We study the degree of nonhomogeneous lattice ideals over arbitrary fields, and give formulas to compute the degree in terms of the torsion of certain factor groups of Zs and in terms of relative volumes of lattice polytopes. We also study primary decompositions of lattice ideals over an arbitrary field using the Eisenbud–Sturmfels theory of binomial ideals over algebraically closed fields. We ...

Proof. If the edge (r, s) from the root to the sink is included in the spanning tree, then each of the principal branches of Tn may be assigned an oriented spanning tree independently, so there are t n−1 such spanning trees. On the other hand, if (r, s) is not included in the spanning tree, there is a directed path r → x1 → . . . → xn−1 → s in the spanning tree from the root to the sink. In thi...

We insert some asymmetries in the continuous Abelian sandpile models, such as directedness and ellipticity. We analyze probability distribution of different heights and also find the field theory corresponding to the models. Also we find the fields associated with some height variables. PACS : 05.65+b, 89.75.Da

We propose a new continuum description of the dynamics of sandpile surfaces, which recognizes the existence of two populations of grains: immobile and rouing. Trie rolling grains are carried clown the slope with a constant drift velocity and have a certain dispersion constant. We introduce a simple bilinear approximation for the interconversion

In this article, we give a partial description of the sandpile group of the cone of the cartesian product of graphs in function of the sandpile group of the cone of their factors. Also, we introduce the concept of uniform homomorphism of graphs and prove that every surjective uniform homomorphism of graphs induces an injective homomorphism between their sandpile groups. As an application of the...

We analyze the dynamics of growth of the number of congressmen supporting the resolution HR1207 to audit the Federal Reserve. The plot of the total number of co-sponsors as a function of time is of “Devil’s staircase” type. The distribution of the numbers of new co-sponsors joining during a particular day (step height) follows a power law. The distribution of the length of intervals between add...

We define stabilizability of an infinite volume height configuration and of a probability measure on height configurations. We show that for high enough densities, a probability measure cannot be stabilized. We also show that in some sense the thermodynamic limit of the uniform measures on the recurrent configurations of the abelian sandpile model (ASM) is a maximal element of the set of stabil...

Consider a network of processors (sites) in which each site x has a finite set N(x) of neighbors. There is a transition function f that for each site x computes the next state ξ(x) from the states in N(x). But these transitions (updates) are applied in arbitrary order, one or many at a time. If the state of site x at time t is η(x , t) then let us define the sequence ζ(x , 0),ζ(x , 1), . . . by...

We consider the subgroup of the abelian sandpile group of the grid graph consisting of configurations of sand that are symmetric with respect to central vertical and horizontal axes. We show that the size of this group is (i) the number of domino tilings of a corresponding weighted rectangular checkerboard; (ii) a product of special values of Chebyshev polynomials; and (iii) a double-product wh...

The scaling properties of granular flows down an inclined plane are investigated in a model previously proposed to describe surface flows on a sandpile. Introducing a depth dependent friction, we are able to reproduce the results obtained experimentally by Pouliquen @Phys. Fluids 11, 542 ~1999!; 11, 1956 ~1999!# on both the fronts velocities and their shapes. © 2002 American Institute of Physic...