Long-term memory effects in closed random aggregating systems
Molecular Modelling of Materials Laboratory,
Institute of Physical Chemistry NRCPS Demokritos,
15310 Ag. Paraskevi, Greece
Faculté des Sciences and
Center for Nonlinear Phenomena and Complex Systems
CP 231, Free University of Brussels,
1050 Brussels, Belgium.
2 Graduate School of Information Sciences, Tohoku University - Sendai 980-77, Japan
3 Research Institute of Fracture Technology, Faculty of Engineering, Tohoku University Sendai 980-77, Japan.
Accepted: 24 November 1995
We study the problem of fractal initial conditions in closed aggregating systems (no external input). When the initial distribution of aggregating particles has a fractal dimension , the number of surviving particles decreases as , for . Logarithmic corrections are necessary for . This fractal decay indicates that in closed aggregating systems the memory of the initial distribution is always present in the dynamical exponent which characterizes the decay of the particle number.
PACS: 05.40.+j – Fluctuation phenomena, random processes, and Brownian motion / 82.20.Db – Statistical theories (including transition state) / 05.70.Ln – Nonequilibrium thermodynamics, irreversible processes
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