相关论文: Effect of Dimensionality on the Percolation Thresh…
Scale-free percolation is a percolation model on $\mathbb{Z}^d$ which can be used to model real-world networks. We prove bounds for the graph distance in the regime where vertices have infinite degrees. We fully characterize transience vs.…
Consider the classical $(2+1)$-dimensional Solid-On-Solid model above a hard wall on an $L\times L$ box of $\bbZ^2$. The model describes a crystal surface by assigning a non-negative integer height $\eta_x$ to each site $x$ in the box and 0…
The random Lorentz gas (RLG) is a minimal model for transport in disordered media. Despite the broad relevance of the model, theoretical grasp over its properties remains weak. For instance, the scaling with dimension d of its localization…
In this paper, a new framework for crossover of scaling law is proposed: a crossover of scaling law can be described by a self-similar solution. A crossover emerges as a result of the interference from similarity parameters of the higher…
We present simulations of a 3-d percolation model studied recently by K.J. Schrenk et al. [Phys. Rev. Lett. 116, 055701 (2016)], obtained with a new and more efficient algorithm. They confirm most of their results in spite of larger systems…
We study the evolution of the particle density, dn/d\eta at fixed \eta with the beam rapidity Y in the framework of string percolation model. Our main results are: (i) The width of the "plateau" increases proportionally to Y, (ii) limiting…
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…
Convex codes were recently introduced as models for neural codes in the brain. Any convex code $\C$ has an associated minimal embedding dimension $d(\C)$, which is the minimal Euclidean space dimension such that the code can be realized by…
Percolation theory has become a useful tool for the analysis of large-scale wireless networks. We investigate the fundamental problem of characterizing the critical density $\lambda_c^{(d)}$ for $d$-dimensional Poisson random geometric…
This work extends the universal finite-size scaling framework for continuum percolation from two-dimensional (2D) to quasi-three-dimensional (Q3D) stick systems, in which sequentially deposited wires of finite diameter stack vertically on a…
This paper presents a Monte-Carlo study of percolation in a distorted square lattice, in which, the adjacent sites are not equidistant. Starting with an undistorted lattice, the position of the lattice sites are shifted through a tunable…
A power law is postulated for both site and bond percolation thresholds. The formula writes $p_c=p_0[(d-1)(q-1)]^{-a}d^{\ b}$, where $d$ is the space dimension and $q$ the coordination number. All thresholds up to $d\rightarrow \infty$ are…
While hard-sphere models form the foundation of theoretical condensed matter physics, real systems often exhibit some degree of softness. We present a theoretical and numerical study of a class of nearly hard-sphere systems, generalized…
The author discusses particular solutions of a second order equation designated by source equation. This equation is special because the metric of the space where it is written is influenced by the solution, rendering the equation…
Hyperbolic lattices interpolate between finite-dimensional lattices and Bethe lattices and are interesting in their own right with ordinary percolation exhibiting not one, but two, phase transitions. We study four constraint percolation…
Simplicial complexes are increasingly used to understand the topology of complex systems as different as brain networks and social interactions. It is therefore of special interest to extend the study of percolation to simplicial complexes.…
This note introduces a novel paradigm for conformal defects with continuously adjustable dimensions. Just as the standard $\varepsilon$ expansion interpolates between integer spacetime dimensions, a new parameter, $\delta$, is used to…
In a recent paper, we have reported a universal power law for both site and bond percolation thresholds in any Bravais lattice with q equivalent nearest neighbors in dimension d. We now extend it to three different classes of lattices which…
This short note is devoted to deriving scaling but hyperscaling violating solutions in a generalised Einstein-Maxwell-Dilaton theory with an arbitrary number of scalars and vectors. We obtain analytic solutions in some special case and…
For a delta-correlated velocity field, simultaneous correlation functions of a passive scalar satisfy closed equations. We analyze the equation for the four-point function. To describe a solution completely, one has to solve the matching…