arXiv subjects

Seung-Woo Son

Publications and source records attributed to Seung-Woo Son.

43 records · Page 3Linked to original sources

arXiv2011

Exact solutions for mass-dependent irreversible aggregations

We consider the mass-dependent aggregation process (k+1)X -> X, given a fixed number of unit mass particles in the initial state. One cluster is chosen proportional to its mass and is merged into one either with k-neighbors in one dimension, or -- in the well-mixed case -- with k other clusters picked randomly. We find the same combinatorial exact solutions for the probability to find any given configuration of particles on a ring or line, and in the well-mixed case. The mass distribution of a single cluster exhibits scaling laws and the finite size scaling form is given. The relation to the classical sum kernel of irreversible aggregation is discussed.

physics.data-an↗

arXiv2011

Explosive Percolation is Continuous, but with Unusual Finite Size Behavior

We study four Achlioptas type processes with "explosive" percolation transitions. All transitions are clearly continuous, but their finite size scaling functions are not entire holomorphic. The distributions of the order parameter, the relative size $s_{\rm max}/N$ of the largest cluster, are double-humped. But -- in contrast to first order phase transitions -- the distance between the two peaks decreases with system size $N$ as $N^{-η}$ with $η> 0$. We find different positive values of $β$ (defined via $< s_{\rm max}/N > \sim (p-p_c)^β$ for infinite systems) for each model, showing that they are all in different universality classes. In contrast, the exponent $Θ$ (defined such that observables are homogeneous functions of $(p-p_c)N^Θ$) is close to -- or even equal to -- 1/2 for all models.

cond-mat.dis-nn↗

arXiv2011

Irreversible Aggregation and Network Renormalization

Irreversible aggregation is revisited in view of recent work on renormalization of complex networks. Its scaling laws and phase transitions are related to percolation transitions seen in the latter. We illustrate our points by giving the complete solution for the probability to find any given state in an aggregation process $(k+1)X\to X$, given a fixed number of unit mass particles in the initial state. Exactly the same probability distributions and scaling are found in one dimensional systems (a trivial network) and well-mixed solutions. This reveals that scaling laws found in renormalization of complex networks do not prove that they are self-similar.

physics.data-an↗

arXiv2010

Enhancing synchronization by directionality in complex networks

We proposed a method called residual edge-betweenness gradient (REBG) to enhance synchronizability of networks by assignment of link direction while keeping network topology and link weight unchanged. Direction assignment has been shown to improve the synchronizability of undirected networks in general, but we find that in some cases incommunicable components emerge and networks fail to synchronize. We show that the REBG method can effectively avoid the synchronization failure ($R=λ_{2}^{r}/λ_{N}^{r}=0$) which occurs in the residual degree gradient (RDG) method proposed in Phys. Rev. Lett. 103, 228702 (2009). Further experiments show that REBG method enhance synchronizability in networks with community structure as compared with the RDG method.

cond-mat.dis-nn↗

arXiv2009

LinkRank: Finding communities in directed networks

To identify communities in directed networks, we propose a generalized form of modularity in directed networks by introducing a new quantity LinkRank, which can be considered as the PageRank of links. This generalization is consistent with the original modularity in undirected networks and the modularity optimization methods developed for undirected networks can be directly applied to directed networks by optimizing our new modularity. Also, a model network, which can be used as a benchmark network in further community studies, is proposed to verify our method. Our method is supposed to find communities effectively in citation- or reference-based directed networks.

physics.soc-ph↗

arXiv2009

Anomalous Scaling Behavior in Polymer Thin Film Growth by Vapor Deposition

As a first step to understand anomalous kinetic roughening with multifractality in recent experiments of the vapor deposition polymerization (VDP) growth, we study a simple toy model of the VDP growth in a (1+1)-dimensional lattice, along with monomer diffusion, polymer nucleation, limited active end bonding, and shadowing effects. Using extensive numerical simulations, we observe that the global roughness exponent is different from the local one. It is argued that such anomalies in VDP growth are attributed to the instability induced by the nonlocal shadowing effects on active ends of polymers. As varying the ratio of diffusion coefficient to the deposition rate by cosine flux, we also discuss the role of diffusion in kinetic roughening of the polymer thin film growth, which is quite different from that of the metal or semiconductor film growth. Finally, we suggest its (2+1)-dimensional version, which can be directly compared with experimental results.

cond-mat.stat-mech↗

arXiv2005

Random field Ising model and community structure in complex networks

We propose a method to find out the community structure of a complex network. In this method the ground state problem of a ferromagnetic random field Ising model is considered on the network with the magnetic field $B_s = +\infty$, $B_{t} = -\infty$, and $B_{i\neq s,t}=0$ for a node pair $s$ and $t$. The ground state problem is equivalent to the so-called maximum flow problem, which can be solved exactly numerically with the help of a combinatorial optimization algorithm. The community structure is then identified from the ground state Ising spin domains for all pairs of $s$ and $t$. Our method provides a criterion for the existence of the community structure, and is applicable to unweighted and weighted networks equally well. We demonstrate the performance of the method by applying it to the Barabási-Albert network, Zachary karate club network, the scientific collaboration network, and the stock price correlation network.

cond-mat.stat-mech↗