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Random-Walk and Pair-Annihilation Processes on Scale-Free Networks
노재동,김상우 한국물리학회 2006 THE JOURNAL OF THE KOREAN PHYSICAL SOCIETY Vol.48 No.II
We investigate the dynamic scaling properties of stochastic particle systems on a non-deterministic scale-free network. It is 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 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 in both cases, but with a different exponent.
Interacting Particle Systems in Complex Networks
노재동 한국물리학회 2007 THE JOURNAL OF THE KOREAN PHYSICAL SOCIETY Vol.50 No.1I
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.
Multiple Condensates in a Driven Diffusive System
노재동,김상우 한국물리학회 2010 THE JOURNAL OF THE KOREAN PHYSICAL SOCIETY Vol.56 No.3
We investigate the nature of condensation in a driven diffusive system. Being motivated by evolving network dynamics, we consider particle dynamics with and without a pairwise repulsion. Without the pairwise repulsion, the model exhibits a condensation with a single macroscopic condensate. When the pairwise repulsion is turned on, a particle cannot hop to a site that is occupied by its own preassigned mate. Surprisingly, the pairwise repulsion breaks a macroscopic condensate into mesoscopic condensates whose number and mass scale algebraically with the system size. Our study shows that even a weak interaction plays an important role in condensation phenomena.
Stochastic Echo Phenomena in Nonequilibrium Systems
노재동 한국물리학회 2014 THE JOURNAL OF THE KOREAN PHYSICAL SOCIETY Vol.64 No.4
A thermodynamic system is driven out of equilibrium by a time-dependent force or a nonconservativeforce represented with a protocol (t). The dynamics of such a system is irreversible so thatthe ensemble of trajectories under a time-reversed protocol (−t) is not equivalent to that of timereversedtrajectories under (t). We raise a question whether one can find a suitable protocol underwhich the system exhibits time-reversed motions of the original system. Such a phenomenon is referredto as a stochastic echo phenomenon. We derive a condition for the optimal protocol that leadsto the stochastic echo phenomenon in Langevin systems. We find that any system driven by timeindependentnonconservative forces has a dual system exhibiting the stochastic echo phenomenonperfectly. The stochastic echo phenomena are also demonstrated for harmonic oscillator systemsdriven by time-dependent forces. Our study provides a novel perspective on the time-irreversibilityof nonequilibrium systems.