ArticleProceedings of the National Academy of Sciences of the United States of America2018
Self-organized criticality and pattern emergence through the lens of tropical geometry.
Article in Proceedings of the National Academy of Sciences of the United States of America, 2018. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 3 papers.
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3 citing papers in PubMed.
- A tropical geometric approach to exceptional points.Proceedings of the National Academy of Sciences of the United States of America · 2023Article
- Multiscale structural complexity of natural patterns.Proceedings of the National Academy of Sciences of the United States of America · 2020Article
- Harmonic dynamics of the abelian sandpile.Proceedings of the National Academy of Sciences of the United States of America · 2019Article
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6 authors.
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Abstract
Tropical geometry, an established field in pure mathematics, is a place where string theory, mirror symmetry, computational algebra, auction theory, and so forth meet and influence one another. In this paper, we report on our discovery of a tropical model with self-organized criticality (SOC) behavior. Our model is continuous, in contrast to all known models of SOC, and is a certain scaling limit of the sandpile model, the first and archetypical model of SOC. We describe how our model is related to pattern formation and proportional growth phenomena and discuss the dichotomy between continuous and discrete models in several contexts. Our aim in this context is to present an idealized tropical toy model (cf. Turing reaction-diffusion model), requiring further investigation.
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