AUTHOR=Kalinin Nikita TITLE=Pattern Formation and Tropical Geometry JOURNAL=Frontiers in Physics VOLUME=8 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 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.