Related papers: Divisible sandpile on Sierpinski gasket graphs
J. Kigami has laid the foundations of what is now known as analysis on fractals, by allowing the construction of an operator of the same nature of the Laplacian, defined locally, on graphs having a fractal character. The Sierpinski gasket…
Diffusion models, as a novel generative paradigm, have achieved remarkable success in various image generation tasks such as image inpainting, image-to-text translation, and video generation. Graph generation is a crucial computational task…
A granular media lattice gas (GMLG) model is used to study avalanches in a two-dimensional granular pile. We demonstrate the efficiency of the algorithm by showing that several features of the non-critical behaviour of real sandpile…
We construct, for the first time, an off-shell supersymmetric continuous spin gauge theory in 4-dimensional Minkowski spacetime, in both constrained and unconstrained Lagrangian formulations. As an extension to the on-shell description [1],…
The Snyder-de Sitter (SdS) model which is invariant under the action of the de Sitter group, is an example of a noncommutative spacetime with three fundamental scales. In this paper, we considered the massless Dirac fermions in graphene…
We study the rotor router model and two deterministic sandpile models. For the rotor router model in $\mathbb{Z}^d$, Levine and Peres proved that the limiting shape of the growth cluster is a sphere. For the other two models, only bounds in…
Recent progress in the fabrication of materials has made it possible to create arbitrary non-periodic two-dimensional structures in the quantum plasmon regime. This paves the way for exploring the plasmonic properties of electron gases in…
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…
This paper investigates the supercloseness of a singularly perturbed convection diffusion problem using the direct discontinuous Galerkin (DDG) method on a Shishkin mesh. The main technical difficulties lie in controlling the diffusion term…
We introduce Discrete Voxel Diffusion (DVD), a discrete diffusion framework to generate, assess, and edit sparse voxels for SLat (Structured LATent) based 3D generative pipelines. Although discrete diffusion has not generally displaced…
Given a graph $G$, we form a random subgraph $G_p$ by including each edge of $G$ independently with probability $p$. We provide an asymptotic expansion of the expected number of independent sets in random subgraphs of regular bipartite…
We introduce an (equi-)affine invariant diffusion geometry by which surfaces that go through squeeze and shear transformations can still be properly analyzed. The definition of an affine invariant metric enables us to construct an invariant…
We consider criteria for the differentiability of functions with continuous Laplacian on the Sierpinski Gasket and its higher-dimensional variants $SG_N$, $N>3$, proving results that generalize those of Teplyaev. When $SG_N$ is equipped…
In this work, we investigate an original strategy in order to derive a statistical modeling of the interface in gas-liquid two-phase flows through geometrical variables. The con- tribution is two-fold. First it participates in the…
This paper constitutes our initial effort in developing sparse grid discontinuous Galerkin (DG) methods for high-dimensional partial differential equations (PDEs). Over the past few decades, DG methods have gained popularity in many…
We consider the fractal Sierpi\'{n}ski gasket or carpet graph in dimension $d\geq 2,$ denoted by $G$. At time $0$, we place a Poisson point process of particles onto the graph and let them perform independent simple random walks, which in…
The majority of graphs whose sandpile groups are known are either regular or simple. We give an explicit formula for a family of non-regular multi-graphs called thick cycles. A thick cycle graph is a cycle where multi-edges are permitted.…
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…
Diffusion models achieve state-of-the-art performance in generating realistic objects and have been successfully applied to images, text, and videos. Recent work has shown that diffusion can also be defined on graphs, including graph…
We investigate the dynamics of spreading in a regime where the shape of the drop is close to a spherical cap. The latter simplification is applicable in the late (viscous) stage of spreading for highly viscous drops with a diameter below…