Related papers: Island and lake size distributions in Gradient Per…
We theoretically investigate the quantum percolation problem on Lieb lattices in two and three dimensions. We study the statistics of the energy levels through random matrix theory, and determine the level spacing distributions, which, with…
Interdependent networks are ubiquitous in our society, ranging from infrastructure to economics, and the study of their cascading behaviors using percolation theory has attracted much attention in the recent years. To analyze the…
In this work we study the set size distribution estimation problem, where elements are randomly sampled from a collection of non-overlapping sets and we seek to recover the original set size distribution from the samples. This problem has…
Percolation is a model for random damage to a network. It is one of the simplest models that displays a phase transition: when the network is severely damaged, it falls apart in many small connected components, while if the damage is light,…
The results of a density-functional-theory study of the formation energies of (100)- and (111)-faceted steps on the Pt(111) surface, as well as of the barrier for diffusion of an adatom on the flat surface, are presented. The step formation…
Simulations of irreversible growth of extended (fractal and square) islands with critical island sizes i=1 and 2 are performed in broad ranges of coverage \theta and diffusion-to-deposition ratios R in order to investigate scaling of island…
The preparation of many composites requires the intermixing of several macromolecular fluids along with the addition of solid filler particles. These fillers are usuallly polydisperse and there is an extensive experimental evidence that…
The self averaging properties of conductance $g$ are explored in random resistor networks with a broad distribution of bond strengths $P(g)\simg^{\mu-1}$. Distributions of equivalent conductances are estimated numerically on hierarchical…
Clusters generated by the product-rule growth model of Achlioptas, D'Souza, and Spencer on a two-dimensional square lattice are shown to obey qualitatively different scaling behavior than standard (random growth) percolation. The threshold…
The present paper describes a stochastic model of fracture, whose fragment size distribution can be calculated analytically as a power-law-like distribution. The model is basically cascade fracture, but incorporates the effect that each…
In this work, noise is used to analyze the penetration of regular islands in conservative dynamical systems. For this purpose we use the standard map choosing nonlinearity parameters for which a mixed phase space is present. The random…
Lattice mismatch of Cu on Ag(111) produces fast diffusion for special "magic sizes" of islands. A size- and shape-dependent reptation mechanism is responsible for low diffusion barriers. Initiating the reptation mechanism requires a…
For ordinary (independent) percolation on a large class of lattices it is well known that below the critical percolation parameter $p_c$ the cluster size distribution has exponential decay and that power-law behavior of this distribution…
Energy dissipation rates are an important characteristic of turbulence; however, their magnitude in observational profiles can be incorrectly determined owing to their irregular appearance during vertical evolution. By analysing the data…
Sea ice is not continuous and homogeneous on large scales. Its morphology is inherently discrete and made of individual floes. In recent years, sea ice models have incorporated this horizontal heterogeneity. The modelling framework…
Percolation on two-dimensional small-world networks has been proposed as a model for the spread of plant diseases. In this paper we give an analytic solution of this model using a combination of generating function methods and high-order…
Gradually Truncated Log-normal distribution - Size distribution of firms Abstract Many natural and economical phenomena are described through power law or log- normal distributions. In these cases, probability decreases very slowly with…
The average scattered intensity is determined by the optical characteristics of particles in dispersion. The normalized time auto-correlation function of the scattered light intensity $g^{(2)}(\tau) $ includes both the optical and…
Wave propagation in architectured materials, or materials with microstructure, is known to be dependent on the ratio between the wavelength and a characteristic size of the microstructure. Indeed, when this ratio decreases (i.e. when the…
The rate of second layer nucleation -- the formation of a stable nucleus on top of a two-dimensional island -- determines both the conditions for layer-by-layer growth, and the size of the top terrace of multilayer mounds in…