Sandpiles Subjected to Sinusoidal Drive

Abstract

This paper considers a sandpile model subjected to a sinusoidal external drive with the time period $T$. We develop a theoretical model for the Green function in a large $T$ limit, which predicts that the avalanches are anisotropic and elongated in the oscillation direction. We track the problem numerically and show that the system shows additionally a regime where the avalanches are elongated in the perpendicular direction with respect to the oscillations. We find a transition point between these two regimes. The power spectrum of avalanche size and the grains wasted from the parallel and perpendicular directions are studied. These functions show power-law behaviour in terms of the frequency with exponents, which run with $T$.

References in corpus (23)

• The abelian sandpile and related models
• Power laws and Self-Organized Criticality in Theory and Nature
• Universality in Sandpile Models
• Universality in sandpiles
• Scaling of waves in the Bak-Tang-Wiesenfeld sandpile model
• Sandpile avalanche dynamics on scale-free networks
• Power spectra of self-organized critical sandpiles
• Some Results and a Conjecture for Manna's Stochastic Sandpile Model
• Large scale simulations of the Zhang sandpile model
• Interplay between network structure and self-organized criticality
• Abelian Sandpile Model: a Conformal Field Theory Point of View
• Universality classes in directed sandpile models
• Pre-logarithmic and logarithmic fields in a sandpile model
• Avalanche frontiers in dissipative abelian sandpile model as off-critical SLE(2)
• Direct Evidence for Conformal Invariance of Avalanche Frontier in Sandpile Models
• Logarithmic conformal invariance in the Abelian sandpile model
• Critical properties of a dissipative sandpile model on small world networks
• Bak-Tang-Wiesenfeld Model in the Finite Range Random Link Lattice
• Some Properties of Sandpile Models as Prototype of Self-Organized Critical Systems
• Sandpile model on an optimized scale-free network on Euclidean space
• Statistical Investigation of Avalanches of Three Dimensional Small-World Networks and their Boundary and Bulk Cross-Sections
• The abelian sandpile model on a random binary tree
• Fillips in Sandpiles; Spanning Avalanches, Bifurcation and Temporal oscillations