Biomedical subjects

Yup Kim

Publications and source records attributed to Yup Kim.

16 recordsLinked to original sources

PubMed2006

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 lifetime {T} of a lamb scales as {T} approximately N and the survival probability S(N-->infinity, t) becomes finite on scale-free networks with degree exponent gamma > 3. However, S(N, t) for gamma < 3 has a long-living tail on tree-structured scale-free networks and decays exponentially on looped scale-free networks. This suggests that the second moment of degree distribution {k2} is the relevant factor for the dynamical properties in the 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) approximately k(-sigma). When gamma < 3, n(k) still increases anomalously for k approximately kmax, where kmax is the maximum value of k of given networks with size N. We analytically show that n(k) satisfies the relation n(k) approximately {k2}P(k) for any degree distribution P(k) and the total number of capture events Ntot is proportional to {k2}, which causes the gamma -dependent behavior of S(N, t) and {T}.

Journal Article↗

PubMed2006

Continuously varying exponents in A+B-->0 reaction with long-ranged attractive interaction.

We investigate kinetics of A+B-->0 reaction with long-range attractive interaction V(r) approximately -r(-2sigma) between A and B or with drift velocity v approximately r(-sigma) in one dimension, where r is the closest distance between A and B . It is analytically shown that dynamical exponents for density of particles (rho) and size of domains (l) continuously vary with sigma when sigma < sigma(c) = 1/2 , while that for the distance between adjacent opposite species (l(AB)) varies when sigma < sigma(c)AB = 7/6 . For sigma > sigma(c)AB diffusive motions dominate the kinetics. These anomalous behaviors with the two crossover values of sigma are supported by numerical simulations.

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PubMed2006

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

We investigate condensation phase transitions of the symmetric conserved-mass aggregation (SCA) model on random networks (RNs) and scale-free networks (SFNs) with degree distribution P(k) approximately k(-gamma). In the SCA model, masses diffuse with unit rate, and unit mass chips off from mass with rate omega. The dynamics conserves total mass density rho. In the steady state, on RNs and SFNs with gamma > 3 for omega is not equal to infinity, we numerically show that the SCA model undergoes the same type of condensation transitions as those on regular lattices. However, the critical line rho(c)(omega) depends on network structures. On SFNs with gamma < or = 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 nonzero density. For the existence of the condensed phase for gamma < or = 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 gamma > 3, and dies out exponentially on SFNs with gamma< or = 3. The finite lifetime of a lamb on SFNs with gamma < or = 3 ensures the existence of the condensation at the zero density limit on SFNs with gamma < or = 3, at which direct numerical simulations are practically impossible. At omega = infinity, we numerically confirm that complete condensation takes place for any rho > 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.

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PubMed2006

Anomalous kinetics of attractive A + B-->0 reactions.

We investigate the kinetics of the A + B-->0 reaction with the 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 and , we analytically and numerically show that the density of particles (rho), the size of domains (l), the distance between the closest neighbor of same species (lAA), and the distance between adjacent opposite species (lAB) scale in time as rho approximately t(-1/3), lAA approximately t(1/3), and l approximately lAB approximately lAB(2/3), respectively. These dynamical exponents define critical behavior distinguished from the class of uniformly driven systems of hard-core particles.

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PubMed2005

Scaling of spreading in models unidirectionally coupled to source particles.

We investigate the spreading behavior of evolving clusters using unidirectionally coupled two-level hierarchies in one spatial dimension. In the hierarchy, while only two source particles (A) hop away from each other without branching its offspring on the bottom level, different species of particles (B) evolve according to given dynamics belonging to one of known universality classes on the top level. Two levels are unidirectionally coupled from the bottom to the top level by the branching A-->A+2B. We derive the spreading exponent zU of the uncoupled region of size RU(t) approximately tzU up to the first order correction in terms of the spreading exponent of source particles (zA) and that of given dynamics of the top level (zo) as zU=(1--zA)zo/(1-zo). From the relation, zA and zU always satisfy the inequality zU< or =zA for zA> or =zo. The inequality confirms that the scaling of the spreading in the slave level should follow the scaling of the source in unidirectionally coupled systems. We numerically confirm the relation for three different B-particle dynamics; annihilating random walks, branching annihilating random walks with one and two offspring which belong to the directed percolation, and the parity conserving universality class respectively.

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PubMed2005

Roughness of two-dimensional surfaces with global constraints.

We study dynamical scaling properties of the two-dimensional surface growth models with global constraints. These include the growth model from a partition function Z = sigma{(h(r)Pi(h = h)(min) (h(max)) 1/2 (1 + z (n(h))), multiparticle-correlated surface growth models and dissociative Q-mer growth models. The equilibrium surfaces of all the models except the dimer model show the same dynamical scaling behavior W2 (L,t) = (1/2piK(G)) ln [L g (t/L(z(W)))] with z(W) = 2.5 and K(G) = 0.916 , whereas the surface in the dimer model has a correction to the scaling. The growing (eroding) surfaces have two phases. The models with z > or = 0 show the normal Kardar-Parisi-Zhang scaling behavior. In contrast the models with -1 < or = z < 0 and multiparticle-correlated growth model manifest grooved surface structures with alpha = 1. The growing surfaces of Q -mer models form rather complex facets.

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PubMed2005

Coevolutionary dynamics on scale-free networks.

We investigate Bak-Sneppen coevolution models on scale-free networks with various degree exponents gamma including random networks. For gamma>3 , the critical fitness value f(c) approaches a nonzero finite value in the limit N --> infinity, whereas f(c) approaches zero as 2 (N) on the networks with size N. The avalanche size distribution P (s) shows the normal power-law behavior for gamma>3. In contrast, P (s) for 2 tau(2) ). The origin of the two power regimes is explained by the dynamics on an artificially made star-linked network.

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PubMed2004

Scaling properties of self-expanding surfaces.

Scaling properties of self-expanding surfaces are studied with a comparison to those of self-flattening surfaces [Phys. Rev. E 66, 040602(R) (2002)]. The evolution of self-expanding surfaces is described by a restricted solid-on-solid type monomer deposition-evaporation model in which both deposition at the globally lowest site and evaporation at the globally highest site are suppressed. We find numerically that equilibrium surface fluctuation has a scaling behavior with a roughness exponent alpha approximately 1 in one dimension (1D). In contrast, 2D equilibrium surfaces show the same dynamical scaling behavior with alpha=0 (log) and dynamic exponent z approximately 5/2 as 2D self-flattening surfaces. Stationary roughness can be understood analytically by relating the self-expanding growth model to self-repelling random walks. In the case of nonequilibrium growing/eroding surfaces, self-expanding dynamics cause the fluctuation of surfaces to be characterized by alpha approximately 1 in both 1D and 2D.

Models, Statistical↗

PubMed2003

Surface growth models with a random-walk-like nonlocality.

To understand the effects of a random-walk-like nonlocality on the dynamical scaling properties of surface growths, a stochastic growth model in which the height difference triangle up h((i,i+1))=|h(i)-h(i+1)| of a chosen nearest neighbor column pair (i,i+1) is decreased by one unit is introduced and studied by simulations. The probability P((i,i+1)) of choosing a column pair (i,i+1) on a one-dimensional substrate is assigned as P((i,i+1))=e(kappa triangle up h((i,i+1)))/ summation operator (L)(j=1)e(kappa triangle up h((j,j+1))). On a substrate of given size L, the dynamical scaling property satisfies a normal scaling behavior as W=L(alpha)f(t/L(z)), when kappa is very small. If kappa becomes moderately large, the scaling property with the dynamic exponent z=1 as in diffusion-limited erosion appears. If kappa becomes very large, no surface roughening is found.

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PubMed2003

Partition functions and metropolis-type evolution rules for surface growth models with constraints.

We study dynamical scaling properties of the surface growth model with the Metropolis-type evolution rule from a partition function Z= sum ([h(r)])II (h(max))(h=h(min))1/2(1+z(n(h))), where z is a fugacity-like quantity and n(h) is the number of sites with height h in a surface configuration [h(r)]. The partition function describes a 2-particle correlated growth model when z=-1 and a self-flattening growth model when z=0. For one-dimensional equilibrium surfaces, the scaling properties for z>or=-1 except z=1 are all one phase with roughness exponent alpha=1/3 and growth exponent beta approximately equal 0.22. For the growing (eroding) surfaces, there exists a phase transition at z=0 from the grooved phase (alpha=1) for -1 0.

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PubMed2003

Time-reversed dielectric-breakdown model for erosion phenomena.

A time-reversed dielectric-breakdown model in which the annihilating probability of a particle on the surface site (x,h) depends on Laplacian field phi(x,h,t) as P(x,h,t)=| inverted Delta phi(x,h,t)|(kappa)/ Sigma(x,h)| inverted Delta phi(x,h,t)|(kappa) is suggested. This model is shown to be a theoretical model that covers a variety of eroding surfaces from the linear phenomena with dynamic exponent z=1 to those showing nonlinear behavior. phi(x,t) is defined to satisfy the Laplace equation inverted Delta (2)phi=0 with the boundary condition phi=0 on the material and phi=1 far from the material. The model with 0.5 < or = kappa < or = 2 is found to follow the linear growth equation with z=1 as the diffusion-limited erosion, which is also a time-reversed version of diffusion-limited deposition. For small kappa, the dynamical scaling property of the eroding surface belongs to the Kardar-Parisi-Zhang universal class as the time-reversed Eden model. The model with kappa >2.5 does not show any surface roughening behavior.

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PubMed2003

Anomaly of the height-height correlation functions in self-flattening surface growth.

By Monte Carlo simulations and scaling theories, we consider the height-height correlation function G(r,t;L) of the one-dimensional equilibrium self-flattening surface growths, where the deposition (evaporation) attempt only at the globally highest (lowest) site is suppressed. G(r,t:L) is shown to satisfy the anomalous scaling behavior G(r,t;L)=L(2alpha)g(1)(r/L(delta),t/L(z)) or G(r,t;L)=t(2beta)g(2)(r/t(1/z(')),L/t(1/z)). Here alpha, beta, and z are the roughness, growth, and dynamic exponents, respectively, for the surface width, with alpha=1/3 and z=alpha/beta=3/2. Anomalous exponents z(') and delta are found to satisfy z(')=9/4 and delta=z/z('). We also show that anomalous behavior of G(r,t;L) can be understood from a scaling theory based on the competition between local random-walk-like behavior and the global-length-scale suppression.

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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.

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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.

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PubMed2002

Effects of biased diffusions on dynamical surface structures for the A+B-->0 reaction.

The dynamical scaling property of surface eroded by a chemical reaction A+B-->0 is studied by the simulation. To consider the effect of interactions between an A particle and the material which consists of B particles, the A particle is assumed to undergo a drifted-diffusive motion or a biased random walk before it touches the material. The surface of the material is eroded by the chemical reaction with a B particle which the A particle first encounters. In dimension d=2, we found three regimes in the dynamical surface structure. When there is attractive bias to the material, the dynamical scaling property belongs to the universality class with the dynamic exponent z=2. When there is no bias or relatively small repulsive bias, the scaling property belongs to the class with z=1. The surface roughening behavior disappears when repulsive bias becomes quite large. We also discuss the properties of the crossover between the existing regimes.

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PubMed2002

Relaxation of particles in the sloped region in a conserved growth model.

The dynamical scaling properties of conserved growth models, in which the downward (upward) movement of a particle dropped only on the sloped region occurs with a probability p (1-p), are investigated by simulations in the substrate dimension d=1. By direct analysis of the surface fluctuation W, the models with p>1/2 are clearly and cleanly shown to have crossover behavior from Mullins-Herring (MH) universality to Edwards-Wilkinson (EW) universality. In contrast, the models with p<1/2 are shown to have an instability eventually, even though they initially follow the MH equation. The model with p=1/2 is shown to belong to the MH universality class and to be the critical model that splits the models with EW behavior from those with the instability. From these results we explain the physical reason for the very slow crossover in models like the Wolf-Villain model.

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