Related papers: Analytical approach to directed sandpile models on…

Undirected hyperbolic graph models have been extensively used as models of scale-free small-world networks with high clustering coefficient. Here we presented a simple directed hyperbolic model, where nodes randomly distributed on a…

We study a general model of random dynamical simplicial complexes and derive a formula for the asymptotic degree distribution. This asymptotic formula encompasses results for a number of existing models, including random Apollonian networks…

We numerically study the directed version of the fixed energy sandpile. On a closed square lattice, the dynamical evolution of a fixed density of sand grains is studied. The activity of the system shows a continuous phase transition around…

An Abelian sandpile model is considered on the Husimi lattice of square plaquettes. Exact expressions for the distribution of height probabilities in the Self-Organized Critical state are derived. The two-point correlation function for the…

We consider spectral methods that uncover hidden structures in directed networks. We establish and exploit connections between node reordering via (a) minimizing an objective function and (b) maximizing the likelihood of a random graph…

In this paper we propose a model for describing advection dynamics on distance-weighted directed graphs. To this end we establish a set of key properties, or axioms, that a discrete advection operator should satisfy, and prove that there…

We examine exhaustively the behavior of avalanches in critical height sandpile models based in two- and three-dimensional lattices of various topologies. We get that for two-dimensional lattices the spatial and temporal distributions…

The main purpose of the present paper is to establish a link between quadrature surfaces (potential theoretic concept) and sandpile dynamics (Laplacian growth models). For this aim, we introduce a new model of Laplacian growth on the…

We present a two-dimensional system which exhibits features of self-organized criticality. The avalanches which occur on the surface of a pile of rice are found to exhibit finite size scaling in their probability distribution. The critical…

Abelian sandpile models, both deterministic, such as the Bak, Tang, Wiesenfeld (BTW) model [P. Bak, C. Tang and K. Wiesenfeld, Phys. Rev. Lett. {\bf 59}, 381 (1987)], and stochastic, such as the Manna model [S.S. Manna, J. Phys. A {\bf 24},…

Conformally symplectic systems include mechanical systems with a friction proportional to the velocity. Geometrically, these systems transform a symplectic form into a multiple of itself making the systems dissipative or expanding. In the…

We give conditions for the existence of the Minkowski content of limit sets stemming from infinite conformal graph directed systems. As an application we obtain Minkowski measurability of Apollonian gaskets, provide explicit formulae of the…

Sandpiles form one of the largest class of models displaying a critical stationary state. Despite a few decades of research, a comprehensive and systematic rigorous characterisation of their spatial and, even more, time dependent properties…

In this paper we study $\infty$-Laplacian type diffusion equations in weighted graphs obtained as limit as $p\to \infty$ to two types of $p$-Laplacian evolution equations in such graphs. We propose these diffusion equations, that are…

We analyze stellar streams in action-angle coordinates combined with recent local direct acceleration measurements to provide joint constraints on the potential of our Galaxy. Our stream analysis uses the Kullback-Leibler divergence with a…

For a variety of quenched random spin systems on an Apollonian network, including ferromagnetic and antiferromagnetic bond percolation and the Ising spin glass, we find the persistence of ordered phases up to infinite temperature over the…

Uniform spherical beads were used to explore the behavior of a granular system near its critical angle of repose on a conical bead pile. We found two tuning parameters that could take the system to a critical point where a simple power-law…

The BTW sandpile model is considered on three dimensional percolation lattice which is tunned with the occupation parameter $p$. Along with the three-dimensional avalanches, we study the energy propagation in two-dimensional cross-sections.…

This paper provides a framework to evaluate the performance of single and double integrator networks over arbitrary directed graphs. Adopting vehicular network terminology, we consider quadratic performance metrics defined by the L2-norm of…

The analysis of complex networks has so far revolved mainly around the role of nodes and communities of nodes. However, the dynamics of interconnected systems is commonly focalised on edge processes, and a dual edge-centric perspective can…