Nucleation pathways on complex networks

Abstract

Identifying nucleation pathway is important for understanding the kinetics of first-order phase transitions in natural systems. In the present work, we study nucleation pathway of the Ising model in homogeneous and heterogeneous networks using the forward flux sampling method, and find that the nucleation processes represent distinct features along pathways for different network topologies. For homogeneous networks, there always exists a dominant nucleating cluster to which relatively small clusters are attached gradually to form the critical nucleus. For heterogeneous ones, many small isolated nucleating clusters emerge at the early stage of the nucleation process, until suddenly they form the critical nucleus through a sharp merging process. Moreover, we also compare the nucleation pathways for different degree-mixing networks. By analyzing the properties of the nucleating clusters along the pathway, we show that the main reason behind the different routes is the heterogeneous character of the underlying networks.

Studying rare events using forward-flux sampling: Recent breakthroughs and future outlook

“…In recent years, FFS has been extensively utilized for studying the sensitivity of the nucleation kinetics in the Ising and lattice gas models to the existence and energetic properties of impurities, 34,36,41 mechanical deformations, 37,38 internal and external interfaces, 35,36,[41][42][43] and the topological properties of the underlying network. 39,40,44,45 Since nucleation will only occur if the underlying transition is first-order, all these simulations were conducted in the presence of an external magnetic field or chemical potential, and the starting basin A is always set to the respective metastable phase in each system. Due to the simplicity of the Ising model, it is possible to conduct FFS using both global and local order parameters, namely the total number of up spins (or occupied sites), and the size of the largest cluster of the new phase, respectively.…”

“…In three subsequent papers 40,44,45 from the same group, nucleation was studied in Barabási-Albert (BA) 191 scale-free random networks.…”

“…They found the enhancement to be more prominent when those impurities are added to high-connectivity nodes. In a later paper, Shen et al 44 compared the mechanism of nucleation in degree-uncorrelated and degree-correlated BA networks. In uncorrelated networks, nucleation was a gradual process.…”

“…Here we present calculations of the rate, mechanism, and free energy profiles of evaporation of water confined between the nanoscale hydrophobic plate-like solutes displayed in Fig. 1, using FFS (31,39,44) in conjunction with MD. Within each atomically detailed solute, each nearest-neighbor pair interacts via a harmonic spring, the strength of which dictates the flexibility of the plate.…”

“…Therefore, developing more robust and efficient variants and implementations of FFS has become an intense focus of research, with earlier methodological efforts covered in several comprehensive reviews published shortly after its development. 32,33 In recent years, FFS has been extensively utilized for studying a wide variety of rare events, such as phase transitions in the Ising [34][35][36][37][38][39][40][41][42][43][44][45] and Potts 46-49 models, crystal nucleation, 50-80 evaporation, [81][82][83][84][85][86] phase separation, 87,88 coalescence, 89 wetting, 90,91 protein folding, rupture and aggregation, [92][93][94][95][96][97][98] DNA hybridization, [99][100][101][102][103][104][105] polymer relaxation and translocation, [106][107][108][109][110][111] ion transport 112 and genetic [113]…”