相关论文: Sandpiles and superconductors: dual variational fo…
Similar evolutionary variational inequalities appear as convenient formulations for continuous quasistationary models for sandpile growth, formation of a network of lakes and rivers, magnetization of type-II superconductors, and…
Similar evolutionary variational and quasi-variational inequalities with gradient constraints arise in the modeling of growing sandpiles and type-II superconductors. Recently, mixed formulations of these inequalities were used for…
The two dimensional directed sandpile with dissipation is transformed into a (1+1) dimensional problem with discrete space and continuous `time'. The master equation for the conditional probability that K grains preserve their initial order…
Two-component sandpile models are investigated numerically and theoretically. Monte Calro simulations are performed to show that probability distribution functions of avalanche size and lifetime obey power laws whose exponents are…
Rotational constraint representing a local external bias generally has non-trivial effect on the critical behavior of lattice statistical models in equilibrium critical phenomena. In order to study the effect of rotational bias in a out of…
The magnetic flux dynamics of type-II superconductors within the critical state regime is posed in a generalized framework, by using a variational theory supported by well established physical principles. The equivalence between the…
A directed dissipative sandpile model is studied in the two-dimension. Numerical results indicate that the long time steady states of this model are critical when grains are dropped only at the top or, everywhere. The critical behaviour is…
Elastoplastic and constitutive equation theories are two approaches based on very different assumptions for creating a continuum theory for the stress distributions in a static sandpile. Both models produce the same surprising prediction…
We perform large-scale simulations of directed sandpile models with both deterministic and stochastic toppling rules. Our results show the existence of two distinct universality classes. We also provide numerical simulations of directed…
We introduce a one-dimensional sandpile model with $N$ different particle types and an infinitesimal driving rate. The parameters for the model are the N^2 critical slopes for one type of particle on top of another. The model is trivial…
Existence of a solution to the quasi-variational inequality problem arising in a model for sand surface evolution has been an open problem for a long time. Another long-standing open problem concerns determining the dual variable, the flux…
Spatial self-similarity is a hallmark of critical phenomena. We study the dynamic process of percolation, in which bonds are incrementally added to an initially empty lattice until the system becomes fully occupied. By tracking the gap --…
Using variational methods, we obtain several multiplicity results for double phase problems that involve variable exponents and a new type of critical growth. This new critical growth is better suited for double phase problems when compared…
We study sandpile models with stochastic toppling rules and having sticky grains so that with a non-zero probability no toppling occurs, even if the local height of pile exceeds the threshold value. Dissipation is introduced by adding a…
We present large scale simulations of a stochastic sandpile model in two dimensions. We use moments analysis to evaluate critical exponents and finite size scaling method to consistently test the obtained results. The general picture…
I report large-scale Monte Carlo studies of a one-dimensional height-restricted stochastic sandpile using the quasistationary simulation method. Results for systems of up to 50 000 sites yield estimates for critical exponents that differ…
We use a phenomenological field theory, reflecting the symmetries and conservation laws of sandpiles, to compare the driven dissipative sandpile, widely studied in the context of self-organized criticality, with the corresponding…
Kinetic equations, which explicitly take into account the branching nature of sandpile avalanches, are derived. The dynamics of the sandpile model is described by the generating functions of a branching process. Having used the results…
We investigate the behavior of a two-state sandpile model subjected to a confining potential in one and two dimensions. From the microdynamical description of this simple model with its intrinsic exclusion mechanism, it is possible to…
We present and analyze a model of an evolving sandpile surface in (2 + 1) dimensions where the dynamics of mobile grains ({\rho}(x, t)) and immobile clusters (h(x, t)) are coupled. Our coupling models the situation where the sandpile is…