Related papers: Scaling and Inverse Scaling in Anisotropic Bootstr…
In standard bootstrap percolation, a subset A of the n x n grid is initially infected. A new site is then infected if at least two of its neighbours are infected, and an infected site stays infected forever. The set A is said to percolate…
Percolation is a cornerstone concept in physics, providing crucial insights into critical phenomena and phase transitions. In this study, we adopt a kinetic perspective to reveal the scaling behaviors of higher-order gaps in the largest…
Consider a $p$-random subset $A$ of initially infected vertices in the discrete cube $[L]^3$, and assume that the neighbourhood of each vertex consists of the $a_i$ nearest neighbours in the $\pm e_i$-directions for each $i \in \{1,2,3\}$,…
We present a review of the recent progress on percolation scaling limits in two dimensions. In particular, we will consider the convergence of critical crossing probabilities to Cardy's formula and of the critical exploration path to…
We propose a novel finite size scaling analysis for percolation transition observed in complex networks. While it is known that cooperative systems in growing networks often undergo an infinite order transition with inverted…
In this work we study the large scale structure bias in models of anisotropic inflation. We use the Peak Background Splitting method in Excursion Set Theory to find the scale-dependent bias. We show that the amplitude of the bias is…
The strength of perpendicular anisotropy is known to drive the spin reorientation in thin magnetic films. Here we consider the effect different order anisotropies have on two phase transitions; the spin reorientation transition and the…
We discuss anisotropic scaling of long-range dependent linear random fields $X$ on ${\mathbb{Z}}^2$ with arbitrary dependence axis (direction in the plane along which the moving-average coefficients decay at a smallest rate). The scaling…
The piezoresistive response of granular metals under uniaxial strain is strongly dependent on the concentration of the conducting phase. Here we show that the piezoresistive anisotropy is reduced as the system approaches its percolation…
In two dimensional isotropic scale invariant theories, the time scaling of the entanglement entropy of a segment is fixed via the conformal symmetry. We consider scale invariance in a more general sense and show that in integrable theories…
We test the universal finite-size scaling of the cluster mass order parameter in two-dimensional (2D) isotropic and directed continuum percolation models below the percolation threshold by computer simulations. We found that the simulation…
We analyze the bootstrap approach (a dual optimization method to the variational approach) to one-dimensional spin chains, leveraging semidefinite programming to extract numerical results. We study how correlation functions in the ground…
We revisit the Bootstrap Percolation model, leveraging recent mathematical advances linking it with its local counterpart. This new perspective resolves, for the first time, historic discrepancies between Monte Carlo simulations and…
We study the existence of distinct failure regimes in a model for fracture in fibrous materials. We simulate a bundle of parallel fibers under uniaxial static load and observe two different failure regimes: a catastrophic and a slowly…
Influence of weak uniaxial small-scale anisotropy on the stability of inertial-range scaling regimes in a model of a passive transverse vector field advected by an incompressible turbulent flow is investigated by means of the field…
We study the numerical anisotropy existent in compact difference schemes as applied to hyperbolic partial differential equations, and propose an approach to reduce this error and to improve the stability restrictions based on a previous…
In this paper a modification of the standard Bootstrap Percolation model is introduced. In our modification a discrete time update rule is constructed that allows for non-monotonicity - unlike its classical counterpart. External inputs to…
We investigate the down-hill creep of a layer of granular material on a slope caused by an oscillatory variation of the size of the particles. The material is modeled as an athermal two dimensional polydisperse system of soft disks under…
Model of a passive scalar field advected by the compressible Gaussian strongly anisotropic velocity field with the covariance $\propto \delta(t-t^{\prime})|{\bf x}-{\bf x^{\prime}}|^{2\epsilon}$ is studied by using the field theoretic…
Scaling laws describe how learning performance improves with data, compute, or training time, and have become a central theme in modern deep learning. We study this phenomenon in a canonical nonlinear model: phase retrieval with anisotropic…