On the interplay between spatial and time symmetry in dynamic and kinetic processes occurring in fractal media

BAB, MARISA ALEJANDRA

La Plata

Conferencia; Humboldt Kolleg-International Conference on Physics; 2011

Alexander von Humboldt foundation

The understanding of kinetic and dynamic behavior of the wide variety of phenomena and processes, taking place in fractal media, is a challenging issue of increasing interdisciplinary interest. As is well known deterministic fractals are built iteratively from a generating cell, as consequence these exhibit discrete scale invariance (DSI) symmetry. DSI means that the fractal is scale invariant only between scales whose ratio is an integer power of the size of the generating cell b, named fundamental scaling ratio. Recent results report a subtle interplay between dynamic and kinetic processes and the DSI symmetry of the underlying fractal where the considered process takes, which leads to time DSI in the behaviour of the relevant observables. The hallmark of the time DSI is the observation of a log-periodic modulation on the dynamics or kinetics that is characterized by a well-defined fundamental time scaling ratio, t. Both fundamental scaling ratios are linked by means of dynamic exponent z of the corresponding physical process. In order to discuss this point, four paradigmatic cases will be addressed in detail: kinetics of diffusion-controlled reaction among random walker; the voter model that involves coarsening dynamic driven by interfacial noise in absence of surface tension; the contact process as representative of an epidemic propagation exhibiting irreversible critical behaviour; and the Ising model that represents a broad universality of reversible critical phenomena.