期刊
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
卷 115, 期 35, 页码 EB135-EB142出版社
NATL ACAD SCIENCES
DOI: 10.1073/pnas.1805847115
关键词
self-organized criticality; tropical geometry; proportional growth; power laws; pattern formation
资金
- Swiss National Science Foundation [168647]
- Young Russian Mathematics award
- Programa para un Avance Global e Integrado de la Matematica Mexicana [FORDECYT-265667]
- Basic Research Program of the National Research University Higher School of Economics
- ABACUS Laboratorio de Matematica Aplicada y Computo de Alto Rendimiento CINVESTAV-EDOMEX Proyecto [CONACYT-EDOMEX-2011-01-165873]
- Institute of Science and Technology
- Laboratory of Mirror Symmetry National Research University Higher School of Economics, Russian Federation Government [14.641.31.0001]
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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