Self-Organized Criticality and Pattern Emergence through the lens of Tropical Geometry
| العنوان: | Self-Organized Criticality and Pattern Emergence through the lens of Tropical Geometry |
|---|---|
| المؤلفون: | Ernesto Lupercio, Nikita Kalinin, Aldo Guzmán-Sáenz, Vera Kalinina, Mikhail Shkolnikov, Yulieth Prieto |
| المساهمون: | Institut de recherche en astrophysique et planétologie (IRAP), Institut national des sciences de l'Univers (INSU - CNRS)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Observatoire Midi-Pyrénées (OMP), Météo France-Centre National d'Études Spatiales [Toulouse] (CNES)-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche pour le Développement (IRD)-Météo France-Centre National d'Études Spatiales [Toulouse] (CNES)-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche pour le Développement (IRD)-Centre National de la Recherche Scientifique (CNRS), Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS) |
| المصدر: | Proc.Nat.Acad.Sci. Proc.Nat.Acad.Sci., 2018, 115 (35), pp.E8135-E8142. ⟨10.1073/pnas.1805847115⟩ |
| بيانات النشر: | HAL CCSD, 2018. |
| سنة النشر: | 2018 |
| مصطلحات موضوعية: | High Energy Physics - Theory, geometry, 70K70, 19H99, Computer science, [PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph], toy model, FOS: Physical sciences, Context (language use), algebra, 01 natural sciences, Mathematics - Algebraic Geometry, pattern formation, 0103 physical sciences, Tropical geometry, FOS: Mathematics, Statistical physics, 0101 mathematics, string model, 010306 general physics, Scaling, Algebraic Geometry (math.AG), power laws, model: discrete, Multidisciplinary, Toy model, Abelian sandpile model, [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th], 010102 general mathematics, scaling, critical phenomena, Self-organized criticality, Nonlinear Sciences - Adaptation and Self-Organizing Systems, [PHYS.PHYS.PHYS-GEN-PH]Physics [physics]/Physics [physics]/General Physics [physics.gen-ph], Scaling limit, High Energy Physics - Theory (hep-th), PNAS Plus, tropical geometry, self-organized criticality, Mirror symmetry, Adaptation and Self-Organizing Systems (nlin.AO), symmetry: mirror, proportional growth |
| الوصف: | Tropical Geometry, an established field in pure mathematics, is a place where String Theory, Mirror Symmetry, Computational Algebra, Auction Theory, etc, meet and influence each other. 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. Comment: 32 pages, 7 Figures |
| اللغة: | English |
| URL الوصول: | https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a78415429c65cfda5ec2af3df23adc0b https://hal.archives-ouvertes.fr/hal-01833770 |
| حقوق: | OPEN |
| رقم الأكسشن: | edsair.doi.dedup.....a78415429c65cfda5ec2af3df23adc0b |
| قاعدة البيانات: | OpenAIRE |
| الوصف غير متاح. |