Related papers: Percolation with Multiple Giant Clusters
In the context of percolation in a regular tree, we study the size of the largest cluster and the length of the longest run starting within the first d generations. As d tends to infinity, we prove almost sure and weak convergence results.
Order parameter fluctuations (the largest cluster size distribution) are studied within a three-dimensional bond percolation model on small lattices. Cumulant ratios measuring the fluctuations exhibit distinct features near the percolation…
The paramagnetic-ferromagnetic transition in the Ising model can be described as percolation of suitably defined clusters. We have tried to extend such picture to the confinement-deconfinement transition of SU(2) pure gauge theory, which is…
In a recent Letter, Friedman and Landsberg discussed the underlying mechanism of explosive phase transitions on complex networks [Phys. Rev. Lett. 103, 255701 (2009)]. This Brief Report presents a modest, though more insightful extension of…
The mechanical and transport properties of jammed materials originate from an underlying per- colating network of contact forces between the grains. Using extensive simulations we investigate the force-percolation transition of this…
We investigate the triggering of star formation and the formation of stellar clusters in molecular clouds that form as the ISM passes through spiral shocks. The spiral shock compresses gas into $\sim$100 pc long main star formation ridge,…
We study clustering and percolation phenomena in the Vicsek model, taken here in its capacity of prototypical model for dry aligning active matter. Our results show that the order-disorder transition is not related in any way to a…
Wet granular materials are characterized by a defined bond energy in their particle interaction such that breaking a bond implies an irreversible loss of a fixed amount of energy. Associated with the bond energy is a nonequilibrium…
Consider "Frozen Random Walk" on $\mathbb{Z}$: $n$ particles start at the origin. At any discrete time, the leftmost and rightmost $\lfloor{\frac{n}{4}}\rfloor$ particles are "frozen" and do not move. The rest of the particles in the "bulk"…
A significant fraction of clusters of galaxies are observed to have substructure, which implies that merging between clusters and subclusters is a rather common physical process of cluster formation. It still remains unclear how cluster…
The fractal structure of directed percolation clusters, grown at the percolation threshold inside parabolic-like systems, is studied in two dimensions via Monte Carlo simulations. With a free surface at y=\pm Cx^k and a dynamical exponent…
In this paper, we consider random trees associated with the genealogy of Crump-Mode-Jagers processes and perform Bernoulli bond-percolation whose parameter depends on the size of the tree. Our purpose is to show the existence of a giant…
Crystal growth and crystal coalescence processes in supercooled systems strongly depend on the concentration of crystallization centers. We perform atomistic dynamics simulations of the crystallization process in the ultrathin metallic film…
A scaling theory is developed for diffusion-limited cluster aggregation in a porous medium, where the primary particles and clusters stick irreversibly to the walls of the pore space as well as to each other. Three scaling regimes are…
Crucial to gaining control over crystallisation in multicomponent materials or accurately modelling rheological behaviour of magma flows is to understand the mechanisms by which crystal nuclei form. The microscopic nature of such nuclei,…
The formation of stellar clusters dictates the pace at which galaxies evolve, and solving the question of their formation will undoubtedly lead to a better understanding of the Universe as a whole. While it is well known that star clusters…
We study the two-dimensional domain morphology of twisted nematic liquid crystals during their phase-ordering kinetics [R. A. L. Almeida, Phys. Rev. Lett. 131 (2023) 268101], which is a physical candidate to self-generate critical clusters…
We present a kinetic model of crystal growth of polymers of finite molecular weight. Experiments help to classify polymer crystallization broadly into two kinetic regimes. One is observed in melts or in high molar mass polymer solutions and…
The formation of galaxy clusters is a complicated process that probably involves the accretion of galaxies in groups, as observed in nearby clusters, such as Virgo and Fornax. The members of the groups undergo "preprocessing" prior to…
The physical and chemical properties of metal nanoparticles differ significantly from those of free metal atoms as well as from the properties of bulk metals, and therefore, they may be viewed as a transition regime between the two physical…