Niehues, Jakob, Jensen, Gorm Gruner and Haerter, Jan O. ORCID: https://orcid.org/0000-0002-8617-3847 (2022) Self-organized quantization and oscillations on continuous fixed-energy sandpiles. Physical Review E, 105 (3). DOI https://doi.org/10.1103/PhysRevE.105.034314.

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Abstract

Atmospheric self-organization and activator-inhibitor dynamics in biology provide examples of checkerboardlike spatiotemporal 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 nonnegative real number, its energy. Upon each timestep all sites with energy exceeding a unit threshold redistribute 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 μ: For low μ, all dynamics ceases after few redistribution events. For large μ, the dynamics is well-described as a diffusion process, where the order parameter, spatial variance σ, is removed. States at intermediate μ are dominated by checkerboardlike period-two phases which are however interspersed by much more complex phases of far longer periods. Phases are separated by discontinuous jumps in σ or ∂μσ—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.

Document Type: Article
Programme Area: PA2
Research affiliation: Integrated Modelling > Complexity and Climate
Affiliations > Not ZMT
Refereed: Yes
Open Access Journal?: No
DOI etc.: https://doi.org/10.1103/PhysRevE.105.034314
ISSN: 2470-0045
Date Deposited: 26 Apr 2022 14:18
Last Modified: 26 Apr 2022 14:18
URI: http://cris.leibniz-zmt.de/id/eprint/4886

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