Conferencia Invitada. On the interplay between spatial and time discrete scale invariance in dynamical processes in fractal media.

EZEQUIEL V ALBANO

Buzios

Taller; LAWNP´09 (Latin American Workshop on Nonlinear Phenomena),; 2009

CNPq, ICTP, CLAF

<!-- /* Style Definitions */ p.MsoNormal, li.MsoNormal, div.MsoNormal {mso-style-parent:""; margin:0cm; margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:12.0pt; font-family:"Times New Roman"; mso-fareast-font-family:"Times New Roman"; mso-ansi-language:EN-US;} @page Section1 {size:612.0pt 792.0pt; margin:70.85pt 3.0cm 70.85pt 3.0cm; mso-header-margin:36.0pt; mso-footer-margin:36.0pt; mso-paper-source:0;} div.Section1 {page:Section1;} --> We address dynamical processes occurring in fractal media having spatial Discrete Scale Invariance (DSI), with a fundamental length scale L. Then, if a dynamical process has a time depending (characteristic) length scale, e.g., a correlation length, of the form x  µ t1/z, we conjectured that it would exhibit time DSI with a fundamental period t = Lz, where z is a dynamical exponent. Time DSI is evidenced in numerical simulations by the onset of log-periodic oscillations of the relevant physical observables. The conjecture is tested in many archetypical models in the field of Statistical Physics, including random walks, diffusion controlled reactions, the Ising and Voter models, the Contact Process, ballistic deposition, etc.