Related papers: Diffusive limits on the Penrose tiling

We study random coloring of the hexagons of a honeycomb lattice into $2^{n-1}$ colors (that is the standard Potts model at infinite temperature). It may be considered as a generalization of percolation to $n$ pairwise independent, but…

We investigate the relationships between the parabolic Harnack inequality, heat kernel estimates, some geometric conditions, and some analytic conditions for random walks with long range jumps. Unlike the case of diffusion processes, the…

This paper discusses a modified penetration theory where the time scale for the momentum wall layer is based on the onset of ejections from the wall but the time scale for the thermal layer is based on the unsteady state diffusion of heat…

In this paper we present analytical and random walk based solutions to diffusion in semi-permeable layered media with varying diffusivity. We propose a new random walk transit model (hybrid model) based on treating the membrane permeability…

Three-dimensional icosahedral random tilings with rhombohedral cells are studied in the semi-entropic model. We introduce a global energy measure defined by the variance of the quasilattice points in the orthogonal space. The internal…

This article studies discrete height functions on the discrete hypertorus. These are functions on the vertices of this hypertorus graph for which the derivative satisfies a specific condition on each edge. We then perform a random walk on…

We computed by a Monte Carlo method the thermal relaxation of a polycrystalline thin film deposited on a Penrose lattice. The thin film was modelled by a 2 dimensional array of elementary domains, which have each a given height. During the…

The probability distributions of discrete-time quantum walks have been often investigated, and many interesting properties of them have been discovered. The probability that the walker can be find at a position is defined by diagonal…

This paper is concerned about random walks on random environments in the lattice $\mathbb{Z}^d$. This model is analyzed through ergodicity in the form of the logarithmic Sobolev inequality. We assume that the environments are random…

We propose a design of interlaced wire medium with quasicrystalline lattice based on five-fold rotation symmetry Penrose tiling. The transport properties of this structure are studied. We distinguish two transport regimes, namely,…

Pump-probe experiments and polarizing microscopy are applied to examine temperature and heat flow in metallic magnetic superlattices on glass substrates. A model of heat diffusion in thin layers for cylindrical symmetry, equivalent to the…

We show that the well known two-dimensional Penrose tiling admits an infinite number of independent scaling factors and an infinite number of inflation centers.

This paper is concerned with the study of a diffusive perturbation of the linear LSW model introduced by Carr and Penrose. A main subject of interest is to understand how the presence of diffusion acts as a selection principle, which…

The potential of lead-halide perovskites for realistic applications is currently hindered by their limited long-term stability under functional activation. While the role of lattice flexibility in the thermal response of perovskites has…

A straightforward analytical scheme is proposed for computing the long-time, asymptotic mean velocity and dispersivity (effective diffusivity) of a particle undergoing a discrete biased random walk on a periodic lattice amongst an array of…

In this paper characterizations of graphs satisfying heat kernel estimates for a wide class of space-time scaling functions are given. The equivalence of the two-sided heat kernel estimate and the parabolic Harnack inequality is also shown…

Results have been moved to a published article, see arXiv:0812.2669v4[math.PR]

We give a simple formula for the looping rate of loop-erased random walk on a finite planar graph. The looping rate is closely related to the expected amount of sand in a recurrent sandpile on the graph. The looping rate formula is…

We investigate the geometric properties displayed by the magnetic patterns developing on a two-dimensional Ising system, when a diffusive thermal dynamics is adopted. Such a dynamics is generated by a random walker which diffuses throughout…

We consider a random walk on the first quadrant of the square lattice, whose increment law is, roughly speaking, homogeneous along a finite number of half-lines near each of the two boundaries, and hence essentially specified by…