arXiv subjects

Sungchul Kwon

Publications and source records attributed to Sungchul Kwon.

16 recordsLinked to original sources

arXiv2024

Joint probability density with radial, tangential, and perturbative forces

We study the Fokker-Planck equation for an active particle with both the radial and tangential forces and the perturbative force. We find the solution of the joint probability density. In the limit of the long-time domain and for the characteristic time=0 domain, the mean squared radial velocity for an active particle leads to a super-diffusive distribution, while the mean squared tangential velocity with both the radial and tangential forces and the perturbative force behaviors as the Gaussian diffusion. Compared with the self-propelled particle, the mean squared tangential velocity is matched with the same value to the time ~t^2, while the mean squared radial velocity is the same as the time ~t.

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

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↗

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

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

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

Molecular Traffic Control in a 3D network of single file channels and fast reactivity

We study the conditions for reactivity enhancement of catalytic processes in porous solids by use of molecular traffic control (MTC) as a function of grain size. We extend a recently introduced two dimensional model system to three dimensions. With dynamic Monte-Carlo simulations and analytical solution of the associated Master equation we obtain a quantitative description of the MTC effect in the limit of fast reactivity. The efficiency ratio (compared with a topologically and structurally similar reference system without MTC) is inversely proportional to the grain diameter.

cond-mat.stat-mech↗

arXiv2005

Anomalous kinetics of attractive $A+B \to 0$ reactions

We investigate the kinetics of $A+B \to 0$ reaction with the local attractive interaction between opposite species in one spatial dimension. The attractive interaction leads to isotropic diffusions inside segregated single species domains, and accelerates the reactions of opposite species at the domain boundaries. At equal initial densities of $A$ and $B$, we analytically and numerically show that the density of particles ($ρ$), the size of domains ($\ell$), the distance between the closest neighbor of same species ($\ell_{AA}$), and the distance between adjacent opposite species ($\ell_{AB}$) scale in time as $ρ\sim t^{-1/3}$, $\ell_{AA} \sim t^{1/3}$, and $\ell \sim \ell_{AB} \sim t^{2/3}$ respectively. These dynamical exponents form a new universality class distinguished from the class of uniformly driven systems of hard-core particles.

cond-mat.stat-mech↗

arXiv2004

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 $A\to 0$ 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 $A+A\to 0$, the vacuum becomes unstable with respect to an arbitrarily small branching rate in a sufficiently strong coupling regime for $N\ge 3$. 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 scaling exponents, $β=ν_{\bot}=1/2$ and $ν_{||}=1$, regardless of the presence of HC interaction. We also discuss the effects of the asymmetric coupling.

cond-mat.stat-mech↗

arXiv2003

Generalized scaling relations for unidirectionally coupled nonequilibrium systems

Unidirectionally coupled systems which exhibit phase transitions into an absorbing state are investigated at the multicritical point. We find that for initial conditions with isolated particles, each hierarchy level exhibits an inhomogeneous active region, coupled and uncoupled respectively. The particle number of each level increases algebraically in time as $N(t) \sim t^η$ with different exponents $η$ in each domain. This inhomogeneity is a quite general feature of unidirectionally coupled systems and leads to two hyperscaling relations between dynamic and static critical exponents. Using the contact process and the branching-annihilating random walk with two offsprings, which belong to the DP and PC classes respectively, we numerically confirm the scaling relations.

cond-mat.stat-mech↗

arXiv2000

Two-species branching annihilating random walks with one offspring

We study the effects of hard core (HC) interactions between different species of particles on two-species branching annihilating random walks with one offspring(BAW$_2$(1)). The single-species model belongs to the directed percolation (DP) universality class. In the BAW$_2$(1) model, a particle creates one particle of the same species in its neighborhood with the probability $σ(1-p)$ and of the different species with $(1-σ)(1-p)$, where $p$ is the hopping probability. Without HC interactions, this model always exhibits the DP-type absorbing transition for all $σ$. Even with HC interactions, the nature of the phase transitions does not change except near $σ=0$, where the HC interaction destabilizes and completely wipes away the absorbing phase. The model is always active except at the annihilation fixed point of zero branching rate ($p=1$). Critical behavior near the annihilation fixed point is characterized by exponents $β= ν_\perp =1/2$ and $ν_{||} = 1$.

cond-mat.stat-mech↗

arXiv2000

Does hardcore interaction change absorbing type critical phenomena?

It has been generally believed that hardcore interaction is irrelevant to absorbing type critical phenomena because the particle density is so low near an absorbing phase transition. We study the effect of hardcore interaction on the N species branching annihilating random walks with two offspring and report that hardcore interaction drastically changes the absorbing type critical phenomena in a nontrivial way. Through Langevin equation type approach, we predict analytically the values of the scaling exponents, $ν_{\perp} = 2, z = 2, α= 1/2, β= 2$ in one dimension for all N > 1. Direct numerical simulations confirm our prediction. When the diffusion coefficients for different species are not identical, $ν_{\perp}$ and $β$ vary continuously with the ratios between the coefficients.

cond-mat.stat-mech↗

arXiv1998

Dynamic behavior of driven interfaces in models with two absorbing states

We study the dynamics of an interface (active domain) between different absorbing regions in models with two absorbing states in one dimension; probabilistic cellular automata models and interacting monomer-dimer models. These models exhibit a continuous transition from an active phase into an absorbing phase, which belongs to the directed Ising (DI) universality class. In the active phase, the interface spreads ballistically into the absorbing regions and the interface width diverges linearly in time. Approaching the critical point, the spreading velocity of the interface vanishes algebraically with a DI critical exponent. Introducing a symmetry-breaking field $h$ that prefers one absorbing state over the other drives the interface to move asymmetrically toward the unpreferred absorbing region. In Monte Carlo simulations, we find that the spreading velocity of this driven interface shows a discontinuous jump at criticality. We explain that this unusual behavior is due to a finite relaxation time in the absorbing phase. The crossover behavior from the symmetric case (DI class) to the asymmetric case (directed percolation class) is also studied. We find the scaling dimension of the symmetry-breaking field $y_h = 1.21(5)$.

cond-mat.stat-mech↗

arXiv1997

Critical phenomena of nonequilibrium dynamical systems with two absorbing states

We study nonequilibrium dynamical models with two absorbing states: interacting monomer-dimer models, probabilistic cellular automata models, nonequilibrium kinetic Ising models. These models exhibit a continuous phase transition from an active phase into an absorbing phase which belongs to the universality class of the models with the parity conservation. However, when we break the symmetry between the absorbing states by introducing a symmetry-breaking field, Monte Carlo simulations show that the system goes back to the conventional directed percolation universality class. In terms of domain wall language, the parity conservation is not affected by the presence of the symmetry-breaking field. So the symmetry between the absorbing states rather than the conservation laws plays an essential role in determining the universality class. We also perform Monte Carlo simulations for the various interface dynamics between different absorbing states, which yield new universal dynamic exponents. With the symmetry-breaking field, the interface moves, in average, with a constant velocity in the direction of the unpreferred absorbing state and the dynamic scaling exponents apparently assume trivial values. However, we find that the hyperscaling relation for the directed percolation universality class is restored if one focuses on the dynamics of the interface on the side of the preferred absorbing state only.

cond-mat.stat-mech↗

arXiv1995

Reentrant phase diagram of branching annihilating random walks with one and two offsprings

We investigate the phase diagram of branching annihilating random walks with one and two offsprings in one dimension. A walker can hop to a nearest neighbor site or branch with one or two offsprings with relative ratio. Two walkers annihilate immediately when they meet. In general, this model exhibits a continuous phase transition from an active state into the absorbing state (vacuum) at a finite hopping probability. We map out the phase diagram by Monte Carlo simulations which shows a reentrant phase transition from vacuum to an active state and finally into vacuum again as the relative rate of the two-offspring branching process increases. This reentrant property apparently contradicts the conventional wisdom that increasing the number of offsprings will tend to make the system more active. We show that the reentrant property is due to the static reflection symmetry of two-offspring branching processes and the conventional wisdom is recovered when the dynamic reflection symmetry is introduced instead of the static one.

cond-mat↗