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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

Log-periodicity in piecewise ballistic superdiffusion: Exact results

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Cressoni, J. C. [1] ; Viswanathan, G. M. [2, 3] ; da Silva, M. A. A. [1]
Total Authors: 3
[1] Univ Sao Paulo, FCFRP, Dept Fis & Quim, BR-14040903 Ribeirao Preto, SP - Brazil
[2] Univ Fed Rio Grande do Norte, Natl Inst Sci & Technol Complex Syst, BR-59078970 Natal, RN - Brazil
[3] Univ Fed Rio Grande do Norte, Dept Phys, BR-59078970 Natal, RN - Brazil
Total Affiliations: 3
Document type: Journal article
Source: Physical Review E; v. 98, n. 5 NOV 1 2018.
Web of Science Citations: 0

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)

FAPESP's process: 16/03918-7 - Characterization and memory effects in stochastic processes
Grantee:Marco Antonio Alves da Silva
Support type: Regular Research Grants
FAPESP's process: 17/01176-6 - Memory effects and characterization in stochastic processes
Grantee:Marco Antonio Alves da Silva
Support type: Research Grants - Visiting Researcher Grant - Brazil