Related papers: Threshold-Controlled Geometric Reorganization in 2…
A region of two-dimensional space has been filled randomly with large number of growing circular discs allowing only a `slight' overlapping among them just before their growth stop. More specifically, each disc grows from a nucleation…
A bonded particle model is used to explore how variations in the material properties of brittle, isotropic solids affect critical behavior in fragmentation. To control material properties, a new model is proposed which includes breakable…
The formation of sintering bridges in amorphous powders affects both flow behavior and perceived material quality. When sintering is driven by surface tension, bridges emerge sequentially, favoring contacts between smaller particles first.…
Bulk-boundary correspondence is the emergence of features at the boundary of a material that are dependent on and yet distinct from the properties of the bulk of the material. The diverse applications of this idea in topological insulators…
Shape-morphing networks of mesoscale filaments are a common hierarchical feature in biology and hold significant potential for a range of technological applications, from micro-muscles to shape-morphing optical devices. Here, we demonstrate…
We present in this paper a quantitative method for defining void size in large-scale structure based on percolation threshold density. Beginning with two-dimensional gravitational clustering simulations smoothed to the threshold of…
In this paper we analyze several anisotropic bootstrap percolation models in three dimensions. We present the order of magnitude for the metastability threshold for a fairly general class of models. In our proofs we use an adaptation of the…
The dimensionality of a system profoundly influences its physical behaviour, leading to the emergence of different states of matter in many-body quantum systems. In lower dimensions, fluctuations increase and lead to the suppression of…
Traditional percolation theory assumes static microscopic rules, limiting its ability to describe real-world complex systems where macroscopic order actively regulates local interactions. Here, we introduce feedback percolation, an unified…
At sufficiently low temperatures and high densities, repulsive spherical particles in two-dimensions (2d) form close-packed structures with six-fold symmetry. By contrast, when the interparticle interaction has an attractive anisotropic…
By bootstrap percolation we mean the following deterministic process on a graph $G$. Given a set $A$ of vertices "infected" at time 0, new vertices are subsequently infected, at each time step, if they have at least $r\in\mathbb{N}$…
We analyze the critical connectivity of systems of penetrable $d$-dimensional spheres having size distributions in terms of weighed random geometrical graphs, in which vertex coordinates correspond to random positions of the sphere centers…
Discrete geometries in hyperbolic space are of longstanding interest in pure mathematics and have come to recent attention in holography, quantum information, and condensed matter physics. Working at a purely geometric level, we describe…
We examine the interplay between anisotropy and percolation, i.e., the spontaneous formation of a system spanning cluster in an anisotropic model. We simulate an extension of a benchmark model of continuum percolation, the Boolean model,…
Higher order interactions are increasingly recognised as a fundamental aspect of complex systems ranging from the brain to social contact networks. Hypergraph as well as simplicial complexes capture the higher-order interactions of complex…
The bulk-boundary correspondence, which links a bulk topological property of a material to the existence of robust boundary states, is a hallmark of topological insulators. However, in crystalline topological materials the presence of…
The excess adsorption $\Gamma $ in two-dimensional Ising strips $(\infty \times L)$ subject to identical boundary fields, at both one-dimensional surfaces decaying in the orthogonal direction $j$ as $-h_1j^{-p}$, is studied for various…
Collective organization in physical, biophysical, and biological systems often emerges from many weak, local interactions, yet the resulting global structures display striking regularities and apparent limits in diversity. Existing…
Understanding how microscopic interactions control macroscopic phase transitions is central to quantum materials, where charge density waves (CDWs), Mott states, and superconductivity often compete. In $1T$-TaS$_2$, this competition is tied…
Scaling theory predicts complete localization in $d=2$ in quantum systems belonging to orthogonal class (i.e. with time-reversal symmetry and spin-rotation symmetry). The conductance $g$ behaves as $g \sim exp(-L/l)$ with system size $L$…