arXiv subjects

Jae Dong Noh

Publications and source records attributed to Jae Dong Noh.

At least 73 records · Page 4Linked to original sources

arXiv2007

Interacting Particle Systems in Complex Networks

We present our recent work on stochastic particle systems on complex networks. As a noninteracting system we first consider the diffusive motion of a random walker on heterogeneous complex networks. We find that the random walker is attracted toward nodes with larger degree and that the random walk motion is asymmetric. The asymmetry can be quantified with the random walk centrality, the matrix formulation of which is presented. As an interacting system, we consider the zero-range process on complex networks. We find that a structural heterogeneity can lead to a condensation phenomenon. These studies show that structural heterogeneity plays an important role in understanding the properties of dynamical systems.

cond-mat.stat-mech↗

arXiv2006

Random field Ising model on networks with inhomogeneous connections

We study a zero-temperature phase transition in the random field Ising model on scale-free networks with the degree exponent $γ$. Using an analytic mean-field theory, we find that the spins are always in the ordered phase for $γ<3$. On the other hand, the spins undergo a phase transition from an ordered phase to a disordered phase as the dispersion of the random fields increases for $γ> 3$. The phase transition may be either continuous or discontinuous depending on the shape of the random field distribution. We derive the condition for the nature of the phase transition. Numerical simulations are performed to confirm the results.

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arXiv2006

Epidemic Dynamics of Interacting Two Particle Species on Scale-free Networks

We study the non-equilibrium phase transition in a model for epidemic spreading on scale-free networks. The model consists of two particle species $A$ and $B$, and the coupling between them is taken to be asymmetric; $A$ induces $B$ while $B$ suppresses $A$. This model describes the spreading of an epidemic on networks equipped with a reactive immune system. We present analytic results on the phase diagram and the critical behavior, which depends on the degree exponent $γ$ of the underlying scale-free networks. Numerical simulation results that support the analytic results are also presented.

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arXiv2005

Stationary and dynamical properties of a zero range process on scale-free networks

We study the condensation phenomenon in a zero range process on scale-free networks. We show that the stationary state property depends only on the degree distribution of underlying networks. The model displays a stationary state phase transition between a condensed phase and an uncondensed phase, and the phase diagram is obtained analytically. As for the dynamical property, we find that the relaxation dynamics depends on the global structure of underlying networks. The relaxation time follows the power law $τ\sim L^z$ with the network size $L$ in the condensed phase. The dynamic exponent $z$ is found to take a different value depending on whether underlying networks have a tree structure or not.

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arXiv2005

Random walk and Pair-Annihilation Processes on Scale-Free Networks

We investigate the dynamic scaling properties of stochastic particle systems on a non-deterministic scale-free network. It has been known that the dynamic scaling behavior depends on the degree distribution exponent of the underlying scale-free network. Our study shows that it also depends on the global structure of the underlying network. In random walks on the tree structure scale-free network, we find that the relaxation time follows a power-law scaling $τ\sim N$ with the network size $N$. And the random walker return probability decays algebraically with the decay exponent which varies from node to node. On the other hand, in random walks on the looped scale-free network, they do not show the power-law scaling. We also study a pair-annihilation process on the scale-free network with the tree and the looped structure, respectively. We find that the particle density decays algebraically in time both cases, but with the different exponent.

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arXiv2005

Complete Condensation in a Zero Range Process on Scale-Free Networks

We study a zero range process on scale-free networks in order to investigate how network structure influences particle dynamics. The zero range process is defined with the particle jumping rate function $p(n)=n^δ$. We show analytically that a complete condensation occurs when $δ\leq δ_c \equiv 1/(γ-1)$ where $γ$ is the degree distribution exponent of the underlying networks. In the complete condensation, those nodes whose degree is higher than a threshold are occupied by macroscopic numbers of particles, while the other nodes are occupied by negligible numbers of particles. We also show numerically that the relaxation time follows a power-law scaling $τ\sim L^z$ with the network size $L$ and a dynamic exponent $z$ in the condensed phase.

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arXiv2005

Growing network model for community with group structure

We propose a growing network model for a community with a group structure. The community consists of individual members and groups, gatherings of members. The community grows as a new member is introduced by an existing member at each time step. The new member then creates a new group or joins one of the groups of the introducer. We investigate the emerging community structure analytically and numerically. The group size distribution shows a power law distribution for a variety of growth rules, while the activity distribution follows an exponential or a power law depending on the details of the growth rule. We also present an analysis of empirical data from on the online communities, the ``Groups'' in \url{http://www.yahoo.com} and the ``Cafe'' in \url{http://www.daum.net}, which shows a power law distribution for a wide range of group sizes.

cond-mat.other↗

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.

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arXiv2005

Asymmetrically coupled directed percolation systems

We introduce a dynamical model of coupled directed percolation systems with two particle species. The two species $A$ and $B$ are coupled asymmetrically in that $A$ particles branch $B$ particles whereas $B$ particles prey on $A$ particles. This model may describe epidemic spreading controlled by reactive immunization agents. We study nonequilibrium phase transitions with focused attention to the multicritical point where both species undergo the absorbing phase transition simultaneously. In one dimension, we find that the inhibitory coupling from $B$ to $A$ is irrelevant and the model belongs to the unidirectionally coupled directed percolation universality class. On the contrary, a mean field analysis predicts that the inhibitory coupling is relevant and a new universality appears with a variable dynamic exponent. Extensive numerical simulations on small-world networks confirm our predictions.

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arXiv2004

Constrained spin dynamics description of random walks on hierarchical scale-free networks

We study a random walk problem on the hierarchical network which is a scale-free network grown deterministically. The random walk problem is mapped onto a dynamical Ising spin chain system in one dimension with a nonlocal spin update rule, which allows an analytic approach. We show analytically that the characteristic relaxation time scale grows algebraically with the total number of nodes $N$ as $T \sim N^z$. From a scaling argument, we also show the power-law decay of the autocorrelation function $C_{\bfsigma}(t)\sim t^{-α}$, which is the probability to find the Ising spins in the initial state ${\bfsigma}$ after $t$ time steps, with the state-dependent non-universal exponent $α$. It turns out that the power-law scaling behavior has its origin in an quasi-ultrametric structure of the configuration space.

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arXiv2004

Scale-free trees: the skeletons of complex networks

We investigate the properties of the spanning trees of various real-world and model networks. The spanning tree representing the communication kernel of the original network is determined by maximizing total weight of edges, whose weights are given by the edge betweenness centralities. We find that a scale-free tree and shortcuts organize a complex network. The spanning tree shows robust betweenness centrality distribution that was observed in scale-free tree models. It turns out that the shortcut distribution characterizes the properties of original network, such as the clustering coefficient and the classification of networks by the betweenness centrality distribution.

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arXiv2004

Random Walks on Complex Networks

We investigate random walks on complex networks and derive an exact expression for the mean first passage time (MFPT) between two nodes. We introduce for each node the random walk centrality $C$, which is the ratio between its coordination number and a characteristic relaxation time, and show that it determines essentially the MFPT. The centrality of a node determines the relative speed by which a node can receive and spread information over the network in a random process. Numerical simulations of an ensemble of random walkers moving on paradigmatic network models confirm this analytical prediction.

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arXiv2002

Novel universality class of absorbing transitions with continuously varying critical exponents

The well-established universality classes of absorbing critical phenomena are directed percolation (DP) and directed Ising (DI) classes. Recently, the pair contact process with diffusion (PCPD) has been investigated extensively and claimed to exhibit a new type of critical phenomena distinct from both DP and DI classes. Noticing that the PCPD possesses a long-term memory effect, we introduce a generalized version of the PCPD (GPCPD) with a parameter controlling the memory effect. The GPCPD connects the DP fixed point to the PCPD point continuously. Monte Carlo simulations show that the GPCPD displays novel type critical phenomena which are characterized by continuously varying critical exponents. The same critical behaviors are also observed in models where two species of particles are coupled cyclically. We suggest that the long-term memory may serve as a marginal perturbation to the ordinary DP fixed point.

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arXiv2002

Exact scaling properties of a hierarchical network model

We report on exact results for the degree $K$, the diameter $D$, the clustering coefficient $C$, and the betweenness centrality $B$ of a hierarchical network model with a replication factor $M$. Such quantities are calculated exactly with the help of recursion relations. Using the results, we show that (i) the degree distribution follows a power law $P_K \sim K^{-γ}$ with $γ= 1+\ln M /\ln (M-1)$, (ii) the diameter grows logarithmically as $D \sim \ln N$ with the number of nodes $N$, (iii) the clustering coefficient of each node is inversely proportional to its degree, $C \propto 1/K$, and the average clustering coefficient is nonzero in the infinite $N$ limit, and (iv) the betweenness centrality distribution follows a power law $P_B \sim B^{-2}$. We discuss a classification scheme of scale-free networks into the universality class with the clustering property and the betweenness centrality distribution.

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arXiv2002

Stability of shortest paths in complex networks with random edge weights

We study shortest paths and spanning trees of complex networks with random edge weights. Edges which do not belong to the spanning tree are inactive in a transport process within the network. The introduction of quenched disorder modifies the spanning tree such that some edges are activated and the network diameter is increased. With analytic random-walk mappings and numerical analysis, we find that the spanning tree is unstable to the introduction of disorder and displays a phase-transition-like behavior at zero disorder strength $ε=0$. In the infinite network-size limit ($N\to \infty$), we obtain a continuous transition with the density of activated edges $Φ$ growing like $Φ\sim ε^1$ and with the diameter-expansion coefficient $Υ$ growing like $Υ\sim ε^2$ in the regular network, and first-order transitions with discontinuous jumps in $Φ$ and $Υ$ at $ε=0$ for the small-world (SW) network and the Barabási-Albert scale-free (SF) network. The asymptotic scaling behavior sets in when $N\gg N_c$, where the crossover size scales as $N_c\sim ε^{-2}$ for the regular network, $N_c \sim \exp[αε^{-2}]$ for the SW network, and $N_c \sim \exp[α|\ln ε| ε^{-2}]$ for the SF network. In a transient regime with $N\ll N_c$, there is an infinite-order transition with $Φ\sim Υ\sim \exp[-α/ (ε^2 \ln N)]$ for the SW network and $\sim \exp[ -α/ (ε^2 \ln N/\ln\ln N)]$ for the SF network. It shows that the transport pattern is practically most stable in the SF network.

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arXiv2002

Numerical study of the disorder-driven roughening transition in an elastic manifold in a periodic potential

We investigate the roughening phase transition of a $(3+1)$-dimensional elastic manifold driven by the completion between a periodic pinning potential and a randomly distributed impurities. The elastic manifold is modeled by a solid-on-solid type interface model, and universal features of the transition from a flat phase (for strong periodic potential) to a rough phase (for strong disorder) are studied at zero temperature using a combinatorial optimization algorithm technique. We find a {\it continuous} transition with a set of numerically estimated critical exponents that we compare with analytic results and those for a periodic elastic medium.

cond-mat.stat-mech↗

arXiv2001

Anomalous Roughness, Localization, and Globally Constrained Random Walks

The scaling properties of a random walker subject to the global constraint that it needs to visit each site an even number of times are determined. Such walks are realized in the equilibrium state of one dimensional surfaces that are subject to dissociative dimer-type surface dynamics. Moreover, they can be mapped onto unconstrained random walks on a random surface, and the latter corresponds to a non-Hermitian random free fermion model which describes electron localization near a band edge. We show analytically that the dynamic exponent of this random walk is $z=d+2$ in spatial dimension $d$. This explains the anomalous roughness, with exponent $α=1/3$, in one dimensional equilibrium surfaces with dissociative dimer-type dynamics.

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arXiv2001

Disorder Driven Critical Behavior of Periodic Elastic Media in a Crystal Potential

We study a lattice model of a three-dimensional periodic elastic medium at zero temperature with exact combinatorial optimization methods. A competition between pinning of the elastic medium, representing magnetic flux lines in the mixed phase of a superconductor or charge density waves in a crystal, by randomly distributed impurities and a periodic lattice potential gives rise to a continuous phase transition from a flat phase to a rough phase. We determine the critical exponents of this roughening transition via finite size scaling obtaining $ν\approx1.3$, $β\approx0.05$, $γ/ν\approx2.9$ and find that they are universal with respect to the periodicity of the lattice potential. The small order parameter exponent is reminiscent of the random field Ising critical behavior in 3$d$.

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