相关论文: A New Universality for Random Sequential Depositio…
Spatial random graphs capture several important properties of real-world networks. We prove quenched results for the continuum space version of scale-free percolation introduced in [DW18]. This is an undirected inhomogeneous random graph…
Consider a discrete locally finite subset $\Gamma$ of $R^d$ and the complete graph $(\Gamma,E)$, with vertices $\Gamma$ and edges $E$. We consider Gibbs measures on the set of sub-graphs with vertices $\Gamma$ and edges $E'\subset E$. The…
We study the percolative properties of bi-dimensional systems generated by a random sequential adsorption of line-segments on a square lattice. As the segment length grows, the percolation threshold decreases, goes through a minimum and…
A new method is used to measure the stress and elastic constants of purely entropic phantom networks, in which a fraction $p$ of neighbors are tethered by inextensible bonds. We find that close to the percolation threshold $p_c$ the shear…
The statistics of a long closed self-avoiding walk (SAW) or polymer ring on a $ d $-dimensional lattice obeys hyperscaling. The combination $ p_N \left\langle R^2 \right\rangle^{ d/2}_N\mu^{ -N}, $ (where $ p_N $ is the number of…
Jamming, or dynamical arrest, is a transition at which many particles stop moving in a collective manner. In nature it is brought about by, for example, increasing the packing density, changing the interactions between particles, or…
One of the most well-known classical results for site percolation on the square lattice is the equation p_c + p_c^* = 1. In words, this equation means that for all values different from p_c of the parameter p the following holds: Either…
We have evaluated a universal ratio between diffusion constants of the ring polymer with a given knot $K$ and a linear polymer with the same molecular weight in solution through the Brownian dynamics under hydrodynamic interaction. The…
The frequency dependence of the Raman coupling coefficient $C(\omega)$ is calculated numerically for square and cubic percolation clusters. No general scaling law in terms of the macroscopic parameters such as the fractal dimension $D$ or…
The connection between friction and jamming in granular media, molecular glasses, and complex fluids is explored. The paper first reviews the way friction is measured, the types of results that are observed, and what is known about the…
Dense suspension of particles in a liquid exhibit rich, non-Newtonian behaviors such as shear thickening and shear jamming. Shear thickening is known to be enhanced by increasing the particles' frictional interactions and also by making…
Site percolation in a distorted simple cubic lattice is characterized numerically employing the Newman-Ziff algorithm. Distortion is administered in the lattice by systematically and randomly dislocating its sites from their regular…
On hypothesis of self-scaling co-flows in tapered rectanglar PMMA micro-channels for producing mono-dispersed liquid cells, universal scalings through all liquid detaching regimes are found under a self-similarity frame. Pan-dripping and…
In $r$-neighbor bootstrap percolation on the vertex set of a graph $G$, a set $A$ of initially infected vertices spreads by infecting, at each time step, all uninfected vertices with at least $r$ previously infected neighbors. When the…
Extensive Monte-Carlo simulations were performed to study bond percolation on the simple cubic (s.c.), face-centered cubic (f.c.c.), and body-centered cubic (b.c.c.) lattices, using an epidemic kind of approach. These simulations provide…
Percolation on a plane is usually associated with clusters spanning two opposite sides of a rectangular system. Here we investigate three-leg clusters generated on a square lattice and spanning the three sides of equilateral triangles. If…
We study mixed long-range percolation on the square lattice. Each vertical edge of unit length is independently open with probability $\varepsilon$, and each horizontal edge of length $i$ is independently open with probability $p_i$. Also,…
The fractions of samples spanning a lattice at its percolation threshold are found by computer simulation of random site-percolation in two- and three-dimensional hypercubic lattices using different boundary conditions. As a byproduct we…
Our interest is in the scaled joint distribution associated with $k$-increasing subsequences for random involutions with a prescribed number of fixed points. We proceed by specifying in terms of correlation functions the same distribution…
We introduce a method to estimate continuum percolation thresholds and illustrate its usefulness by investigating geometric percolation of non-interacting line segments and disks in two spatial dimensions. These examples serve as models for…