Pattern Formation and Tropical Geometry

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Pattern Formation and Tropical Geometry. / Kalinin, Nikita.

In: Frontiers in Physics, Vol. 8, 581126, 20.11.2020.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{277e874046ae4adeb97035a4147eefc1,

title = "Pattern Formation and Tropical Geometry",

abstract = "Sandpile models exhibit fascinating pattern structures: patches, characterized by quadratic functions, and line-shaped patterns (also called solitons, webs, or linear defects). It was predicted by Dhar and Sadhu that sandpile patterns with line-like features may be described in terms of tropical geometry. We explain the main ideas and technical tools—tropical geometry and discrete superharmonic functions—used to rigorously establish certain properties of these patterns. It seems that the aforementioned tools have great potential for generalization and application in a variety of situations.",

keywords = "discrete harmonic analysis, pattern formation, sandpile, solitons, tropical curves, CELLULAR-AUTOMATA, WAVES, SKIN",

author = "Nikita Kalinin",

note = "Funding Information: NK was supported in part by Young Russian Mathematics award. Support from the Basic Research Program of the National Research University Higher School of Economics was gratefully acknowledged. Publisher Copyright: {\textcopyright} Copyright {\textcopyright} 2020 Kalinin. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.",

year = "2020",

month = nov,

day = "20",

doi = "10.3389/fphy.2020.581126",

language = "English",

volume = "8",

journal = "Frontiers in Physics",

issn = "2296-424X",

publisher = "MIT Press",

}

RIS

TY - JOUR

T1 - Pattern Formation and Tropical Geometry

AU - Kalinin, Nikita

N1 - Funding Information: NK was supported in part by Young Russian Mathematics award. Support from the Basic Research Program of the National Research University Higher School of Economics was gratefully acknowledged. Publisher Copyright: © Copyright © 2020 Kalinin. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2020/11/20

Y1 - 2020/11/20

N2 - Sandpile models exhibit fascinating pattern structures: patches, characterized by quadratic functions, and line-shaped patterns (also called solitons, webs, or linear defects). It was predicted by Dhar and Sadhu that sandpile patterns with line-like features may be described in terms of tropical geometry. We explain the main ideas and technical tools—tropical geometry and discrete superharmonic functions—used to rigorously establish certain properties of these patterns. It seems that the aforementioned tools have great potential for generalization and application in a variety of situations.

AB - Sandpile models exhibit fascinating pattern structures: patches, characterized by quadratic functions, and line-shaped patterns (also called solitons, webs, or linear defects). It was predicted by Dhar and Sadhu that sandpile patterns with line-like features may be described in terms of tropical geometry. We explain the main ideas and technical tools—tropical geometry and discrete superharmonic functions—used to rigorously establish certain properties of these patterns. It seems that the aforementioned tools have great potential for generalization and application in a variety of situations.

KW - discrete harmonic analysis

KW - pattern formation

KW - sandpile

KW - solitons

KW - tropical curves

KW - CELLULAR-AUTOMATA

KW - WAVES

KW - SKIN

UR - http://www.scopus.com/inward/record.url?scp=85097249590&partnerID=8YFLogxK

U2 - 10.3389/fphy.2020.581126

DO - 10.3389/fphy.2020.581126

M3 - Article

AN - SCOPUS:85097249590

VL - 8

JO - Frontiers in Physics

JF - Frontiers in Physics

SN - 2296-424X

M1 - 581126

ER -

ID: 71947877

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