Biomedical subjects

Hyunggyu Park

Publications and source records attributed to Hyunggyu Park.

13 recordsLinked to original sources

PubMed2006

Crossover from the pair contact process with diffusion to directed percolation.

Crossover behaviors from the pair contact process with diffusion (PCPD) and the driven PCPD (DPCPD) to the directed percolation (DP) are studied in one dimension by introducing a single particle annihilation and/or branching dynamics. The crossover exponents phi are estimated numerically as 1/phi approximately 0.58 +/- 0.03 for the PCPD and 1/phi approximately 0.49+/-0.02 for the DPCPD. Nontriviality of the PCPD crossover exponent strongly supports the non-DP nature of the PCPD critical scaling, which is further evidenced by the anomalous critical amplitude scaling near the PCPD point. In addition, we find that the DPCPD crossover is consistent with the mean field prediction of the tricritical DP class as expected.

Journal Article↗

PubMed2005

Collective synchronization in spatially extended systems of coupled oscillators with random frequencies.

We study collective behavior of locally coupled limit-cycle oscillators with random intrinsic frequencies, spatially extended over d -dimensional hypercubic lattices. Phase synchronization as well as frequency entrainment are explored analytically in the linear (strong-coupling) regime and numerically in the nonlinear (weak-coupling) regime. Our analysis shows that the oscillator phases are always desynchronized up to d=4 , which implies the lower critical dimension dP(l) =4 for phase synchronization. On the other hand, the oscillators behave collectively in frequency (phase velocity) even in three dimensions (d=3) , indicating that the lower critical dimension for frequency entrainment is dF(l)=2 . Nonlinear effects due to the periodic nature of limit-cycle oscillators are found to become significant in the weak-coupling regime: So-called runaway oscillators destroy the synchronized (ordered) phase and there emerges a fully random (disordered) phase. Critical behavior near the synchronization transition into the fully random phase is unveiled via numerical investigation. Collective behavior of globally coupled oscillators is also examined and compared with that of locally coupled oscillators.

Action Potentials↗

PubMed2005

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 attention focused on 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 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. Numerical simulations on small-world networks confirm our predictions.

Journal Article↗

PubMed2005

Slow relaxation in the Ising model on a small-world network with strong long-range interactions.

We consider the Ising model on a small-world network, where the long-range interaction strength J2 is in general different from the local interaction strength J1, and examine its relaxation behaviors as well as phase transitions. As J(2)/J(1) is raised from zero, the critical temperature also increases, manifesting contributions of long-range interactions to ordering. However, it becomes saturated eventually at large values of J(2)/J(1) and the system is found to display very slow relaxation, revealing that ordering dynamics is inhibited rather than facilitated by strong long-range interactions. To circumvent this problem, we propose a modified updating algorithm in Monte Carlo simulations, assisting the system to reach equilibrium quickly.

Journal Article↗

PubMed2005

Driven pair contact process with diffusion.

The pair contact process with diffusion (PCPD) has been recently investigated extensively, but its critical behavior is not yet clearly established. By introducing biased diffusion, we show that the external driving is relevant and the driven PCPD exhibits a mean-field-type critical behavior even in one dimension. In systems which can be described by a single-species bosonic field theory, the Galilean invariance guarantees that the driving is irrelevant. The well-established directed percolation (DP) and parity-conserving (PC) classes are such examples. This leads us to conclude that the PCPD universality class should be distinct from the DP or the PC class. Moreover, it implies that the PCPD is generically a multispecies model and a field theory of two species is suitable for proper description.

Journal Article↗

PubMed2005

Cluster mean-field approximations with the coherent-anomaly-method analysis for the driven pair contact process with diffusion.

The cluster mean-field approximations are performed, up to 13 cluster sizes, to study the critical behavior of the driven pair contact process with diffusion (DPCPD) and its precedent, the PCPD in one dimension. Critical points are estimated by extrapolating our data to the infinite cluster size limit, which are in good accordance with recent simulation results. Within the cluster mean-field approximation scheme, the PCPD and the DPCPD share the same mean-field critical behavior. The application of the coherent anomaly method, however, shows that the two models develop different coherent anomalies, which lead to different true critical scaling. The values of the critical exponents for the particle density, the pair density, the correlation length, and the relaxation time are fairly well estimated for the DPCPD. These results support and complement our recent simulation results for the DPCPD.

Journal Article↗

PubMed2004

Collective phase synchronization in locally coupled limit-cycle oscillators.

We study collective behavior of locally coupled limit-cycle oscillators with scattered intrinsic frequencies on d -dimensional lattices. A linear analysis shows that the system should always be desynchronized up to d=4 . On the other hand, numerical investigation for d=5 and d=6 reveals the emergence of the synchronized (ordered) phase via a continuous transition from the fully random desynchronized phase. This demonstrates that the lower critical dimension for the phase synchronization in this system is d(l) =4 .

Journal Article↗

PubMed2004

Stability of vacuum in coupled directed percolation processes.

We study the absorbing phase transitions in coupled directed percolation (DP) processes with N -species particles in one dimension. The interspecies coupling is linear, bidirectional, and excitatory. We find that the presence of a spontaneous annihilation process A-->0 is essential in stabilizing the absorbing phase (vacuum). In the coupled contact processes, the vacuum is stable and the system exhibits DP type transitions, regardless of the coupling strength, for all N. However, in the coupled branching annihilation random walks with one offspring (BAW), where particle annihilations occur only through binary diffusion processes A+A-->0, the vacuum becomes unstable with respect to an arbitrarily small branching rate in a sufficiently strong coupling regime for N> or =3. The N=2 BAW exhibits the DP type transition for any coupling strength, but the inclusion of interspecies hard core (HC) interaction makes the vacuum unstable again and the system is always active in a strong coupling regime. Critical behavior near the zero branching point is characterized by the mean-field scaling exponents, beta= nu(radially) = 1/2 and nu(axially) =1, regardless of the presence of HC interaction. We also discuss the effects of the asymmetric coupling.

Journal Article↗

PubMed2004

Factors that predict better synchronizability on complex networks.

While shorter characteristic path length has in general been believed to enhance synchronizability of a coupled oscillator system on a complex network, the suppressing tendency of the heterogeneity of the degree distribution, even for shorter characteristic path length, has also been reported. To see this, we investigate the effects of various factors such as the degree, characteristic path length, heterogeneity, and betweenness centrality on synchronization, and find a consistent trend between the synchronization and the betweenness centrality. The betweenness centrality is thus proposed as a good indicator for synchronizability.

Computer Simulation↗

PubMed2004

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 different type of critical phenomenon 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 strength. The GPCPD connects the DP fixed point to the PCPD point continuously. Monte Carlo simulations strongly suggest that the GPCPD displays, to our knowledge, novel 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 present one possible scenario that the long-term memory may serve as a marginal perturbation to the ordinary DP fixed point.

Journal Article↗

PubMed2003

Comment on "Restricted curvature model with suppression of extremal height".

Recently Jeong and Kim [Phys. Rev. E 66, 051605 (2002)] investigated the scaling properties of equilibrium self-flattening surfaces subject to a restricted curvature constraint. In one dimension (1D), they found numerically that the stationary roughness exponent alpha approximately 0.561 and the window exponent delta approximately 0.423. We present an analytic argument for general self-flattening surfaces in D dimensions, leading to alpha=Dalpha(0)/(D+alpha(0)) and delta=D/(D+alpha(0)), where alpha(0) is the roughness exponent for equilibrium surfaces without the self-flattening mechanism. In case of surfaces subject to a restricted curvature constraint, it is known exactly that alpha(0)=3/2 in 1D, which leads to alpha=3/5 and delta=2/5. Small discrepancies between our analytic values and their numerical values may be attributed to finite size effects.

Comment↗

PubMed2002

Fluctuations of self-flattening surfaces.

We study the scaling properties of self-flattening surfaces under global suppression on surface fluctuations. Evolution of self-flattening surfaces is described by restricted solid-on-solid type monomer deposition-evaporation model with reduced deposition (evaporation) at the globally highest (lowest) site. We find numerically that equilibrium surface fluctuations are anomalous with roughness exponent alpha approximately equal to 1/3 and dynamic exponent z(W) approximately equal to 3/2 in one dimension (1D) and alpha=0 (log) and z(W) approximately 5/2 in 2D. Stationary roughness can be understood analytically by relating our model to the static self-attracting random walk model and the dissociative dimer-type deposition-evaporation model. In case of nonequilibrium growing-eroding surfaces, self-flattening dynamics turns out to be irrelevant and the normal Kardar-Parisi-Zhang universality is recovered in all dimensions.

Journal Article↗

PubMed2002

Dynamical surface structures in multiparticle-correlated surface growths.

We investigate the scaling properties of the interface fluctuation width for the Q-mer and Q-particle-correlated deposition-evaporation models. These models are constrained with a global conservation law that the particle number at each height is conserved modulo Q. In equilibrium, the stationary roughness is anomalous but universal with the roughness exponent alpha=1/3, while the early time evolution shows nonuniversal behavior with the growth exponent beta varying with models and Q. Nonequilibrium surfaces display diverse growing and stationary behaviors. The Q-mer model shows a faceted structure, while the Q-particle-correlated model shows a macroscopically grooved structure.

Journal Article↗