16–19 May 2022
Utrecht
Europe/Amsterdam timezone

Self-organized quantization and oscillations on continuous fixed-energy sandpiles

16 May 2022, 12:04
2m
Public Library (Utrecht)

Public Library

Utrecht

Neude 11, 3512 AE Utrecht, the Netherlands

Speaker

Jan Haerter (Niels Bohr Institute, Copenhagen University)

Description

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 μ: For low μ, all dynamics ceases after few re-distribution 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 checkerboard-like period-two phases which are however inter-spersed by much more complex phases of far longer periods. Phases are separated by discontinuous jumps in σ or ∂σ/∂μ — 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.

Primary authors

Dr Gorm Gruner Jensen (Niels Bohr Institute) Jan Haerter (Niels Bohr Institute, Copenhagen University)

Presentation materials

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