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Self-organized quantization and oscillations on continuous fixed-energy sandpiles
- Publication Year :
- 2021
-
Abstract
- Atmospheric self-organization and activator-inhibitor dynamics in biology provide examples of checkerboard-like spatio-temporal organization. We study a simple model for local activation-inhibition processes. Our model, first introduced in the context of atmospheric moisture dynamics, is a continuous-energy and non-Abelian version of the fixed-energy sandpile model. Each lattice site is populated by a non-negative real number, its energy. Upon each timestep all sites with energy exceeding a unit threshold re-distribute their energy at equal parts to their nearest neighbors. The limit cycle dynamics gives rise to a complex phase diagram in dependence on the mean energy $\mu$: For low $\mu$, all dynamics ceases after few re-distribution events. For large $\mu$, the dynamics is well-described as a diffusion process, where the order parameter, spatial variance $\sigma$, is removed. States at intermediate $\mu$ are dominated by checkerboard-like period-two phases which are however interspersed by much more complex phases of far longer periods. Phases are separated by discontinuous jumps in $\sigma$ or $\partial_{\mu}\sigma$ - akin to first and higher-order phase transitions. Overall, the energy landscape is dominated by few energy levels which occur as sharp spikes in the single-site density of states and are robust to noise.<br />Comment: 13 pages, 7 figures, plus supplement, to be submitted to Physical Review E
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2111.04470
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1103/PhysRevE.105.034314