others. In this part it is studied the random growth of surfaces from within the perspective of a single column, namely, the fluctuation of the column height around the mean value, which is depicted as being subordinated to a standard fluctuation-dissipation process with friction g. It is argued that the main properties of Kardar-Parisi-Zhang theory are derived by identifying the distribution of return times to y(0) = 0, which is a truncated inverse power law, with the distribution of subordination times. The agreement of the theoretical prediction with the numerical treatment of the model of ballistic deposition is remarkably good, in spite of the finite size effects affecting this model. The second part of the paper deals with the efficiency of the diffusion entropy analysis (DEA) when applied to the studies of stromatolites. In this case it is shown that this tool can be confidently used for the detection of complexity. The connection between the two studies is established by the use of the DEA itself. In fact, in both analyses, that is, the random growth of interfaces and the study of stromatolites, the method of diffusion entropy is able to detect the real scaling of the system, namely, the scaling of the process is determined by genuinely random events, also called critical events.
Date: August 2004
Creator: Failla, Roberto