arXiv subjects

Yup Kim

Publications and source records attributed to Yup Kim.

At least 19 recordsLinked to original sources

arXiv2013

Phase transitions in Paradigm models

In this letter we propose two general models for paradigm shift, deterministic propagation model (DM) and stochastic propagation model (SM). By defining the order parameter $m$ based on the diversity of ideas, $Δ$, we study when and how the transition occurs as a cost $C$ in DM or an innovation probability $α$ in SM increases. In addition, we also investigate how the propagation processes affect on the transition nature. From the analytical calculations and numerical simulations $m$ is shown to satisfy the scaling relation $m=1-f(C/N)$ for DM with the number of agents $N$. In contrast, $m$ in SM scales as $m=1-f(α^a N)$.

physics.soc-ph↗

arXiv2012

Agglomerative percolation on the Bethe lattice and the triangular cactus

We study the agglomerative percolation (AP) models on the Bethe lattice and the triangular cactus to establish the exact mean-field theory for AP. Using the self-consistent simulation method, based on the exact self-consistent equation, we directly measure the order parameter $P_{\infty}$ and average cluster size $S$. From the measured $P_{\infty}$ and $S$ we obtain the critical exponents $β_k$ and $γ_k$ for $k=2$ and 3. Here $β_k$ and $γ_k$ are the critical exponents for $P_\infty$ and $S$ when the growth of clusters spontaneously breaks the $Z_k$ symmetry of the $k$-partite graph (Lau, Paczuski, and Grassberger, 2012). The obtained values are $β_2=1.79(3)$, $γ_2=0.88(1)$, $β_3=1.35(5)$, and $γ_3=0.94(2)$. By comparing these values of exponents with those for ordinary percolation ($β_{\infty}=1$ and $γ_{\infty}=1$) we also find the inequalities between the exponents, as $β_\infty<β_3<β_2$ and $γ_\infty>γ_3>γ_2$. These results quantitatively verify the conjecture that the AP model belongs to a new universality class if $Z_k$ symmetry is broken spontaneously, and the new universality class depends on $k$ [Lau et al., Phys. Rev. E 86, 011118 (2012)].

cond-mat.stat-mech↗

arXiv2012

Bond-site duality and phase transition nature of explosive percolations on a two-dimensional lattice

To establish the bond-site duality of explosive percolations in 2 dimension, the site and bond explosive percolation models are carefully defined on a square lattice. By studying the cluster distribution function and the behavior of the second largest cluster, it is shown that the duality in which the transition is discontinuous exists for the pairs of the site model and the corresponding bond model which relatively enhances the intra-bond occupation. In contrast the intra-bond-suppressed models which have no corresponding site models undergo the continuous transition and satisfy the normal scaling ansatz as ordinary percolation.

cond-mat.stat-mech↗

arXiv2012

Explosive percolations on the Bethe Lattice

Based on the self-consistent equations of the order parameter $P_\infty$ and the mean cluster size $S$, we develop a novel self-consistent simulation (SCS) method for arbitrary percolation on the Bethe lattice (infinite homogeneous Cayley tree). By applying SCS to the well-known percolation models, random bond percolation and bootstrap percolation, we obtain prototype functions for continuous and discontinuous phase transitions. By comparing the key functions obtained from SCSs for the Achlioptas processes (APs) with a product rule and a sum rule to the prototype functions, we show that the percolation transition of AP models on the Bethe lattice is continuous regardless of details of growth rules.

cond-mat.stat-mech↗

arXiv2011

Explosive site percolation with a product rule

We study the site percolation under Achlioptas process (AP) with a product rule in a $2-dimensional$ (2D) square lattice. From the measurement of the cluster size distribution, $P_s$, we find that $P_s$ has a very robust power-law regime followed by a stable hump near the transition threshold. Based on the careful analysis on the $P_s$ distribution, we show that the transition should be discontinuous. The existence of the hysteresis loop in order parameter also verifies that the transition is discontinuous in 2D. Moreover we also show that the transition nature from the product rule is not the same as that from a sum rule in 2D.

cond-mat.stat-mech↗

arXiv2008

Condensation phenomena of conserved-mass aggregation model on weighted complex networks

We investigate the condensation phase transitions of conserved-mass aggregation (CA) model on weighted scale-free networks (WSFNs). In WSFNs, the weight $w_{ij}$ is assigned to the link between the nodes $i$ and $j$. We consider the symmetric weight given as $w_{ij}=(k_i k_j)^α$. In CA model, the mass $m_i$ on the randomly chosen node $i$ diffuses to a linked neighbor of $i$,$j$, with the rate $T_{ji}$ or an unit mass chips off from the node $i$ to $j$ with the rate $ωT_{ji}$. The hopping probability $T_{ji}$ is given as $T_{ji}= w_{ji}/\sum_{ } w_{li}$, where the sum runs over the linked neighbors of the node $i$. On the WSFNs, we numerically show that a certain critical $α_c$ exists below which CA model undergoes the same type of the condensation transitions as those of CA model on regular lattices. However for $α\geq α_c$, the condensation always occurs for any density $ρ$ and $ω$. We analytically find $α_c = (γ-3)/2$ on the WSFN with the degree exponent $γ$. To obtain $α_c$, we analytically derive the scaling behavior of the stationary distribution $P^{\infty}_k$ of finding a walker at nodes with degree $k$, and the probability $D(k)$ of finding two walkers simultaneously at the same node with degree $k$. We find $P^{\infty}_k \sim k^{α+1-γ}$ and $D(k) \sim k^{2(α+1)-γ}$ respectively. With $P^{\infty}_k$, we also show analytically and numerically that the average mass $m(k)$ on a node with degree $k$ scales as $k^{α+1}$ without any jumps at the maximal degree of the network for any $ρ$ as in the SFNs with $α=0$.

cond-mat.stat-mech↗

arXiv2007

Conserved mass aggregation model with mass-dependent fragmentation

We study a conserved mass aggregation model with mass-dependent fragmentation in one dimension. In the model, the whole mass $m$ of a site isotropically diffuse with unit rate. With rate $ω$, a mass $m^λ$ is fragmented from the site and moves to a randomly selected nearest neighbor site. Since the fragmented mass is smaller than the whole mass $m$ of a site for $λ< 1$, the on-site attractive interaction exists for the case. For $λ= 0$, the model is known to undergo the condensation phase transitions from a fluid phase into a condensed phase as the density of total masses ($ρ$) increases beyond a critical density $ρ_c$. For $0< λ<1$, we numerically confirm for several values of $ω$ that $ρ_c$ diverges with the system size $L$. Hence in thermodynamic limit, the condensed phase disappears and no transitions take place in one dimension. We also explain that there are no transitions in any dimensions.

cond-mat.stat-mech↗

arXiv2007

Diffusive capture processes for information search

We show how effectively the diffusive capture processes (DCP) on complex networks can be applied to information search in the networks. Numerical simulations show that our method generates only 2% of traffic compared with the most popular flooding-based query-packet-forwarding (FB) algorithm. We find that the average searching time, $ $, of the our model is more scalable than another well known $n$-random walker model and comparable to the FB algorithm both on real Gnutella network and scale-free networks with $γ=2.4$. We also discuss the possible relationship between $ $ and $ $, the second moment of the degree distribution of the networks.

physics.soc-ph↗

arXiv2007

The double domain structure of pair contact process with diffusion

We investigate the domain structure of pair contact process with diffusion (PCPD). PCPD is a stochastic reaction-diffusion model which evolves by the competition of two binary reactions, $2A \to 3A$ and $2A \to 0$. In addition, each particle diffuses isotropically, which leads to the bidirectional coupling between solitary particles and pairs. The coupling from pairs to solitary particles is linear, while the opposite coupling is quadratic. The spreading domain formed from localized activities in vacuum consists of two regions, the coupled region of size $R_p$ where pairs and solitary particles coexist and the uncoupled region of size $R_U$ where only solitary particles exist respectively. As the size of the whole domain $R$ is given as $R=R_p + R_U$, $R_p$ and $R_U$ are the basic length scales of PCPD. At criticality, $R_p$ and $R_U$ scale as $R_p \sim t^{1/Z_p}$ and $R_U \sim t^{1/Z_U}$ with $Z_U > Z_p$. We estimate $Z_p =1.61(1)$ and $Z_U =1.768(8)$. Hence, the correction to the scaling of $R$, $Q=R_U /R_p$ extremely slowly decays, which makes it practically impossible to identify the asymptotic scaling behavior of $R$. In addition to the generic feature of the bidirectional coupling, the double domain structure is another reason for the extremely slow approach to the asymptotic scaling regime of PCPD.

cond-mat.stat-mech↗

arXiv2007

Random walks and diameter of finite scale-free networks

Dynamical scalings for the end-to-end distance $R_{ee}$ and the number of distinct visited nodes $N_v$ of random walks (RWs) on finite scale-free networks (SFNs) are studied numerically. $\left< R_{ee} \right>$ shows the dynamical scaling behavior $\left = \bar{\ell}^α(γ, N) g(t/\bar{\ell}^z)$, where $\bar{\ell}$ is the average minimum distance between all possible pairs of nodes in the network, $N$ is the number of nodes, $γ$ is the degree exponent of the SFN and $t$ is the step number of RWs. Especially, $\left $ in the limit $t \to \infty$ satisfies the relation $\left< R_{ee} \right> \sim \bar{\ell}^α\sim d^α$, where $d$ is the diameter of network with $d ({\bar \ell}) \simeq \ln N$ for $γ\ge 3$ or $d ({\bar \ell}) \simeq \ln \ln N$ for $γ< 3$. Based on the scaling relation $\left< R_{ee} \right>$, we also find that the scaling behavior of the diameter of networks can be measured very efficiently by using RWs.

cond-mat.stat-mech↗

arXiv2006

Kinetics of the $A+B \to 0$ reaction with mass-dependent fragmentation

We investigate the kinetics of uniformly driven $A+B \to 0$ reaction with mass-dependent fragmentation in one dimension. In this model, the fragmented mass $m$ of a site with mass $n_i$ is given as $m=n^λ_i$, and it is driven to the one direction. When opposite species masses occupy the same site, mass reaction takes place instantaneously. Since the fragmented mass $m$ of $λ<1$ is less than mass $n_i$ of a site, the exponent $λ$ controls the attractive interaction between particles at the same site. The $λ=0$ case corresponds to hard-core (HC) particle system. With equal initial densities of both species, we numerically confirm that the scaling behaviors of density and lengths except the domain length $\ell$ are the same as that of the uniformly driven HC particle system. The scaling behavior of $\ell$ is $\ell \sim t^{2/3}$. The kinetics of the reaction is independent of $λ$ as long as $λ<1$. The $λ$-independent kinetics results from the $λ$-independent collective motions of single species domains.

cond-mat.stat-mech↗

arXiv2006

Statistical properties of sampled networks by random walks

We study the statistical properties of the sampled networks by a random walker. We compare topological properties of the sampled networks such as degree distribution, degree-degree correlation, and clustering coefficient with those of the original networks. From the numerical results, we find that most of topological properties of the sampled networks are almost the same as those of the original networks for $γ\lesssim 3$. In contrast, we find that the degree distribution exponent of the sampled networks for $γ>3$ somewhat deviates from that of the original networks when the ratio of the sampled network size to the original network size becomes smaller. We also apply the sampling method to various real networks such as collaboration of movie actor, world wide web, and peer-to-peer networks. All topological properties of the sampled networks show the essentially same as the original real networks.

physics.soc-ph↗

arXiv2006

Diffusive Capture Process on Complex Networks

We study the dynamical properties of a diffusing lamb captured by a diffusing lion on the complex networks with various sizes of $N$. We find that the life time $ of a lamb scales as \sim N$ and the survival probability $S(N\to \infty,t)$ becomes finite on scale-free networks with degree exponent $γ>3$. However, $S(N,t)$ for $γ<3$ has a long-living tail on tree-structured scale-free networks and decays exponentially on looped scale-free networks. It suggests that the second moment of degree distribution $ is the relevant factor for the dynamical properties in diffusive capture process. We numerically find that the normalized number of capture events at a node with degree $k$, $n(k)$, decreases as $n(k)\sim k^{-σ}$. When $γ<3$, $n(k)$ still increases anomalously for $k\approx k_{max}$. We analytically show that $n(k)$ satisfies the relation $n(k)\sim k^2P(k)$ and the total number of capture events $N_{tot}$ is proportional to $, which causes the $γ$ dependent behavior of $S(N,t)$ and $.

cond-mat.dis-nn↗

arXiv2006

Continuously varying exponents in $A+B \to 0$ reaction with long-ranged attractive interaction

We investigate the kinetics of the $A+B \to 0$ reaction with long-range attractive interaction $V(r) \sim -r^{-2σ}$ between $A$ and $B$ or with the drift velocity $v \sim r^{-σ}$ in one dimension, where $r$ is the closest distance between $A$ and $B$. It is analytically show that the dynamical exponents for density of particles ($ρ$) and the size of domains ($\ell$) continuously vary with $σ$ when $σ< σ_c =/1/2$, while that for the distance between adjacent opposite species ($\ell_{AB}$) varies when $σ< σ_c^{AB}= 7/6$. Beyond $σ_c^{AB}$, diffusive motions dominate the kinetics, so that the dynamical behavior for diffusive systems is completely recovered. These anomalous behaviors with the two crossover values of $σ$ are supported by numerical simulations and the argument of effective repulsion between the opposite species domains.

cond-mat.stat-mech↗

arXiv2005

Correlation functions and queuing phenomena in growth processes with drift

We suggest a novel stochastic discrete growth model which describes the drifted Edward-Wilkinson (EW) equation $\partial h /\partial t = ν\partial_x^2 h - v\partial_x h +η(x,t)$. From the stochastic model, the anomalous behavior of the drifted EW equation with a defect is analyzed. To physically understand the anomalous behavior the height-height correlation functions $C(r)=< |h({x_0}+r)-h(x_0)|>$ and $G(r)=< |h({x_0}+r)-h(x_0)|^2>$ are also investigated, where the defect is located at $x_0$. The height-height correlation functions follow the power law $C(r)\sim r^{α'}$ and $G(r)\sim r^{α''}$ with $α'=α''=1/4$ around a perfect defect at which no growth process is allowed. $α'=α''=1/4$ is the same as the anomalous roughness exponent $α=1/4$. For the weak defect at which the growth process is partially allowed, the normal EW behavior is recovered. We also suggest a new type queuing process based on the asymmetry $C(r) \neq C(-r)$ of the correlation function around the perfect defect.

cond-mat.stat-mech↗

arXiv2005

Dynamical Structures of High-Frequency Financial Data

We study the dynamical behavior of high-frequency data from the Korean Stock Price Index (KOSPI) using the movement of returns in Korean financial markets. The dynamical behavior for a binarized series of our models is not completely random. The conditional probability is numerically estimated from a return series of KOSPI tick data. Non-trivial probability structures can be constituted from binary time series of autoregressive (AR), logit, and probit models, for which the Akaike Information Criterion shows a minimum value at the 15th order. From our results, we find that the value of the correct match ratio for the AR model is slightly larger than the findings of other models.

physics.soc-ph↗

arXiv2005

Condensation phase transitions of symmetric conserved-mass aggregation model on complex networks

We investigate condensation phase transitions of symmetric conserved-mass aggregation (SCA) model on random networks (RNs) and scale-free networks (SFNs) with degree distribution $P(k) \sim k^{-γ}$. In SCA model, masses diffuse with unite rate, and unit mass chips off from mass with rate $ω$. The dynamics conserves total mass density $ρ$. In the steady state, on RNs and SFNs with $γ>3$ for $ω\neq \infty$, we numerically show that SCA model undergoes the same type condensation transitions as those on regular lattices. However the critical line $ρ_c (ω)$ depends on network structures. On SFNs with $γ\leq 3$, the fluid phase of exponential mass distribution completely disappears and no phase transitions occurs. Instead, the condensation with exponentially decaying background mass distribution always takes place for any non-zero density. For the existence of the condensed phase for $γ\leq 3$ at the zero density limit, we investigate one lamb-lion problem on RNs and SFNs. We numerically show that a lamb survives indefinitely with finite survival probability on RNs and SFNs with $γ>3$, and dies out exponentially on SFNs with $γ\leq 3$. The finite life time of a lamb on SFNs with $γ\leq 3$ ensures the existence of the condensation at the zero density limit on SFNs with $γ\leq 3$ at which direct numerical simulations are practically impossible. At $ω= \infty$, we numerically confirm that complete condensation takes place for any $ρ> 0$ on RNs. Together with the recent study on SFNs, the complete condensation always occurs on both RNs and SFNs in zero range process with constant hopping rate.

cond-mat.stat-mech↗

arXiv2005

Flux fluctuations in a multi-random-walker model and surface growth dynamics

We study the dynamics of visitation flux in a multi-random-walker model by comparison to surface growth dynamics in which one random walker drops a particle to a node at each time the walker visits the node. In each independent experiment (trial or day) for the multi-random-walker model, the number of walkers are randomly chosen from the uniform distribution $[< N_{RW} > -\triangle N_{RW}, < N_{RW} > +\triangle N_{RW} ]$. The averaged fluctuation $\bar σ ({T_{RW}})$ of the visitations over all nodes $i$ and independent experiments is shown to satisfy the power-law dependence on the walk step $T_{RW}$ as $\bar σ ({T_{RW}})\simeq {T_{RW}}^β$. Furthermore two distinct values of the exponent $β$ are found on a scale-free network, a random network and regular lattices. One is $β_i$, which is equal to the growth exponent $β$ for the surface fluctuation $W$ in one-random-walker model, and the other is $β=1$. $β_i$ is found for small $\triangle N_{RW}$ or for the system governed by the internal intrinsic dynamics. In contrast $β=1$ is found for large $\triangle N_{RW}$ or for the system governed by the external flux variations. The implications of our results to the recent studies on fluctuation dynamics of the nodes on networks are discussed.

cond-mat.stat-mech↗