Related papers: Nanopercolation
We propose a method of studying the continuous percolation of aligned objects as a limit of a corresponding discrete model. We show that the convergence of a discrete model to its continuous limit is controlled by a power-law dependency…
We investigate the dynamics of passive particles in a two-dimensional incompressible open flow composed of a fixed topographical point vortex and a background current with a periodic component. The tracer dynamics is found to be typically…
Methane hydrate nucleation under nanoconfinement remains poorly understood due to the complex interplay between geometric restriction and molecular ordering. Here, we investigate the structural organization of water-methane systems confined…
Frozen percolation on the binary tree was introduced by Aldous around fifteen years ago, inspired by sol-gel transitions. We investigate a version of the model on the triangular lattice, where connected components stop growing ("freeze") as…
As circuitry approaches single nanometer length scales, it is important to predict the stability of metals at these scales. The behavior of metals at larger scales can be predicted based on the behavior of dislocations, but it is unclear if…
Recent developments in hydraulic fracturing (fracking) have enabled the recovery of large quantities of natural gas and oil from old, low permeability shales. These developments include a change from low-volume, high-viscosity fluid…
Our first experience of dimension typically comes in the intuitive Euclidean sense: a line is one dimensional, a plane is two-dimensional, and a volume is three-dimensional. However, following the work of Mandelbrot \cite{mandelbrot},…
Numerical investigation of critical exponents on a hypercubic with L^d random sites with L up to $33 and d up to 7 show that above the critical dimension the phase transitions in Ising model and percolation are not alike.
Directed and heterogeneous hypergraphs capture directional higher-order interactions with intrinsically asymmetric functional dependencies among nodes. As a result, damage to certain nodes can suppress entire hyperedges, whereas failure of…
The Gaussian model of discontinuous percolation, recently introduced by Ara\'ujo and Herrmann [Phys. Rev. Lett., 105, 035701 (2010)], is numerically investigated in three dimensions, disclosing a discontinuous transition. For the…
Results of systematic molecular dynamics studies of ethanol-water mixtures, over the entire concentration range, were reported previously to agree with experimental X-ray diffraction data. These simulated systems are analyzed in this work…
We present Monte Carlo estimates for site and bond percolation thresholds in simple hypercubic lattices with 4 to 13 dimensions. For d<6 they are preliminary, for d >= 6 they are between 20 to 10^4 times more precise than the best previous…
The methods of determining the fractal dimension and irregularity scale in simulated galaxy catalogs and the application of these methods to the data of the 2dF and 6dF catalogs are analyzed. Correlation methods are shown to be correctly…
We study low-Reynolds-number fluid flow through a two-dimensional porous medium modeled as a Lorentz gas. Using extensive finite element simulations we fully resolve the flow fields for packing fractions approaching the percolation…
We study the slippage on hierarchical fractal superhydrophobic surfaces, and find an unexpected rich behavior for hydrodynamic friction on these surfaces. We develop a scaling law approach for the effective slip length, which is validated…
We establish a correspondence between Pavlovian conditioning processes and fractals. The association strength at a training trial corresponds to a point in a disconnected set at a given iteration level. In this way, one can represent a…
In the paper we investigate statistical and topological properties of fractional Brownian polymer chains, equipped with the short-range volume interactions. The attention is paid to statistical properties of collapsed conformations with the…
We investigate bond- and site-percolation models on several two-dimensional lattices numerically, by means of transfer-matrix calculations and Monte Carlo simulations. The lattices include the square, triangular, honeycomb kagome and diced…
Consider a Boolean model $\Sigma$ in $\R^d$. The centers are given by a homogeneous Poisson point process with intensity $\lambda$ and the radii of distinct balls are i.i.d.\ with common distribution $\nu$. The critical covered volume is…
Macroscopic fibres of carbon nanotubes are hierarchical structures combining long building blocks preferentially oriented along the fibre axis and a large porosity arising from the imperfect packing of bundles. Synchrotron small-angle X-ray…