Pattern Formation and Tropical Geometry

Nikita Kalinin*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Article number581126
JournalFrontiers in Physics
Volume8
DOIs
StatePublished - 20 Nov 2020
Externally publishedYes

Keywords

  • discrete harmonic analysis
  • pattern formation
  • sandpile
  • solitons
  • tropical curves

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