| Full text | |
| Author(s): |
Cressoni, J. C.
;
Viswanathan, G. M.
;
da Silva, M. A. A.
Total Authors: 3
|
| Document type: | Journal article |
| Source: | PHYSICAL REVIEW E; v. 98, n. 5, p. 7-pg., 2018-11-01. |
| Abstract | |
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 Opportunities: | Regular Research Grants |
| FAPESP's process: | 17/01176-6 - Memory effects and characterization in stochastic processes |
| Grantee: | Marco Antonio Alves da Silva |
| Support Opportunities: | Research Grants - Visiting Researcher Grant - Brazil |