arXiv subjects

Jae Dong Noh

Publications and source records attributed to Jae Dong Noh.

At least 55 records · Page 3Linked to original sources

arXiv2012

Epidemic Threshold of Susceptible-Infected-Susceptible Model on Complex Networks

We demonstrate that the susceptible-infected-susceptible (SIS) model on complex networks can have an inactive Griffiths phase characterized by a slow relaxation dynamics. It contrasts with the mean field theoretical prediction that the SIS model on complex networks is active at any nonzero infection rate. The dynamic fluctuation of infected nodes, ignored in the mean field approach, is responsible for the inactive phase. It is proposed that the question whether the epidemic threshold of the SIS model on complex networks is zero or not can be resolved by the percolation threshold in a model where nodes are occupied in the degree-descending order. Our arguments are supported by the numerical studies on scale-free network models.

physics.soc-ph↗

arXiv2012

Coarsening Dynamics of Nonequilibrium Chiral Ising Models

We investigate a nonequilibrium coarsening dynamics of a one-dimensional Ising spin system with chirality. Only spins at domain boundaries are updated so that the model undergoes a coarsening to either of equivalent absorbing states with all spins + or -. Chirality is imposed by assigning different transition rates to events at down (+-) kinks and up (-+) kinks. The coarsening is characterized by power-law scalings of the kink density $ρ\sim t^{-δ}$ and the characteristic length scale $ξ\sim t^{1/z}$ with time $t$. Surprisingly the scaling exponents vary continuously with model parameters, which is not the case for systems without chirality. These results are obtained from extensive Monte Carlo simulations and spectral analyses of the time evolution operator. Our study uncovers the novel universality class of the coarsening dynamics with chirality.

cond-mat.stat-mech↗

arXiv2012

Fluctuation Relation for Heat

We present a fluctuation relation for heat dissipation in a nonequilibrium system. A nonequilibrium work is known to obey the fluctuation theorem in any time interval $t$. A heat, which differs from a work by an energy change, is shown to satisfy a modified fluctuation relation. Modification is brought by correlation between a heat and an energy change during nonequilibrium processes whose effect may not be negligible even in the $t\to\infty$ limit. The fluctuation relation is derived for overdamped Langevin equation systems, and tested in a linear diffusion system.

cond-mat.stat-mech↗

arXiv2012

Percolation transitions with nonlocal constraint

We investigate percolation transitions in a nonlocal network model numerically. In this model, each node has an exclusive partner and a link is forbidden between two nodes whose $r$-neighbors share any exclusive pair. The $r$-neighbor of a node $x$ is defined as a set of at most $N^r$ neighbors of $x$, where $N$ is the total number of nodes. The parameter $r$ controls the strength of a nonlocal effect. The system is found to undergo a percolation transition belonging to the mean field universality class for $r< 1/2$. On the other hand, for $r>1/2$, the system undergoes a peculiar phase transition from a non-percolating phase to a quasi-critical phase where the largest cluster size $G$ scales as $G \sim N^α$ with $α= 0.74 (1)$. In the marginal case with $r=1/2$, the model displays a percolation transition that does not belong to the mean field universality class.

cond-mat.stat-mech↗

arXiv2012

Phenomenology of ageing in the Kardar-Parisi-Zhang equation

We study ageing during surface growth processes described by the one-dimensional Kardar-Parisi-Zhang equation. Starting from a flat initial state, the systems undergo simple ageing in both correlators and linear responses and its dynamical scaling is characterised by the ageing exponents a=-1/3, b=-2/3, lambda_C=lambda_R=1 and z=3/2. The form of the autoresponse scaling function is well described by the recently constructed logarithmic extension of local scale-invariance.

cond-mat.stat-mech↗

arXiv2012

Condensation and Clustering in the Driven Pair Exclusion Process

We investigate particle condensation in a driven pair exclusion process on one- and two- dimensional lattices under the periodic boundary condition. The model describes a biased hopping of particles subject to a pair exclusion constraint that each particle cannot stay at a same site with its pre-assigned partner. The pair exclusion causes a mesoscopic condensation characterized by the scaling of the condensate size $m_{\rm con}\sim N^β$ and the number of condensates $N_{\rm con}\sim N^α$ with the total number of sites $N$. Those condensates are distributed randomly without hopping bias. We find that the hopping bias generates a spatial correlation among condensates so that a cluster of condensates appears. Especially, the cluster has an anisotropic shape in the two-dimensional system. The mesoscopic condensation and the clustering are studied by means of numerical simulations.

cond-mat.stat-mech↗

arXiv2011

Scaling of cluster heterogeneity in percolation transitions

We investigate a critical scaling law for the cluster heterogeneity $H$ in site and bond percolations in $d$-dimensional lattices with $d=2,...,6$. The cluster heterogeneity is defined as the number of distinct cluster sizes. As an occupation probability $p$ increases, the cluster size distribution evolves from a monodisperse distribution to a polydisperse one in the subcritical phase, and back to a monodisperse one in the supercritical phase. We show analytically that $H$ diverges algebraically approaching the percolation critical point $p_c$ as $H\sim |p-p_c|^{-1/σ}$ with the critical exponent $σ$ associated with the characteristic cluster size. Interestingly, its finite-size-scaling behavior is governed by a new exponent $ν_H = (1+d_f/d)ν$ where $d_f$ is the fractal dimension of the critical percolating cluster and $ν$ is the correlation length exponent. The corresponding scaling variable defines a singular path to the critical point. All results are confirmed by numerical simulations.

cond-mat.stat-mech↗

arXiv2011

Asymmetric simple exclusion process in one-dimensional chains with long-range links

We study the boundary-driven asymmetric simple exclusion process (ASEP) in a one-dimensional chain with long-range links. Shortcuts are added to a chain by connecting $pL$ different pairs of sites selected randomly where $L$ and $p$ denote the chain length and the shortcut density, respectively. Particles flow into a chain at one boundary at rate $α$ and out of a chain at the other boundary at rate $β$, while they hop inside a chain via nearest-neighbor bonds and long-range shortcuts. Without shortcuts, the model reduces to the boundary-driven ASEP in a one-dimensional chain which displays the low density, high density, and maximal current phases. Shortcuts lead to a drastic change. Numerical simulation studies suggest that there emerge three phases; an empty phase with $ ρ= 0 $, a jammed phase with $ ρ= 1 $, and a shock phase with $ 0<ρ<1$ where $ρ$ is the mean particle density. The shock phase is characterized with a phase separation between an empty region and a jammed region with a localized shock between them. The mechanism for the shock formation and the non-equilibrium phase transition is explained by an analytic theory based on a mean-field approximation and an annealed approximation.

cond-mat.stat-mech↗

arXiv2011

Non-equilibrium fluctuations for linear diffusion dynamics

We present the theoretical study on non-equilibrium (NEQ) fluctuations for diffusion dynamics in high dimensions driven by a linear drift force. We consider a general situation in which NEQ is caused by two conditions: (i) drift force not derivable from a potential function and (ii) diffusion matrix not proportional to the unit matrix, implying non-identical and correlated multi-dimensional noise. The former is a well-known NEQ source and the latter can be realized in the presence of multiple heat reservoirs or multiple noise sources. We develop a statistical mechanical theory based on generalized thermodynamic quantities such as energy, work, and heat. The NEQ fluctuation theorems are reproduced successfully. We also find the time-dependent probability distribution function exactly as well as the NEQ work production distribution $P({\mathcal W})$ in terms of solutions of nonlinear differential equations. In addition, we compute low-order cumulants of the NEQ work production explicitly. In two dimensions, we carry out numerical simulations to check out our analytic results and also to get $P({\mathcal W})$. We find an interesting dynamic phase transition in the exponential tail shape of $P({\mathcal W})$, associated with a singularity found in solutions of the nonlinear differential equation. Finally, we discuss possible realizations in experiments.

cond-mat.stat-mech↗

arXiv2010

Particle Condensation in Pair Exclusion Process

Condensation is characterized with a single macroscopic condensate whose mass is proportional to a system size $N$. We demonstrate how important particle interactions are in condensation phenomena. We study a modified version of the zero-range process by including a pair exclusion. Each particle is associated with its own partner, and particles of a pair are forbidden to stay at the same site. The pair exclusion is weak in that a particle interacts with only a single one among all others. It turns out that such a weak interaction changes the nature of condensation drastically. There appear a number of mesoscopic condensates: the mass of a condensate scales as $m_{\rm con}\sim N^{1/2}$ and the number of condensates scales as $N_{\rm con} \sim N^{1/2}$ with a logarithmic correction. These results are derived analytically through a mapping to a solvable model under a certain assumption, and confirmed numerically.

cond-mat.stat-mech↗

arXiv2009

Critical behavior of the Ising model in annealed scale-free networks

We study the critical behavior of the Ising model in annealed scale-free (SF) networks of finite system size with forced upper cutoff in degree. By mapping the model onto the weighted fully connected Ising model, we derive analytic results for the finite-size scaling (FSS) near the phase transition, characterized by the cutoff-dependent two-parameter scaling with four distinct scaling regimes, in highly heterogeneous networks. These results are essentially the same as those found for the nonequilibrium contact process in annealed SF networks, except for an additional complication due to the trivial critical point shift in finite systems. The discrepancy of the FSS theories between annealed and quenched SF networks still remains in the equilibrium Ising model, like some other nonequilibrium models. All of our analytic results are confirmed reasonably well by numerical simulations.

cond-mat.stat-mech↗

arXiv2009

Relaxation dynamics of an elastic string in random media

We investigate numerically the relaxation dynamics of an elastic string in two-dimensional random media by thermal fluctuations starting from a flat configuration. Measuring spatial fluctuations of its mean position, we find that the correlation length grows in time asymptotically as $ξ\sim (\ln t)^{1/\tildeχ}$. This implies that the relaxation dynamics is driven by thermal activations over random energy barriers which scale as $E_B(\ell) \sim \ell^{\tildeχ}$ with a length scale $\ell$. Numerical data strongly suggest that the energy barrier exponent $\tildeχ$ is identical to the energy fluctuation exponent $χ=1/3$. We also find that there exists a long transient regime, where the correlation length follows a power-law dynamics as $ξ\sim t^{1/z}$ with a nonuniversal dynamic exponent $z$. The origin of the transient scaling behavior is discussed in the context of the relaxation dynamics on finite ramified clusters of disorder.

cond-mat.stat-mech↗

arXiv2009

Critical behavior of the contact process in annealed scale-free networks

Critical behavior of the contact process is studied in annealed scale-free networks by mapping it on the random walk problem. We obtain the analytic results for the critical scaling, using the event-driven dynamics approach. These results are confirmed by numerical simulations. The disorder fluctuation induced by the sampling disorder in annealed networks is also explored. Finally, we discuss over the discrepancy of the finite-size-scaling theory in annealed and quenched networks in spirit of the droplet size scale and the linking disorder fluctuation.

cond-mat.stat-mech↗

arXiv2009

Structural phase transition in evolving networks

A network as a substrate for dynamic processes may have its own dynamics. We propose a model for networks which evolve together with diffusing particles through a coupled dynamics, and investigate emerging structural property. The model consists of an undirected weighted network of fixed mean degree and randomly diffusing particles of fixed density. The weight $w$ of an edge increases by the amount of traffics through its connecting nodes or decreases by a constant factor. Edges are removed with the probability $P_{rew.}=1/(1+w)$ and replaced by new ones having $w=0$ at random locations. We find that the model exhibits a structural phase transition between the homogeneous phase characterized by an exponentially decaying degree distribution and the heterogeneous phase characterized by the presence of hubs. The hubs emerge as a consequence of a positive feedback between the particle and the edge dynamics.

cond-mat.stat-mech↗

arXiv2008

Percolation transition in correlated static model

We introduce a correlated static model and investigate a percolation transition. The model is a modification of the static model and is characterized by assortative degree-degree correlation. As one varies the edge density, the network undergoes a percolation transition. The percolation transition is characterized by a weak singular behavior of the mean cluster size and power-law scalings of the percolation order parameter and the cluster size distribution in the entire non-percolating phase. These results suggest that the assortative degree-degree correlation generates a global structural correlation which is relevant to the percolation critical phenomena of complex networks.

cond-mat.stat-mech↗

arXiv2007

Instability in a Network Coevolving with a Particle System

We study a coupled dynamics of a network and a particle system. Particles of density $ρ$ diffuse freely along edges, each of which is rewired at a rate given by a decreasing function of particle flux. We find that the coupled dynamics leads to an instability toward the formation of hubs and that there is a dynamic phase transition at a threshold particle density $ρ_c$. In the low density phase, the network evolves into a star-shaped one with the maximum degree growing linearly in time. In the high density phase, the network exhibits a fat-tailed degree distribution and an interesting dynamic scaling behavior. We present an analytic theory explaining mechanism for the instability and a scaling theory for the dynamic scaling behavior.

cond-mat.stat-mech↗

arXiv2007

Percolation and Loop Statistics in Complex Networks

Complex networks display various types of percolation transitions. We show that the degree distribution and the degree-degree correlation alone are not sufficient to describe diverse percolation critical phenomena. This suggests that a genuine structural correlation is an essential ingredient in characterizing networks. As a signature of the correlation we investigate a scaling behavior in $M_N(h)$, the number of finite loops of size $h$, with respect to a network size $N$. We find that networks, whose degree distributions are not too broad, fall into two classes exhibiting $M_N(h)\sim ({constant})$ and $M_N(h) \sim (\ln N)^ψ$, respectively. This classification coincides with the one according to the percolation critical phenomena.

cond-mat.stat-mech↗

arXiv2007

Percolation transition in networks with degree-degree correlation

We introduce an exponential random graph model for networks with a fixed degree distribution and with a tunable degree-degree correlation. We then investigate the nature of a percolation transition in the correlated network with the Poisson degree distribution. It is found that negative correlation is irrelevant in that the percolation transition in the disassortative network belongs to the same universality class of the uncorrelated network. Positive correlation turns out to be relevant. The percolation transition in the assortative network is characterized by the non-diverging mean size of finite clusters and power-law scalings of the density of the largest cluster and the cluster size distribution in the non-percolating phase as well as at the critical point. Our results suggest that the unusual type percolation transition in the growing network models reported recently may be inherited from the assortative degree-degree correlation.

cond-mat.stat-mech↗