We consider the directed Abelian sandpile model in the presence of sink sites whose density ft at depth t below the top surface varies as c t . For χ > 1 the disorder is irrelevant. For χ < 1, it is relevant and the model is no longer critical for any nonzero c. For χ = 1 the exponents of the avalanche distributions depend continuously on the amplitude c of the disorder. We calculate this depen...

In this work we study the complexity of Sandpile prediction problems on several classes of directed graphs. We focus our research on low-dimensional directed lattices. We prove some upper and lower bounds for those problems. Our approach is based on the analysis of some reachability problems related to sandpiles.

We study the probability distribution of residence time, T , of the sand grains in the one dimensional abelian sandpile model on a lattice of L sites, for T << L and T >> L. The distribution function decays as exp(−L L2 ). We numerically calculate the coefficient KL for the value of L upto 150 . Interestingly the distribution function has a scaling form 1 La f( T Lb ) with a 6= b for large L. K...

Alessandro Chessa,1,2 Enzo Marinari,1,3 and Alessandro Vespignani4 1Dipartimento di Fisica, Università di Cagliari, Via Ospedale 72, 09124 Cagliari, Italy 2Istituto Nazionale di Fisica della Materia (INFM), Sezione di Cagliari, Italy 3Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Cagliari, Italy 4International Center for Theoretical Physics (ICTP), P.O. Box 586, 34100 Trieste, Italy ...

Confinement phenomenology characteristic of magnetically confined plasmas emerges naturally from a simple sandpile algorithm when the parameter controlling redistribution scalelength is varied. Close analogues are found for enhanced confinement, edge pedestals, and edge localised modes (ELMs), and for the qualitative correlations between them. These results suggest that tokamak observations of ...

This paper presents a generalization of the sandpile model, called the parallel symmetric sandpile model, which inherits the rule of the symmetric sandpile model and implements them in parallel. We prove that although the parallel model produces really less number of fixed points than that by the sequential model, the forms of fixed points of the two models are the same. Moreover, our proof is ...

let $g$ be a non-abelian finite group. in this paper, we prove that $gamma(g)$ is $k_4$-free if and only if $g cong a times p$, where $a$ is an abelian group, $p$ is a $2$-group and $g/z(g) cong mathbb{ z}_2 times mathbb{z}_2$. also, we show that $gamma(g)$ is $k_{1,3}$-free if and only if $g cong {mathbb{s}}_3,~d_8$ or $q_8$.

abstractlet w be a non-empty subset of a free group. the automorphism of a group g is said to be a marginal automorphism, if for all x in g,x^−1alpha(x) in w^*(g), where w^*(g) is the marginal subgroup of g.in this paper, we give necessary and sufficient condition for a purelynon-abelian p-group g, such that the set of all marginal automorphismsof g forms an elementary abelian p-group.

Assume that $(N,L)$, is a pair of finite dimensional nilpotent Lie algebras, in which $L$ is non-abelian and $N$ is an ideal in $L$ and also $mathcal{M}(N,L)$ is the Schur multiplier of the pair $(N,L)$. Motivated by characterization of the pairs $(N,L)$ of finite dimensional nilpotent Lie algebras by their Schur multipliers (Arabyani, et al. 2014) we prove some properties of a pair of nilpoten...

Let G be a group. A subset X of G is a set of pairwise noncommuting elements if xy ̸= yx for any two distinct elements x and y in X. If |X| ≥ |Y | for any other set of pairwise non-commuting elements Y in G, then X is said to be a maximal subset of pairwise non-commuting elements. In this paper we determine the cardinality of a maximal subset of pairwise non-commuting elements in any non-abelian...