Absorbing boundaries in the conserved Manna model
Arthur Hipke, Sven Lubeck, and Haye Hinrichsen
TL;DR
This paper investigates the effects of absorbing boundaries in the conserved Manna model across different dimensions, providing analytical and mean field solutions for critical exponents and PDEs.
Contribution
It offers the first analytical computation of the surface critical exponent in one dimension and explores the mean field limit in higher dimensions.
Findings
Analytical surface critical exponent in 1D derived
Mean field PDE solutions demonstrated for d>4
Insights into boundary effects in conserved sandpile models
Abstract
The conserved Manna model with a planar absorbing boundary is studied in various space dimensions. We present a heuristic argument that allows one to compute the surface critical exponent in one dimension analytically. Moreover, we discuss the mean field limit that is expected to be valid in d>4 space dimensions and demonstrate how the corresponding partial differential equations can be solved.
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