Layer Features of the Lattice Gas Model for Self-Organized Criticality

TL;DR

This paper analyzes the layer-specific features of an asymmetric lattice gas model to understand the emergence of 1/f-noise from white noise input, considering various boundary conditions and particle interactions.

Contribution

It provides a layer-by-layer analysis of the lattice gas model, revealing how 1/f-noise develops and varies across layers under different driving conditions.

Findings

Power spectra of lattice layers exhibit different $eta_x$ exponents.

$eta_x$ approaches 1.9 near the outer boundary.

High boundary drive influences the power spectrum of diffusing particles.

Abstract

A layer-by-layer description of the asymmetric lattice gas model for 1/f-noise suggested by Jensen [Phys. Rev. Lett. 64, 3103 (1990)] is presented. The power spectra of the lattice layers in the direction perpendicular to the particle flux is studied in order to understand how the white noise at the input boundary evolves, on the average, into 1/f-noise for the system. The effects of high boundary drive and uniform driving force on the power spectrum of the total number of diffusing particles are considered. In the case of nearest-neighbor particle interactions, high statistics simulation results show that the power spectra of single lattice layers are characterized by different $\beta_x$ exponents such that $\beta_x \to 1.9$ as one approaches the outer boundary.