Log-periodicity in piecewise ballistic superdiffusion: Exact results

Autor(es)

Cressoni, J. C. ; Viswanathan, G. M. ; da Silva, M. A. A.

• Tipo de documento: Artigo Científico
• Fonte: PHYSICAL REVIEW E; v. 98, n. 5, p. 7-pg., 2018-11-01.

Resumo

Small log-periodic oscillations have been observed in many systems and have previously been studied via renormalization-group approaches in the context of critical phenomena [Gluzman and Sornette, Phys. Rev. E 65, 036142 (2002); Derrida and Giacomin, J. Stat. Phys. 154, 286 (2014)]. Here we report their appearance in a random walk model with damaged memory, and we develop an exact discrete-time solution, free from adjustable parameters. Our results shed light on log-periodicity and how it arises. We also discuss continuous-time approaches to the solution along with their limitations and advantages. We show that, as a direct consequence of memory damage, the first moment for the model acquires piecewise ballistic behavior. The piecewise segments are separated by regularly placed singular points. Log-periodicity in this model is seen to be due to memory damage. Remarkably, piecewise ballistic behavior is only observed if one uses the discrete-time solution, because the continuous-time solution does not correctly account for the model's discrete-time dynamics. (AU)

• Processo FAPESP: 16/03918-7 - Caracterização e efeitos de memória em processos estocásticos
• Beneficiário: Marco Antonio Alves da Silva
• Modalidade de apoio: Auxílio à Pesquisa - Regular
• Processo FAPESP: 17/01176-6 - Caracterização e efeitos de memória em processos estocásticos
• Beneficiário: Marco Antonio Alves da Silva
• Modalidade de apoio: Auxílio à Pesquisa - Pesquisador Visitante - Brasil