We investigate the condensation phase transitions of conserved-mass aggregation (CA) model on weighted scale-free networks (WSFNs). In WSFNs, the weight $w_{ij}$ is assigned to the link between the nodes $i$ and $j$. We consider the symmetric weight given as $w_{ij}=(k_i k_j)^α$. In CA model, the mass $m_i$ on the randomly chosen node $i$ diffuses to a linked neighbor of $i$,$j$, with the rate $T_{ji}$ or an unit mass chips off from the node $i$ to $j$ with the rate $ωT_{ji}$. The hopping probability $T_{ji}$ is given as $T_{ji}= w_{ji}/\sum_{<l>} w_{li}$, where the sum runs over the linked neighbors of the node $i$. On the WSFNs, we numerically show that a certain critical $α_c$ exists below which CA model undergoes the same type of the condensation transitions as those of CA model on regular lattices. However for $α\geq α_c$, the condensation always occurs for any density $ρ$ and $ω$. We analytically find $α_c = (γ-3)/2$ on the WSFN with the degree exponent $γ$. To obtain $α_c$, we analytically derive the scaling behavior of the stationary distribution $P^{\infty}_k$ of finding a walker at nodes with degree $k$, and the probability $D(k)$ of finding two walkers simultaneously at the same node with degree $k$. We find $P^{\infty}_k \sim k^{α+1-γ}$ and $D(k) \sim k^{2(α+1)-γ}$ respectively. With $P^{\infty}_k$, we also show analytically and numerically that the average mass $m(k)$ on a node with degree $k$ scales as $k^{α+1}$ without any jumps at the maximal degree of the network for any $ρ$ as in the SFNs with $α=0$.
We draw an analogy between droplet formation in dilute particle and polymer systems. Our arguments are based on finite-size scaling results from studies of a two-dimensional lattice gas to three-dimensional bead-spring polymers. To set the results in perspective, we compare with in part rigorous theoretical scaling laws for canonical condensation in a supersaturated gas at fixed temperature, and derive corresponding scaling predictions for an undercooled gas at fixed density. The latter allows one to efficiently employ parallel multicanonical simulations and to reach previously not accessible …
A conserved generalized zero range process is considered in which two sites interact such that particles hop from the more populated site to the other with a probability $p$. The steady state particle distribution function $P(n)$ is obtained using both analytical and numerical methods. The system goes through several phases as $p$ is varied. In particular, a condensate phase appears for $p_l < p < p_c$, where the bounding values depend on the range of interaction, with $p_c < 0.5$ in general. Analysis of $P(n)$ in the condensate phase using a known scaling form shows there is universal behavio…
We calculate the bulk-diffusion coefficient and the conductivity in a broad class of conserved-mass aggregation processes on a ring of discrete sites. These processes involve chipping and fragmentation of masses, which diffuse around and aggregate upon contact with their neighboring masses. We find that, even in the absence of microscopic time reversibility, the systems satisfy an Einstein relation, which connects the ratio of the conductivity and the bulk-diffusion coefficient to mass fluctuation. Interestingly, when aggregation dominates over chipping, the conductivity or, equivalently, the …
We use extreme value statistics to study the dynamics of coarsening in aggregation-fragmentation models which form condensates in the steady state. The dynamics is dominated by the formation of local condensates on a coarsening length scale which grows in time in both the zero range process and conserved mass aggregation model. The local condensate mass distribution exhibits scaling, which implies anomalously large fluctuations, with mean and standard deviation both proportional to the coarsening length. Remarkably, the state of the system during coarsening is governed not by the steady state,…
In a process of aggregation, a finite number of particles merge irreversibly to create growing clusters. In this work, impact of particular initial conditions: monodisperse, power-law, exponential, and inspired by condensation nuclei was tested against several aggregation processes: constant, additive, product, electrorheological, anti-social, Berry's, Brownian, shear, and gravitational kernels. Coagulating systems consisting of a thousand monomers were observed in the late time of the evolution, for the moment when only fifty clusters were left in the system. In this way, the impact of partic…
Real space condensation is known to occur in stochastic models of mass transport in the regime in which the globally conserved mass density is greater than a critical value. It has been shown within models with factorised stationary states that the condensation can be understood in terms of sums of independent and identically distributed random variables: these exhibit condensation when they are conditioned to a large deviation of their sum. It is well understood that the condensation, whereby one of the random variables contributes a finite fraction to the sum, occurs only if the underlying p…
Mass conservation in chemical species appears in a broad class of reaction-diffusion systems (RDs) and is known to bring about coarsening of the pattern in chemical concentration. Recent theoretical studies on RDs with mass conservation (MCRDs) reported that the interfacial curvature between two states contributes to the coarsening process, reminiscent of phase separation phenomena. However, since MCRDs do not presuppose a variational principle, it is largely unknown whether description of surface tension is operative or not. In this study, we numerically and theoretically explore the coarseni…
Scaling and Condensation of Dry Active Matter Around Circular Obstacles
Faculdade de Física, Universidade Federal do Pará（帕拉联邦大学物理学院）；MMML Lab, Department of Physics, University of Latvia（拉脱维亚大学物理系）；Departamento de Física, Universidade Federal do Ceará（塞阿拉联邦大学物理系）
