Related papers: Voter model on Sierpinski fractals
We propose a mathematical model to describe the athermal fluctuations of thin sheets driven by the type of random driving that might be experienced prior to weak crumpling. The model is obtained by merging the F\"oppl-von K\'arm\'an…
Topological phases of matter have been extensively investigated in solid state materials and classical wave systems with integer dimensions. However, topological states in non-integer dimensions remain largely unexplored. Fractals, being…
The voter model with stirring is a variant of the classical voter model on $\mathbb{Z}^d$ with two possible opinions (0 and 1) that, in addition to copying neighbouring opinions at rate 1, allows voters to interchange their opinions at…
We study the Ginzburg-Landau model with a nonlocal quartic term as a simple phenomenological model for superconductors in the presence of coupling between the vortex lattice and the underlying crystal lattice. In mean-field theory, our…
We calculate zeros of the $q$-state Potts model partition function on $m$'th-iterate Sierpinski graphs, $S_m$, in the variable $q$ and in a temperature-like variable, $y$. We infer some asymptotic properties of the loci of zeros in the…
We investigate how the topology of small-world networks affects the dynamics of the voter model for opinion formation. We show that, contrary to what occurs on regular topologies with local interactions, the voter model on small-world…
We use Dirac matrix representations of the Clifford algebra to build fracton models on the lattice and their effective Chern-Simons-like theory. As an example we build lattice fractons in odd $D$ spatial dimensions and their $(D+1)$…
We obtain a nature generalization for an affine Sierpinski carpet and Sierpinski triangle to $n$-dimensional space, by using the generations and characterizations of affinely-equivalent Sierpinski carpet. Exactly, in this paper, a Menger…
This paper presents an interesting experimental example of voter-model statistics in biology. In recent work on mouse tail-skin, where proliferating cells are confined to a two-dimensional layer, we showed that cells proliferate and…
In this paper, we introduce a couple of dynamical systems that are related to the Chaos Game. We begin by discussing different methods of generating the Sierpinski gasket. Then we show how the transition from random to uniform selection…
There has been much recent work on multiwinner voting systems. However, sometimes a committee is highly structured, and if we want to vote for such a committee, our voting method should be more structured as well. We consider committees…
The structure and the degenracy of the ground state of a fully-frustrated XY-model are investigated for the case of a dice lattice geometry. The results are applicable for the description of Josephson junction arrays and thin…
The voter model is a classical interacting particle system, modelling how global consensus is formed by local imitation. We analyse the time to consensus for a particular family of voter models when the underlying structure is a scale-free…
We establish properties of a new type of fractal which has partial self similarity at all scales. For any collection of iterated functions systems with an associated probability distribution and any positive integer V there is a…
In this work, we examine the relationship between geometry and spectrum of regions with fractal boundary. The relationship is well-understood for fractal harps in one dimension, but largely open for fractal drums in larger dimensions. To…
We study the spectral properties and local topology of the Kane-Mele-Rashba model on a Sierpinski Carpet (SC) fractal, constructed from a rectangular flake with an underlying honeycomb arrangement and open boundary conditions. When the…
We introduce and investigate new models of the Chern-Simons type in the three-dimensional spacetime, focusing on the existence of compact vortices. The models are controlled by potentials driven by a single real parameter that can be used…
The method of counting loops for calculating the partition function of the Ising model on the two dimensional square lattice is extended to lacunary planar lattices, especially scale invariant fractal lattices, the Sierpi\'nsky carpets with…
We study ballistic aggregation on a two dimensional square lattice, where particles move ballistically in between momentum and mass conserving coalescing collisions. Three models are studied based on the shapes of the aggregates: in the…
Pattern forming with externally imposed symmetry is ubiquitous in nature but lightly studied.We present experimental studies of pattern formation and selection by spatial periodic forcing in rapidly rotating convection. We observe symmetric…