On the occurrence of oscillatory modulations in the power law behavior of dynamic and kinetic processes in fractalsM. A. Bab, G. Fabricius and E. V. Albano
Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas (INIFTA), UNLP, CONICET Casilla de Correo 16, Sucursal 4, (1900) La Plata, Argentina
received 15 August 2007; accepted in final form 25 October 2007; published January 2008
published online 20 November 2007
The dynamic and kinetic behavior of processes occurring in fractals with spatial discrete scale invariance (DSI) is considered. Spatial DSI implies the existence of a fundamental scaling ratio (b1). We address time-dependent physical processes which, as a consequence of the time evolution, develop a characteristic length of the form , where z is the dynamic exponent. So, we conjecture that the interplay between the physical process and the symmetry properties of the fractal leads to the occurrence of time DSI evidenced by soft log-periodic modulations of physical observables, with a fundamental time scaling ratio given by . The conjecture is tested numerically for single random walks, annihilating random walks, and representative systems of broad universality classes in the fields of irreversible and equilibrium critical phenomena.
02.50.Ey - Stochastic processes.
05.50.+q - Lattice theory and statistics (Ising, Potts, etc.).
64.60.Ht - Dynamic critical phenomena.
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