AUTHOR=Kalinin Nikita 

TITLE=Pattern Formation and Tropical Geometry

JOURNAL=Frontiers in Physics

VOLUME=Volume 8 - 2020

YEAR=2020

URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2020.581126

DOI=10.3389/fphy.2020.581126

ISSN=2296-424X

ABSTRACT=Sandpile model exhibits 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 generalizing and applying in a variety of situations.