Universal finite-size effects in the rate of growth processes

Dimensional crossover in Kardar-Parisi-Zhang growth

Two-dimensional (2D) Kardar-Parisi-Zhang (KPZ) growth is usually investigated on substrates of lateral sizes L_{x}=L_{y}, so that L_{x} and the correlation length (ξ) are the only relevant lengths determining the scaling behavior. However, in cylindrical geometry, as well as in flat rectangular substrates L_{x}≠L_{y} and, thus, the surfaces can become correlated in a single direction, when ξ∼L_{x}≪L_{y}. From extensive simulations of several KPZ models, we demonstrate that this yields a dimensional crossover in their dynamics, with the roughness scaling as W∼t^{β_{2D}} for t≪t_{c} and W∼t^{β_{1D}} for t≫t_{c}, where t_{c}∼L_{x}^{1/z_{2D}}. The height distributions (HDs) also cross over from the 2D flat (cylindrical) HD to the asymptotic Tracy-Widom Gaussian orthogonal ensemble (Gaussian unitary ensemble) distribution. Moreover, 2D to one-dimensional (1D) crossovers are found also in the asymptotic growth velocity and in the steady-state regime of flat systems, where a family of universal HDs exists, interpolating between the 2D and 1D ones as L_{y}/L_{x} increases. Importantly, the crossover scalings are fully determined and indicate a possible way to solve 2D KPZ models.

Kardar-Parisi-Zhang universality in a one-dimensional polariton condensate

Revealing universal behaviours is a hallmark of statistical physics. Phenomena such as the stochastic growth of crystalline surfaces¹ and of interfaces in bacterial colonies², and spin transport in quantum magnets^3-6 all belong to the same universality class, despite the great plurality of physical mechanisms they involve at the microscopic level. More specifically, in all these systems, space-time correlations show power-law scalings characterized by universal critical exponents. This universality stems from a common underlying effective dynamics governed by the nonlinear stochastic Kardar-Parisi-Zhang (KPZ) equation⁷. Recent theoretical works have suggested that this dynamics also emerges in the phase of out-of-equilibrium systems showing macroscopic spontaneous coherence^8-17. Here we experimentally demonstrate that the evolution of the phase in a driven-dissipative one-dimensional polariton condensate falls in the KPZ universality class. Our demonstration relies on a direct measurement of KPZ space-time scaling laws^18,19, combined with a theoretical analysis that reveals other key signatures of this universality class. Our results highlight fundamental physical differences between out-of-equilibrium condensates and their equilibrium counterparts, and open a paradigm for exploring universal behaviours in driven open quantum systems.

Scaling of roughness and porosity in thin film deposition with mixed transport mechanisms and adsorption barriers

Thin film deposition with particle transport mixing collimated and diffusive components and with barriers for adsorption are studied using numerical simulations and scaling approaches. Biased random walks on lattices are used to model the particle flux and the analogy with advective-diffusive transport is used to define a Peclet number P that represents the effect of the bias towards the substrate. An aggregation probability that relates the rates of adsorption and of the dominant transport mechanism plays the role of a Damkohler number D, where D≲1 is set to describe moderate to low adsorption rates. Very porous deposits with sparse branches are obtained with P≪1, whereas low porosity deposits with large height fluctuations at short scales are obtained with P≫1. For P≳1 in which the field bias is intense, an initial random deposition is followed by Kardar-Parisi-Zhang (KPZ) roughening. As the transport is displaced from those limiting conditions, the interplay of the transport and adsorption mechanisms establishes a condition to produce films with the smoothest surfaces for a constant deposited mass: with low adsorption barriers, a balance of random and collimated flux is required, whereas for high barriers the smoothest surfaces are obtained with P∼D^{1/2}. For intense bias, the roughness is shown to be a power law of P/D, whose exponent depends on the growth exponent β of the KPZ class, and the porosity has a superuniversal scaling as (P/D)^{-1/3}. We also study a generalized ballistic deposition model with slippery particle aggregation that shows the universality of these relations in growth with dominant collimated flux, particle adsorption at any point of the deposit, and negligible adsorbate diffusion, in contrast with the models where aggregation is restricted to the outer surface.

Universality and crossover behavior of single-step growth models in 1+1 and 2+1 dimensions

We study the kinetic roughening of the single-step (SS) growth model with a tunable parameter p in 1+1 and 2+1 dimensions by performing extensive numerical simulations. We show that there exists a very slow crossover from an intermediate regime dominated by the Edwards-Wilkinson class to an asymptotic regime dominated by the Kardar-Parisi-Zhang (KPZ) class for any p<1/2. We also identify the crossover time, the nonlinear coupling constant, and some nonuniversal parameters in the KPZ equation as a function p. The effective nonuniversal parameters are continuously decreasing with p but not in a linear fashion. Our results provide complete and conclusive evidence that the SS model for p≠1/2 belongs to the KPZ universality class in 2+1 dimensions.

Competing Universalities in Kardar-Parisi-Zhang Growth Models

We report on the universality of height fluctuations at the crossing point of two interacting (1+1)-dimensional Kardar-Parisi-Zhang interfaces with curved and flat initial conditions. We introduce a control parameter p as the probability for the initially flat geometry to be chosen and compute the phase diagram as a function of p. We find that the distribution of the fluctuations converges to the Gaussian orthogonal ensemble Tracy-Widom distribution for p<0.5, and to the Gaussian unitary ensemble Tracy-Widom distribution for p>0.5. For p=0.5 where the two geometries are equally weighted, the behavior is governed by an emergent Gaussian statistics in the universality class of Brownian motion. We propose a phenomenological theory to explain our findings and discuss possible applications in nonequilibrium transport and traffic flow.

Synchronization of conservative parallel discrete event simulations on a small-world network

We examine the question of the influence of sparse long-range communications on the synchronization in parallel discrete event simulations. We build a model of the evolution of local virtual times in a conservative algorithm including several choices of local links. All network realizations belong to the small-world network class. We find that synchronization depends on the average shortest path of the network. The time profile dynamics are similar to the surface profile growth, which helps to analyze synchronization effects using a statistical physics approach. Without long-range links of the nodes, the model belongs to the universality class of the Kardar-Parisi-Zhang equation for surface growth. We find that the critical exponents depend logarithmically on the fraction of long-range links. We present the results of simulations and discuss our observations.

Optimal detrended fluctuation analysis as a tool for the determination of the roughness exponent of the mounded surfaces

We present an optimal detrended fluctuation analysis (DFA) and apply it to evaluate the local roughness exponent in nonequilibrium surface growth models with mounded morphology. Our method consists in analyzing the height fluctuations computing the shortest distance of each point of the profile to a detrending curve that fits the surface within the investigated interval. We compare the optimal DFA (ODFA) with both the standard DFA and nondetrended analysis. We validate the ODFA method considering a one-dimensional model in the Kardar-Parisi-Zhang universality class starting from a mounded initial condition. We applied the methods to the Clarke-Vvedensky (CV) model in 2+1 dimensions with thermally activated surface diffusion and absence of step barriers. It is expected that this model belongs to the nonlinear molecular beam epitaxy (nMBE) universality class. However, an explicit observation of the roughness exponent in agreement with the nMBE class was still missing. The effective roughness exponent obtained with ODFA agrees with the value expected for the nMBE class, whereas using the other methods it does not agree. We also characterize the transient anomalous scaling of the CV model and obtained that the corresponding exponent is in agreement with the value reported for other nMBE models with weaker corrections to the scaling.

Probability distributions for directed polymers in random media with correlated noise

The probability distribution for the free energy of directed polymers in random media (DPRM) with uncorrelated noise in d=1+1 dimensions satisfies the Tracy-Widom distribution. We inquire if and how this universal distribution is modified in the presence of spatially correlated noise. The width of the distribution scales as the DPRM length to an exponent β, in good (but not full) agreement with previous renormalization group and numerical results. The scaled probability is well described by the Tracy-Widom form for uncorrelated noise, but becomes symmetric with increasing correlation exponent. We thus find a class of distributions that continuously interpolates between Tracy-Widom and Gaussian forms.

Scaling, cumulant ratios, and height distribution of ballistic deposition in 3+1 and 4+1 dimensions

We investigate the origin of the scaling corrections in ballistic deposition models in high dimensions using the method proposed by Alves et al. [Phys. Rev. E 90, 052405 (2014)PLEEE81539-375510.1103/PhysRevE.90.052405] in d=2+1 dimensions, where the intrinsic width associated with the fluctuations of the height increments during the deposition processes is explicitly taken into account. In the present work, we show that this concept holds for d=3+1 and 4+1 dimensions. We have found that growth and roughness exponents and dimensionless cumulant ratios are in agreement with other models, presenting small finite-time corrections to the scaling, that in principle belong to the Kardar-Parisi-Zhang (KPZ) universality class in both d=3+1 and 4+1. Our results constitute further evidence that the upper critical dimension of the KPZ class, if it exists, is larger than 4.

Origins of scaling corrections in ballistic growth models

We study the ballistic deposition and the grain deposition models on two-dimensional substrates. Using the Kardar-Parisi-Zhang (KPZ) ansatz for height fluctuations, we show that the main contribution to the intrinsic width, which causes strong corrections to the scaling, comes from the fluctuations in the height increments along deposition events. Accounting for this correction in the scaling analysis, we obtain scaling exponents in excellent agreement with the KPZ class. We also propose a method to suppress these corrections, which consists in dividing the surface in bins of size ɛ and using only the maximal height inside each bin to do the statistics. Again, scaling exponents in remarkable agreement with the KPZ class are found. The binning method allows the accurate determination of the height distributions of the ballistic models in both growth and steady-state regimes, providing the universal underlying fluctuations foreseen for KPZ class in 2 + 1 dimensions. Our results provide complete and conclusive evidences that the ballistic model belongs to the KPZ universality class in 2+1 dimensions. Potential applications of the methods developed here, in both numerics and experiments, are discussed.

Universality of fluctuations in the Kardar-Parisi-Zhang class in high dimensions and its upper critical dimension

We show that the theoretical machinery developed for the Kardar-Parisi-Zhang (KPZ) class in low dimensions is obeyed by the restricted solid-on-solid model for substrates with dimensions up to d=6. Analyzing different restriction conditions, we show that the height distributions of the interface are universal for all investigated dimensions. It means that fluctuations are not negligible and, consequently, the system is still below the upper critical dimension at d=6. The extrapolation of the data to dimensions d≥7 predicts that the upper critical dimension of the KPZ class is infinite.

Universal aspects of curved, flat, and stationary-state Kardar-Parisi-Zhang statistics

Motivated by the recent exact solution of the stationary-state Kardar-Parisi-Zhang (KPZ) statistics by Imamura and Sasamoto [ Phys. Rev. Lett. 108 190603 (2012)], as well as a precursor experimental signature unearthed by Takeuchi [ Phys. Rev. Lett. 110 210604 (2013)], we establish here the universality of these phenomena, examining scaling behaviors of directed polymers in a random medium, the stochastic heat equation with multiplicative noise, and kinetically roughened KPZ growth models. We emphasize the value of cross KPZ-class universalities, revealing crossover effects of experimental relevance. Finally, we illustrate the great utility of KPZ scaling theory by an optimized numerical analysis of the Ulam problem of random permutations.

Extremal paths, the stochastic heat equation, and the three-dimensional Kardar-Parisi-Zhang universality class

Following our numerical work [Phys. Rev. Lett. 109, 170602 (2012)] focused upon the 2+1 Kardar-Parisi-Zhang (KPZ) equation with flat initial condition, we return here to study, in depth, the three-dimensional (3D) radial KPZ problem, comparing common scaling phenomena exhibited by the pt-pt directed polymer in a random medium (DPRM), the stochastic heat equation (SHE) with multiplicative noise in three dimensions, and kinetic roughening phenomena associated with 3D Eden clusters. Examining variants of the 3D DPRM, as well as numerically integrating, via the Itô prescription, the constrained SHE for different values of the KPZ coupling, we provide strong evidence for universality within this 3D KPZ class, revealing shared values for the limit distribution skewness and kurtosis, along with universal first and second moments. Our numerical analysis of the 3D SHE, well flanked by the DPRM results, appears without precedent in the literature. We consider, too, the 2+1 KPZ equation in the deeply evolved kinetically roughened stationary state, extracting the essential limit distribution characterizing fluctuations therein, revealing a higher-dimensional relative of the 1+1 KPZ Baik-Rains distribution. Complementary, corroborative findings are provided via the Gaussian DPRM, as well as the restricted-solid-on-solid model of stochastic growth, stalwart members of the 2+1 KPZ class. Next, contact is made with a recent nonperturbative, field-theoretic renormalization group calculation for the key universal amplitude ratio in this context. Finally, in the crossover from transient to stationary-state statistics, we observe a higher dimensional manifestation of the skewness minimum discovered by Takeuchi [Phys. Rev. Lett. 110, 210604 (2013)] in 1+1 KPZ class liquid-crystal experiments.

Crystal growth inside an octant

We study crystal growth inside an infinite octant on a cubic lattice. The growth proceeds through the deposition of elementary cubes into inner corners. After rescaling by the characteristic size, the interface becomes progressively more deterministic in the long-time limit. Utilizing known results for the crystal growth inside a two-dimensional corner, we propose a hyperbolic partial differential equation for the evolution of the limiting shape. This equation is interpreted as a Hamilton-Jacobi equation, which helps in finding an analytical solution. Simulations of the growth process are in excellent agreement with analytical predictions. We then study the evolution of the subleading correction to the volume of the crystal, the asymptotic growth of the variance of the volume of the crystal, and the total number of inner and outer corners. We also show how to generalize the results to arbitrary spatial dimension.

Normal dynamic scaling in the class of the nonlinear molecular-beam-epitaxy equation

The scaling of local height fluctuations is studied numerically in lattice growth models of the class of the nonlinear stochastic equation of Villain-Lai-Das Sarma (VLDS) in substrate dimensions d=1 and 2. In d=1, the average local slopes of the conserved restricted solid-on-solid (CRSOS) models converge to a finite value in the long-time limit, with power-law corrections in time whose exponents are close to 0.1. Other VLDS models in d=1, such as that of Das Sarma and Tamborenea, show a divergence of local slopes up to 10(6) monolayers, typical of anomalous roughening, but a comparison of roughness distributions shows that they scale as the linear fourth-order growth equation in those time scales. Normal scaling is also obtained in a modified VLDS equation with instability suppression, in contrast to recent numerical works. In d=2, a CRSOS model and a model with lateral aggregation of diffusing particles show normal scaling of the local slopes, also with small correction exponents. These results consistently show that the VLDS class has normal dynamic scaling in d=1 and 2, in agreement with the theoretical predictions of Phys. Rev. Lett. 94, 166103 (2005), and they show that the apparently anomalous features observed in previous works are effects of large scaling correction terms or crossover effects.

Stiff directed lines in random media

We investigate the localization of stiff directed lines with bending energy by a short-range random potential. We apply perturbative arguments, Flory scaling arguments, a variational replica calculation, and functional renormalization to show that a stiff directed line in 1+d dimensions undergoes a localization transition with increasing disorder for d>2/3. We demonstrate that this transition is accessible by numerical transfer matrix calculations in 1+1 dimensions and analyze the properties of the disorder-dominated phase in detail. On the basis of the two-replica problem, we propose a relation between the localization of stiff directed lines in 1+d dimensions and of directed lines under tension in 1+3d dimensions, which is strongly supported by identical free-energy distributions. This shows that pair interactions in the replicated Hamiltonian determine the nature of directed line localization transitions with consequences for the critical behavior of the Kardar-Parisi-Zhang equation. We support the proposed relation to directed lines via multifractal analysis, revealing an analogous Anderson transition-like scenario and a matching correlation length exponent. Furthermore, we quantify how the persistence length of the stiff directed line is reduced by disorder.

(2+1)-Dimensional directed polymer in a random medium: scaling phenomena and universal distributions

We examine numerically the zero-temperature (2+1)-dimensional directed polymer in a random medium, along with several of its brethren via the Kardar-Parisi-Zhang (KPZ) equation. Using finite-size and KPZ scaling Ansätze, we extract the universal distributions controlling fluctuation phenomena in this canonical model of nonequilibrium statistical mechanics. Specifically, we study point-point, point-line, and point-plane directed polymer geometries, scenarios which yield higher-dimensional analogs of the Tracy-Widom distributions of random matrix theory. Our analysis represents a robust, multifaceted numerical characterization of the 2+1 KPZ universality class and its limit distributions.

Growth inside a corner: the limiting interface shape

We investigate the growth of a crystal that is built by depositing cubes inside a corner. The interface of this crystal approaches a deterministic growing limiting shape in the long-time limit. Building on known results for the corresponding two-dimensional system and accounting for basic three-dimensional symmetries, we conjecture a governing equation for the evolution of the interface profile. We solve this equation analytically and find excellent agreement with simulations of the growth process. We also present a generalization to arbitrary spatial dimension.

Logarithmic bred vectors in spatiotemporal chaos: structure and growth

Bred vectors are a type of finite perturbation used in prediction studies of atmospheric models that exhibit spatially extended chaos. We study the structure, spatial correlations, and the growth rates of logarithmic bred vectors (which are constructed by using a given norm). We find that, after a suitable transformation, logarithmic bred vectors are roughly piecewise copies of the leading Lyapunov vector. This fact allows us to deduce a scaling law for the bred vector growth rate as a function of its amplitude. In addition, we relate growth rates with the spectrum of Lyapunov exponents corresponding to the most expanding directions. We illustrate our results with simulations of the Lorenz 1996 model.

Critical wetting of a class of nonequilibrium interfaces: a computer simulation study

Critical wetting transitions under nonequilibrium conditions are studied numerically and analytically by means of an interface-displacement model defined by a Kardar-Parisi-Zhang equation, plus some extra terms representing a limiting, short-ranged attractive wall. Its critical behavior is characterized in detail by providing a set of exponents for both the average height and the surface order-parameter in one dimension. The emerging picture is qualitatively and quantitatively different from recently reported mean-field predictions for the same problem. Evidence is shown that the presence of the attractive wall induces an anomalous scaling of the interface local slopes.

Error growth patterns in systems with spatial chaos: from coupled map lattices to global weather models

Error growth in spatiotemporal chaotic systems is investigated by analyzing the interplay between temporal and spatial dynamics. The spatial correlation and localization of relative fluctuations grow and decay indicating two different regimes, before and after saturation by nonlinear effects. This general behavior is shown to hold both in simple coupled map lattices and in global weather models. This explains the increasing or decreasing trends previously observed in the exponential growth rate of these spatiotemporal systems.

Fisher waves and front roughening in a two-species invasion model with preemptive competition

We study front propagation when an invading species competes with a resident; we assume nearest-neighbor preemptive competition for resources in an individual-based, two-dimensional lattice model. The asymptotic front velocity exhibits an effective power-law dependence on the difference between the two species' clonal propagation rates (key ecological parameters). The mean-field approximation behaves similarly, but the power law's exponent slightly differs from the individual-based model's result. We also study roughening of the front, using the framework of nonequilibrium interface growth. Our analysis indicates that initially flat, linear invading fronts exhibit Kardar-Parisi-Zhang (KPZ) roughening in one transverse dimension. Further, this finding implies, and is also confirmed by simulations, that the temporal correction to the asymptotic front velocity is of O(t(-2/3)).

Universal and nonuniversal features in the crossover from linear to nonlinear interface growth

We study a restricted solid-on-solid model involving deposition and evaporation with probabilities p and 1 - p, respectively, in one-dimensional substrates. It presents a crossover from Edwards-Wilkinson (EW) to Kardar-Parisi-Zhang (KPZ) scaling for p approximately 0.5. The associated KPZ equation is analytically derived, exhibiting a coefficient lambda of the nonlinear term proportional to q identical with p - 1/2, which is confirmed numerically by calculation of tilt-dependent growth velocities for several values of p. This linear lambda - q relation contrasts to the apparently universal parabolic law obtained in competitive models mixing EW and KPZ components. The regions where the interface roughness shows pure EW and KPZ scaling are identified for 0.55< or =p< or =0.8, which provides numerical estimates of the crossover times tc. They scale as tc approximately lambda -phi with phi=4.1+/-0.1, which is in excellent agreement with the theoretically predicted universal value phi=4 and improves previous numerical estimates, which suggested phi approximately 3.

Synchronization landscapes in small-world-connected computer networks

Motivated by a synchronization problem in distributed computing we studied a simple growth model on regular and small-world networks, embedded in one and two dimensions. We find that the synchronization landscape (corresponding to the progress of the individual processors) exhibits Kardar-Parisi-Zhang-like kinetic roughening on regular networks with short-range communication links. Although the processors, on average, progress at a nonzero rate, their spread (the width of the synchronization landscape) diverges with the number of nodes (desynchronized state) hindering efficient data management. When random communication links are added on top of the one and two-dimensional regular networks (resulting in a small-world network), large fluctuations in the synchronization landscape are suppressed and the width approaches a finite value in the large system-size limit (synchronized state). In the resulting synchronization scheme, the processors make close-to-uniform progress with a nonzero rate without global intervention. We obtain our results by "simulating the simulations," based on the exact algorithmic rules, supported by coarse-grained arguments.

Exact scaling in competitive growth models

A competitive growth model (CGM) describes the aggregation of a single type of particle under two different growth rules with occurrence probabilities p and 1-p . We explain the origin of the scaling behavior of the resulting surface roughness at small p for two CGM's which describe random deposition (RD) competing with ballistic deposition and RD competing with the Edward-Wilkinson (EW) growth rule. Exact scaling exponents are derived. The scaling behavior of the coefficients in the corresponding continuum equations are also deduced. Furthermore, we suggest that, in some CGM's, the p dependence on the coefficients of the continuum equation that represents their universality class can be nontrivial. In some cases, the process cannot be represented by a unique universality class. In order to show this, we introduce a CGM describing RD competing with a constrained EW model. This CGM shows a transition in the scaling exponents from RD to a Kardar-Parisi-Zhang behavior when p is close to 0 and to a Edward-Wilkinson one when p is close to 1 at practical time and length scales. Our simulation results are in excellent agreement with the analytic predictions.

Universality in two-dimensional Kardar-Parisi-Zhang growth

We analyze simulation results of a model proposed for etching of a crystalline solid and results of other discrete models in the (2+1)-dimensional Kardar-Parisi-Zhang (KPZ) class. In the steady states, the moments W(n) of orders n=2,3,4 of the height distribution are estimated. Results for the etching model, the ballistic deposition model, and the temperature-dependent body-centered restricted solid-on-solid model suggest the universality of the absolute value of the skewness S identical with W(3)/W(3/2)(2) and of the value of the kurtosis Q identical with W(4)/W(2)(2)-3. The sign of the skewness is the same as of the parameter lambda of the KPZ equation which represents the process in the continuum limit. The best numerical estimates, obtained from the etching model, are absolute value of S=0.26+/-0.01 and Q=0.134+/-0.015. For this model, the roughness exponent alpha=0.383+/-0.008 is obtained, accounting for a constant correction term (intrinsic width) in the scaling of the squared interface width. This value is slightly below previous estimates of extensive simulations and rules out the proposal of the exact value alpha=2/5. The conclusion is supported by results for the ballistic deposition model. Independent estimates of the dynamical exponent and of the growth exponent are 1.605< or =z< or =1.64 and beta=0.229+/-0.005, respectively, which are consistent with the relations alpha+z=2 and z=alpha/beta.

Phase-separation transition in one-dimensional driven models

A class of models of two-species driven diffusive systems which is shown to exhibit phase separation in d=1 dimensions is introduced. Unlike previously studied models exhibiting similar phenomena, here the relative density of the two species is fluctuating within the macroscopic domain of the phase separtated state. The nature of the phase transition from the homogeneous to the phase-separated state is discussed in view of a recently introduced criterion for phase separation in one-dimensional driven systems.

Algorithmic scalability in globally constrained conservative parallel discrete event simulations of asynchronous systems

We consider parallel simulations for asynchronous systems employing L processing elements that are arranged on a ring. Processors communicate only among the nearest neighbors and advance their local simulated time only if it is guaranteed that this does not violate causality. In simulations with no constraints, in the infinite L limit the utilization scales [Korniss et al., Phys. Rev. Lett. 84, 1351 (2000)]; but, the width of the virtual time horizon diverges (i.e., the measurement phase of the algorithm does not scale). In this work, we introduce a moving Delta-window global constraint, which modifies the algorithm so that the measurement phase scales as well. We present results of systematic studies in which the system size (i.e., L and the volume load per processor) as well as the constraint are varied. The Delta constraint eliminates the extreme fluctuations in the virtual time horizon, provides a bound on its width, and controls the average progress rate. The width of the Delta window can serve as a tuning parameter that, for a given volume load per processor, could be adjusted to optimize the utilization, so as to maximize the efficiency. This result may find numerous applications in modeling the evolution of general spatially extended short-range interacting systems with asynchronous dynamics, including dynamic Monte Carlo studies.

Nonequilibrium wetting transitions with short range forces

We analyze within mean-field theory as well as numerically a Kardar-Parisi-Zhang equation that describes nonequilibrium wetting. Both complete and critical wettitng transitions were found and characterized in detail. For one-dimensional substrates the critical weting temperature is depressed by fluctuations. In addition, we have investigated a region in the space of parameters (temperature and chemical potential) where the wet and nonwet phases coexist. Finite-size scaling analysis of the interfacial detaching times indicates that the finite coexistence region survives in the thermodynamic limit. Within this region we have observed (stable or very long lived) structures related to spatiotemporal intermittency in other systems. In the interfacial representation these structures exhibit perfect triangular (pyramidal) patterns in one dimension (two dimensions), which are characterized by their slope and size distribution.

Crossover effects in a discrete deposition model with Kardar-Parisi-Zhang scaling

We simulated a growth model in (1+1) dimensions in which particles are aggregated according to the rules of ballistic deposition with probability p or according to the rules of random deposition with surface relaxation (Family model) with probability 1-p. For any p>0, this system is in the Kardar-Parisi-Zhang (KPZ) universality class, but it presents a slow crossover from the Edwards-Wilkinson class (EW) for small p. From the scaling of the growth velocity, the parameter p is connected to the coefficient lambda of the nonlinear term of the KPZ equation, giving lambda approximately p(gamma), with gamma=2.1+/-0.2. Our numerical results confirm the interface width scaling in the growth regime as W approximately lambda(beta)t(beta) and the scaling of the saturation time as tau approximately lambda(-1)L(z), with the expected exponents beta=1/3 and z=3/2, and strong corrections to scaling for small lambda. This picture is consistent with a crossover time from EW to KPZ growth in the form t(c) approximately lambda(-4) approximately p(-8), in agreement with scaling theories and renormalization group analysis. Some consequences of the slow crossover in this problem are discussed and may help investigations of more complex models.

Critical properties of the synchronization transition in space-time chaos

We study two coupled spatially extended dynamical systems which exhibit space-time chaos. The transition to the synchronized state is treated as a nonequilibrium phase transition, where the average synchronization error is the order parameter. The transition in one-dimensional systems is found to be generically in the universality class of the Kardar-Parisi-Zhang equation with a growth-limiting term ("bounded KPZ"). For systems with very strong nonlinearities in the local dynamics, however, the transition is found to be in the universality class of directed percolation.

Kinetic roughening model with opposite Kardar-Parisi-Zhang nonlinearities

We introduce a model that simulates a kinetic roughening process with two kinds of particle: one follows ballistic deposition (BD) kinetics and the other restricted solid-on-solid Kim-Kosterlitz (KK) kinetics. Both of these kinetics are in the universality class of the nonlinear Kardar-Parisi-Zhang equation, but the BD kinetics has a positive nonlinear constant while the KK kinetics has a negative one. In our model, called the BD-KK model, we assign the probabilities p and (1-p) to the KK and BD kinetics, respectively. For a specific value of p, the system behaves as a quasilinear model and the up-down symmetry is restored. We show that nonlinearities of odd order are relevant in this low nonlinear limit.

Extremal-point densities of interface fluctuations

We introduce and investigate the stochastic dynamics of the density of local extrema (minima and maxima) of nonequilibrium surface fluctuations. We give a number of analytic results for interface fluctuations described by linear Langevin equations, and for on-lattice, solid-on-solid surface-growth models. We show that, in spite of the nonuniversal character of the quantities studied, their behavior against the variation of the microscopic length scales can present generic features, characteristic of the macroscopic observables of the system. The quantities investigated here provide us with tools that give an unorthodox approach to the dynamics of surface morphologies: a statistical analysis from the short-wavelength end of the Fourier decomposition spectrum. In addition to surface-growth applications, our results can be used to solve the asymptotic scalability problem of massively parallel algorithms for discrete-event simulations, which are extensively used in Monte Carlo simulations on parallel architectures.