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We performed molecular dynamics simulations of the high-temperature oxidation of metal alloys composed of Al, Cr, and Fe and compared their behavior with that of pure Fe. The metal alloy elements (Al and Cr) segregated to the surface during oxidation, producing a lower stress gradient at the metal/environment interface compared to pure Fe. We have found that the lowered stress gradients produced in the alloy material appear to play a key role in the development of corrosion. Interfaces with lower stress gradients have reduced rates of ${\mathrm{H}}_{2}\mathrm{O}$ adsorption, especially for the ferritic (bcc) alloys. The diffusivity of oxygen and hydrogen drops more rapidly for the interfaces with reduced stress gradients. The stress gradient is also diminished when the gas pressure is increased, indicating that the Fe-Cr-Al alloy system is more resistant to oxidation than pure Fe at higher pressures. Therefore, we conclude that the lower stress gradients at the alloy/environment interface reduce the stress concentration and can slow down the rate of the initial oxide scale growth. We also compared bcc and fcc alloys with pure Fe based on our three evaluation criteria (peak stress, stress gradient, and summation of stress in the oxide scale). We found that the alloys have lower values under the three criteria compared to pure Fe. The bcc alloy has the best score under a water rich environment and the fcc alloy is proven to be better for peak stress and summation of stress in the oxide scale under an oxygen rich environment. For surface segregation to occur, we find that a minimum content of Al or Cr in the near-surface region must be achieved. We also learned that the role of Al is more important than that of Cr in terms of corrosion resistant behavior at relatively higher temperatures for the Fe-Cr-Al ternary alloys.

We study the origin of the log-normal popularity distribution of trending memes observed in many real social networks. Based on a biological analogy, we introduce a fitness of each meme, which is a natural assumption based on sociological reasons. From numerical simulations, we find that the relative popularity distribution of the trending memes becomes a log-normal distribution when the fitness of the meme increases exponentially. On the other hand, if the fitness grows slowly, then the distribution significantly deviates from the log-normal distribution. This indicates that the fast growth of fitness is the necessary condition for the trending meme. Furthermore, we also show that the popularity of the trending topic grows linearly. These results provide a clue to understand long-lasting questions, such as what causes some memes to become extremely popular and how such memes are exposed to the public much longer than others.

We investigate the behavior of two different order parameters for the Kuramoto model in the desynchronized phase. Since the primary role of the order parameter is to distinguish different phases, we focus on the ability to discern the desynchronized phase from the synchronized one on complex networks with the size N. From the exact derivation of the difference between two order parameters, Δ, on a star network, we find that these order parameters disagree in the desynchronized phase. We also show that the hub plays an important role and provide an analytic conjecture on the condition that the two order parameters agree with each other as N→∞. The conjecture is numerically confirmed.

We study the mean first passage time (MFPT) of true self-avoiding walks (TSAWs) on various networks as a measure of searching efficiency. From the numerical analysis, we find that the MFPT of TSAWs, τ^{TSAW}, approaches the theoretical minimum τ^{th}/N=1/2 on synthetic networks whose degree-degree correlations are positive. On the other hand, for biased random walks (BRWs) we find that the MFPT, τ^{BRW}, depends on the parameter α, which controls the degree-dependent bias. More importantly, we find that the minimum MFPT of BRWs, τ_{min}^{BRW}, always satisfies the inequality τ_{min}^{BRW}>τ^{TSAW} on any synthetic network. The inequality is also satisfied on various real networks. From these results, we show that the TSAW is one of the most efficient models, whose efficiency approaches the theoretical limit in network explorations.

To understand the effects of nonidentical processing elements (PEs) on parallel discrete-event simulation (PDES) schemes, two stochastic growth models, the restricted solid-on-solid (RSOS) model and the Family model, are investigated by simulations. The RSOS model is the model for the PDES scheme governed by the Kardar-Parisi-Zhang equation (KPZ scheme). The Family model is the model for the scheme governed by the Edwards-Wilkinson equation (EW scheme). Two kinds of distributions for nonidentical PEs are considered. In the first kind computing capacities of PEs are not much different, whereas in the second kind the capacities are extremely widespread. The KPZ scheme on the complex networks shows the synchronizability and scalability regardless of the kinds of PEs. The EW scheme never shows the synchronizability for the random configuration of PEs of the first kind. However, by regularizing the arrangement of PEs of the first kind, the EW scheme is made to show the synchronizability. In contrast, EW scheme never shows the synchronizability for any configuration of PEs of the second kind.

Transport properties in random and scale-free (SF) networks are studied by analyzing the betweenness centrality (BC) distribution $P(B)$ in the minimum spanning trees (MSTs) and infinite incipient percolation clusters (IIPCs) of the networks. It is found that $P(B)$ in MSTs scales as $P(B)\ensuremath{\sim}{B}^{\ensuremath{-}\ensuremath{\delta}}$. The obtained values of $\ensuremath{\delta}$ are classified into two different categories, $\ensuremath{\delta}\ensuremath{\simeq}1.6$ and $\ensuremath{\delta}\ensuremath{\simeq}2.0$. Using the mapping between BC and the branch size of tree structures, it is proved that $\ensuremath{\delta}$ in MSTs which are close to critical trees is 1.6. In contrast, $\ensuremath{\delta}$ in MSTs which are supercritical trees is shown to be 2.0. We also find $\ensuremath{\delta}=1.5$ in IIPCs, which is a natural result because IIPC is physically critical. Based on the results in MSTs, a physical reason why $\ensuremath{\delta}\ensuremath{\ge}2$ in the original networks is suggested.

The dynamical anisotropic scaling properties of the surface growth models are restudied by use of the damage spreading concept. For that the vertical damage spreading distance d( perpendicular) of a damaged column as well as the lateral damage spreading distance d(||) is introduced. The scaling Ansatze fordmacr;( perpendicular)(d(||),t), D(||) identical withd(||)and D( perpendicular) identical withdmacr;( perpendicular)are suggested. The critical property of the probability distribution P(d(||),t) for the survived damages is also suggested. The suggested scaling relations are tested by simulating various growth models with substrate dimension d=1. From these results it can be concluded that the critical property or dynamical self-affinity of a surface growth model can also be determined by investigating the damage spreading.

Growth models for vapor depositions in which evaporation and deposition can occur, both at a randomly chosen column and at its nearest neighbor columns (NNCs), are studied by Monte Carlo simulations. The growth processes in these models are determined by comparing local chemical potentials of the chosen column and its NNCs to the chemical potential of vapor. The universality classes and the characteristics of the models are studied by the scaling ansatz of kinetic roughening and by measurements of tilt-dependent currents and height step widths. Through measurements of the ratio of number of growth processes at NNCs to those at the chosen column, the key processes which are relevant to the determination of the universality class are also studied.

A conserved growth model with a constraint on neighboring interface heights in substrate dimensions ${d}_{s}=2,3,4,5$ is investigated. A randomly dropped particle is allowed to hop to the nearest site satisfying the restricted solid-on-solid condition. The scaling properties of the surface in ${d}_{s}=2$, 3, and 4 are consistent with those of the continuum equation $\ensuremath{\partial}h/\ensuremath{\partial}t=\ensuremath{-}\ensuremath{\nu}{\ensuremath{\nabla}}^{4}h+\ensuremath{\lambda}{\ensuremath{\nabla}}^{2}(\ensuremath{\nabla}{h)}^{2}+\ensuremath{\eta}$. The upper critical dimension of the model is also discussed.

A conserved growth model with a restricted solid-on-solid (RSOS) condition is described. A randomly dropped particle is allowed to hop to the nearest site satisfying the RSOS condition. The values of the dynamic exponents in the conserved growth model are consistent with those of the nonlinear equation {partial_derivative}h/{partial_derivative}t={minus}{nu}{nabla}{sup 4}h+{lambda}{nabla}{sup 2}({nabla}h){sup 2}+{eta}, where {eta} is a random noise. The surface current measurement shows the absence of the Edwards-Wilkinson-type diffusion term. The surfaces in the steady-state regime have a grooved phase characterized by the roughness exponent {alpha}=1. The physical origin of the conserved nonlinear term is also discussed. {copyright} {ital 1997} {ital The American Physical Society}

Kinetics of irreversible bimolecular chemical reactions A+A→0 and A+B→0 on directed scale-free networks with the in-degree distribution P(in)(k)∼k(-γ)(in) and the out-degree distribution P(out)(l)∼l(-γ)(out) are investigated. Since the correlation between k and l of each node generally exists in directed networks, we control the correlation (kl) with the probability r∈[0,1] by two different algorithms for the construction of the directed networks, i.e., the so-called k and l algorithms. For r=1, the k algorithm gives (kl)=(k(2)), whereas the l algorithm gives (kl)=(l(2). For r=0, (kl)=(k)(l) for both algorithms. The kinetics of both reactions are analyzed using heterogeneous mean-field (HMF) theory and Monte Carlo simulations. The density of particles (ρ) algebraically decays in time t as ρ(t)∼t(-α). The kinetics of both reactions are determined by the same rate equation, dρ/dt=aρ(2)+bρ(θ-1), apart from coefficients. The exponent θ is determined by the algorithm: θ=γ(in) for the k algorithm (r≥0) and θ=γ(min) for the l algorithm (r>0), where γ(min) is the smaller exponent between γ(in) and γ(out). For θ>3, one observes the ordinary mean-field kinetics, ρ∼1/t (α=1). In contrast, for θ

To establish the bond-site duality of explosive percolations in two dimensions, 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 intrabond occupation. In contrast the intrabond-suppressed models which have no corresponding site models undergo a continuous transition and satisfy the normal scaling ansatz as ordinary percolation.

Irreversible stochastic models of growth in which particles are globally biased to seed are formulated and studied by Monte Carlo simulations on triangular, hexagonal, and square lattices. In the deterministic aggregation model (DAM), where only the effect of attraction between particles and the seed is considered, the particles have peculiar paths of motion on each lattice. Aggregates with biased random walks manifest special anisotropies on the two-dimensional lattices which are the same as those in DAM's. We discuss the universal and nonuniversal properties of these aggregates on the twodimensional lattices

We investigate the kinetics of bimolecular chemical reactions $A+A\ensuremath{\rightarrow}0$ and $A+B\ensuremath{\rightarrow}0$ on weighted scale-free networks (WSFNs) with degree distribution $P(k)\ensuremath{\sim}{k}^{\ensuremath{-}\ensuremath{\gamma}}$. On WSFNs, a weight ${w}_{ij}$ is assigned to the link between node $i$ and $j$. We consider the symmetric weight given as ${w}_{ij}={({k}_{i}{k}_{j})}^{\ensuremath{\mu}}$, where ${k}_{i}$ and ${k}_{j}$ are the degree of node $i$ and $j$. The hopping probability ${T}_{ij}$ of a particle from node $i$ to $j$ is then given as ${T}_{ij}\ensuremath{\propto}{({k}_{i}{k}_{j})}^{\ensuremath{\mu}}$. From a mean-field analysis, we analytically show in the thermodynamic limit that the kinetics of $A+A\ensuremath{\rightarrow}0$ and $A+B\ensuremath{\rightarrow}0$ are identical and there exist two crossover $\ensuremath{\mu}$ values, ${\ensuremath{\mu}}_{1c}=\ensuremath{\gamma}\ensuremath{-}2$ and ${\ensuremath{\mu}}_{2c}=(\ensuremath{\gamma}\ensuremath{-}3)/2$. The density of particles $\ensuremath{\rho}(t)$ algebraically decays in time $t$ as ${t}^{\ensuremath{-}\ensuremath{\alpha}}$ with $\ensuremath{\alpha}=1$ for $\ensuremath{\mu}l{\ensuremath{\mu}}_{2c}$ and $\ensuremath{\alpha}=(\ensuremath{\mu}+1)/(\ensuremath{\gamma}\ensuremath{-}\ensuremath{\mu}\ensuremath{-}2)$ for ${\ensuremath{\mu}}_{2c}\ensuremath{\le}\ensuremath{\mu}l{\ensuremath{\mu}}_{1c}$. For $\ensuremath{\mu}\ensuremath{\ge}{\ensuremath{\mu}}_{1c}$, $\ensuremath{\rho}$ decays exponentially. With the mean-field rate equation for $\ensuremath{\rho}(t)$, we also analytically show that the kinetics on the WSFNs is mapped onto that on unweighted SFNs with $P(k)\ensuremath{\sim}{k}^{\ensuremath{-}{\ensuremath{\gamma}}^{\ensuremath{'}}}$ with ${\ensuremath{\gamma}}^{\ensuremath{'}}=(\ensuremath{\mu}+\ensuremath{\gamma})/(\ensuremath{\mu}+1)$.

We investigate the kinetics of general two species annihilation nA+mB→0 of driven hard-core (HC) particles with N=n+m in one dimension. With uniform drift velocity, all particles are driven to the right. HC exclusion forbids the interchange of any particles and restricts the number of particles on a site to 0 or 1. The reaction is classified into two classes, the symmetric and the asymmetric reaction. The symmetric reaction means both nA+mB→0 and mA+nB→0 , while the asymmetric reaction means only nA+mB→0 for a given (n,m) pair. As N increases, the trains of particles causing the reaction rarely form. Hence, for sufficiently large N, particles are evenly distributed before the reaction, so one expects a crossover N(c) above which the kinetics follows the classical mean-field rate equation. We show the existence of N(c) and that the kinetics for N

Irreversible stochastic models for the growth of clusters on a square lattice are formulated and studied by Monte Carlo simulation in which diffusing particles are biased globally and locally. In the case of global bias, the preferred directions of incoming particles are diagonal. Contrary to the biased walks on continuum space, the lattice anisotropy is enhanced and results in diagonally elongated clusters. With the local biased walk controlled by a parametric \ensuremath{\zeta}, it seems that there is a crossover length L(\ensuremath{\zeta}). For the region rL(\ensuremath{\zeta}), the cluster is more or less compact while for the region rgL(\ensuremath{\zeta}) the shape of the clusters becomes similar to that of the ordinary diffusion-limited aggregation. The comparison of clusters of our model is made with those of the model considered recently by Meakin, Feder, and Jo/ssang [Phys. Rev. A 43, 1952 (1991)].

Information search is closely related to the first-passage property of diffusing particle. The physical properties of diffusing particle is affected by the topological structure of the underlying network. Thus, the interplay between dynamical process and network topology is important to study information search on complex networks. Designing an efficient method has been one of main interests in information search. Both reducing the network traffic and decreasing the searching time have been two essential factors for designing efficient method. Here we propose an efficient method based on biased random walks. Numerical simulations show that the average searching time of the suggested model is more efficient than other well-known models. For a practical interest, we demonstrate how the suggested model can be applied to the peer-to-peer system.

We investigate the kinetics of irreversible reaction nA+mB → 0. When nA particles and mB particles encounter on the same site, the reaction takes place. We classify the reaction into two classes, the symmetric and the asymmetric reactions. The symmetric reaction means both nA+mB → 0 and mA + nB → 0, while the asymmetric reaction means only nA+mB→0 for a given (n,m) pair. The kinetics of the reaction follows the fluctuation-dominated kinetics of A+B→0 for N

We study a microscopic model for financial markets on complex networks, motivated by the dynamics of agents and their structure of interaction. The model consists of interacting agents (spins) with local ferromagnetic coupling and global antiferromagnetic coupling. In order to incorporate more realistic situations, we also introduce an external field which changes in time. From numerical simulations, we find that the model shows two-phase phenomena. When the local ferromagnetic interaction is balanced with the global antiferromagnetic interaction, the resulting return distribution satisfies a power law having a single peak at zero values of return, which corresponds to the market equilibrium phase. On the other hand, if local ferromagnetic interaction is dominant, then the return distribution becomes double peaked at nonzero values of return, which characterizes the out-of-equilibrium phase. On random networks, the crossover between two phases comes from the competition between two different interactions. However, on scale-free networks, not only the competition between the different interactions but also the heterogeneity of underlying topology causes the two-phase phenomena. Possible relationships between the critical phenomena of spin system and the two-phase phenomena are discussed.

We study the conserved-mass aggregation model with mass-dependent fragmentation on random networks (RNs) and scale-free networks (SFNs) with degree distribution Pk approximately k(-gamma). In the model, masses isotropically diffuse with unit rate. With rate omega, a mass m(lambda) is fragmented from a node with mass m , and moves to one of the linked nodes with the equal probability. For lambda=0 , the model is known to undergo the condensation phase transitions at a certain criticality rho(c) . From the mean-field balance equation for an aggregate, we analytically show that the present model exhibits different behavior depending on network structures. The condensation always occurs for lambda0 . For 0lambda1 , finite-sized systems on RNs and SFNs with gamma3 undergoes the condensation transitions (sharp crossovers) at rho(c) which diverges with network size N as N(lambda). Hence, in the limit N--infinity , masses uniformly distribute without the condensation (fluid phase). On the other hand, for gammaor =3 , a crossover lambda(c)=1(gamma-1) exists. The condensation always occurs for lambdalambda(c) , while the fluid phase is always stable at any nonzero density for lambdaor =lambda(c) . The phase separation results from the competition between the heterogeneity of network structure and the enhanced chipping by lambda . We numerically confirm all the predictions.

We investigate kinetics of the uniformly driven bosonic $A+B\ensuremath{\rightarrow}0$ reaction with on-site attractive interaction in one dimension. In this model, ${n}_{i}^{\ensuremath{\lambda}}$ particles from a site with ${n}_{i}$ particles are driven to the right. When particles of opposite species occupy the same site, the reaction takes place instantaneously. Since ${n}_{i}^{\ensuremath{\lambda}}l{n}_{i}$ for $\ensuremath{\lambda}l1$, $\ensuremath{\lambda}$ controls the on-site attractive interaction between like particles. The $\ensuremath{\lambda}=0$ case corresponds to the hard-core (HC) particle model. With equal initial densities of both species, we numerically confirm that the scaling behaviors of density and lengths are the same as those of the uniformly driven HC particle system. Especially the domain length $l$ satisfies the power law $l\ensuremath{\sim}{t}^{2∕3}$. The kinetics of the reaction is independent of $\ensuremath{\lambda}$ as long as $\ensuremath{\lambda}l1$. The $\ensuremath{\lambda}$-independent kinetics results from the $\ensuremath{\lambda}$-independent collective motions of single species domains.

Department of Physics and Research Institute for Basic Sciences, Kyung-Hee University, Seoul 130-701, Korea~Received 29 May 1998!To test the corrected scaling relation a1z5423dof the conserved Kardar-Parisi-Zhang~CKPZ! equationsuggested by Janssen @Phys. Rev. Lett. 78, 1082 ~1997!#, a stochastic growth model that follows the CKPZequation with the conserved noise is restudied. We have found a consistent nonzero correction term d, whichis somewhat larger than that estimated from the two-loop renormalization group calculation.@S1063-651X~98!10010-7#PACS number~s!: 05.40.1j, 05.70.Ln, 68.35.Fx

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 $\gamma>3$. However, $S(N,t)$ for $\gamma$ 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 $n(k)\sim k^{-\sigma}$. When $\gamma$, which causes the $\gamma$ dependent behavior of $S(N,t)$ and $., Comment: 9 pages, 6 figures

Jungho Kim,1 Sunghoon Jung,2 M. S. Park,3 Sung-Ik Lee,3 H. D. Drew,4 H. Cheong,5 K. H. Kim,1 and E. J. Choi2,* 1School of Physics, Center for Strongly Correlated Materials Research, Seoul National University, Seoul 151-742, Republic of Korea 2Department of Physics, University of Seoul, Seoul 130-743, Republic of Korea 3National Creative Research Initiative Center for Superconductivity and Department of Physics, Pohang University of Science and Technology, Pohang 790-784, Republic of Korea 4Department of Physics, University of Maryland, College Park, Maryland 20742, USA 5Department of Physics, Sogang University, Seoul 121-742, Republic of Korea Received 23 April 2006; revised manuscript received 28 June 2006; published 29 August 2006

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)AB diffusive motions dominate the kinetics. These anomalous behaviors with the two crossover values of sigma are supported by numerical simulations.

We investigate condensation phase transitions of symmetric conserved-mass aggregation (SCA) model on random networks (RNs) and scale-free networks (SFNs) with degree distribution $P(k) \sim k^{-\gamma}$. In SCA model, masses diffuse with unite 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 $\omega \neq \infty$, we numerically show that SCA model undergoes the same type condensation transitions as those on regular lattices. However the critical line $\rho_c (\omega)$ depends on network structures. On SFNs with $\gamma \leq 3$, 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 $\gamma \leq 3$ 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 $\gamma >3$, and dies out exponentially on SFNs with $\gamma \leq 3$. The finite life time of a lamb on SFNs with $\gamma \leq 3$ ensures the existence of the condensation at the zero density limit on SFNs with $\gamma \leq 3$ at which direct numerical simulations are practically impossible. At $\omega = \infty$, 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., Comment: 6 pages, 6 figures

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 ($\rho$), 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 $\rho \sim t^{-1/3}$, $\ell_{AA} \sim t^{1/3}$, 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., Comment: 4 pages, 4 figures

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 zUor =zA for zAor =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.

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.

We study dynamical scaling properties of the surface growth model with the Metropolis-type evolution rule from a partition function $Z={\ensuremath{\sum}}_{{h(\stackrel{\ensuremath{\rightarrow}}{r})}}{\ensuremath{\prod}}_{{h=h}_{\mathrm{min}}}^{{h}_{\mathrm{max}}}\frac{1}{2}{(1+z}^{{n}_{h}}),$ where z is a fugacity-like quantity and ${n}_{h}$ is the number of sites with height h in a surface configuration ${h(\stackrel{\ensuremath{\rightarrow}}{r})}.$ The partition function describes a 2-particle correlated growth model when $z=\ensuremath{-}1$ and a self-flattening growth model when $z=0.$ For one-dimensional equilibrium surfaces, the scaling properties for $zg~\ensuremath{-}1$ except $z=1$ are all one phase with roughness exponent $\ensuremath{\alpha}=1/3$ and growth exponent $\ensuremath{\beta}\ensuremath{\simeq}0.22.$ For the growing (eroding) surfaces, there exists a phase transition at $z=0$ from the grooved phase $(\ensuremath{\alpha}=1)$ for $\ensuremath{-}1l~zl0$ to the ordinary Kardar-Parisi-Zhang phase $(\ensuremath{\alpha}=1/2)$ for $zg0.$

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.

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 $\alpha\simeq 1/3$ and dynamic exponent $z_W \simeq 3/2$ in one dimension (1D) and $\alpha=0 (\log)$ and $z_W \simeq 5/2$ 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., Comment: 4 pages, to appear in Phys. Rev. E (RC)

The dynamical scaling property of surface eroded by a chemical reaction $A+\stackrel{\ensuremath{\rightarrow}}{B}0$ 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.

The optical response of semiconductor heterostructure under a combined dc-ac fields, ${F}_{\mathrm{dc}}{+F}_{\mathrm{ac}}\mathrm{cos}{\ensuremath{\omega}}_{L}t,$ is studied by calculating absorption spectra based on semiconductor Bloch equations. First, we investigate the periodic motion of the carrier in a band under a ac field or dc field. Under the ac field with the frequency ${\ensuremath{\omega}}_{L},$ we find the periodic motion of ${\ensuremath{\omega}}_{L},$ which is very similar to the Bloch oscillation under the dc field. The ladder spacing of quasienergy states under the ac field is observed to be $\ensuremath{\Elzxh}{\ensuremath{\omega}}_{L}.$ Under combined ac-dc fields, we discover the absorption peaks corresponding to the so-called dynamical fractional Stark ladders with ladder spacing $m\ensuremath{\Elzxh}{\ensuremath{\omega}}_{B}{+m}^{\ensuremath{'}}\ensuremath{\Elzxh}{\ensuremath{\omega}}_{L}$ where m and ${m}^{\ensuremath{'}}$ are integers and ${\ensuremath{\omega}}_{B}$ is the Bloch oscillation frequency.

Based on the recently suggested scaling ansatz [Phys. Rev. E 62, 3376 (2000)] for damage spreading in the surface roughening phenomenon, the characteristics of the damage-spreading phase and damage-frozen phase in a two-dimensional solid-on-solid model that has a roughening transition at T=T(R) are studied. In the damage-spreading phase, which exists for TT(R), the average vertical damage-spreading distance d(perpendicular)(d(//)=0,L,T) and the average lateral damage-spreading distance D(//)(L,T) are shown to satisfy d(perpendicular)(d(//)=0,L,T) approximately ln L and D(//)(L,T) approximately L, respectively. In the damage-frozen phase, which exists for TT(R), it is shown that d( perpendicular)(d(//)=0,L--infinity,T) approximately finite and D(//)(L--infinity,T) approximately finite. From these results it is concluded that the damage-spreading phase describes the surface roughening phase well and the damage-frozen phase describe the smooth phase well.

We present the results of Monte Carlo simulation for self-avoiding walks on a percolation cluster for square and simple cubic lattices performed very close to the percolation thresholds and estimate critical exponents \ensuremath{\nu} and \ensuremath{\gamma} defined by the disorder averages of the mean-square radius of gyration and the number of self-avoiding walks, respectively. Our results for \ensuremath{\nu} indicate a behavior rather similar to the self-avoiding walks on fully occupied lattice unlike the large increase in \ensuremath{\nu} reported in the only previous work of this kind by Kremer given for the diamond lattice. Our results for \ensuremath{\gamma} suggest an increase from the full lattice value just at ${p}_{c}$ in three dimensions, while in two dimensions the asymptotic behavior appears to be similar to that of the ordinary self-avoiding walks. We also consider the possible crossover from fractal to Euclidean behavior and discuss the reasons why no crossover scaling is observed for the mean-square radius of gyration in the present calculation.

We report a Monte Carlo study of the hysteretic behavior of the site-diluted Ising antiferromagnet on a simple-cubic lattice. States found by reducing the magnetic field from an initial value in the paramagnetic phase show no long-range antiferromagnetic order, whereas states found by increasing the magnetic field from an initially ordered state do show long-range order until the field is increased to a critical value. These ‘‘increasing-field’’ states are presumably nearly representative of true thermodynamic equilibrium. This hysteretic behavior is due to metastable interfaces which are formed when the field is decreased from the paramagnetic phase. To see the physical origin of the formation of the metastable interfaces, we do computer experiments for the dynamics of initially flat interfaces with and without uniform applied fields. From this result, we show that metastable interfaces are formed, because even a small uniform applied field roughens the interface.

A modified self-consistent phonon theory based on the Green's-function method is developed and is applied to a melting of the hydrogen bonds in DNA polymer poly(dG)-poly(dC), where dG refers to repeating guanine bases on one strand and dC the repeating cytosine bases on the other strand. The model predicts melting at 380 K. The calculation has no parameters adjusted to fit the melting and the hydrogen-bond potentials are adjusted to fit data of vibrational modes of DNA at room temperature.

Two growing kinetics of self-avoiding walks on dilute lattices are considered for discussion of the crossover scaling behavior of self-avoiding walks near percolation threshold. The crossover properties for each kinetics are exactly calculated on a diluted linear chain and on a Cayley tree. We also consider crossover properties for each kinetics on general lattices. From the results the recent controversies of self-avoiding walks near the threshold are analyzed.