Kardar-Parisi-Zhang universality class in the synchronization of oscillator lattices with time-dependent noise.

Systems of oscillators subject to time-dependent noise typically achieve synchronization for long times when their mutual coupling is sufficiently strong. The dynamical process whereby synchronization is reached can be thought of as a growth process in which an interface formed by the local phase field gradually roughens and eventually saturates. Such a process is here shown to display the generic scale invariance of the one-dimensional Kardar-Parisi-Zhang universality class, including a Tracy-Widom probability distribution for phase fluctuations around their mean.

Erratum: Large-scale kinetic roughening behavior of coffee-ring fronts [Phys. Rev. E 106, 044801 (2022)].

This corrects the article DOI: 10.1103/PhysRevE.106.

Shape effects in the fluctuations of random isochrones on a square lattice.

We consider the isochrone curves in first-passage percolation on a 2D square lattice, i.e., the boundary of the set of points which can be reached in less than a given time from a certain origin.

Universal fluctuations of global geometrical measurements in planar clusters.

We characterize universal features of the sample-to-sample fluctuations of global geometrical observables, such as the area, width, length, and center-of-mass position, in random growing planar clusters. Our examples are taken from simulations of both continuous and discrete models of kinetically rough interfaces, including several universality classes, such as Kardar-Parisi-Zhang. We mostly focus on the scaling behavior with time of the sample-to-sample deviation for those global magnitudes, but we have also characterized their histograms and correlations.

Universal interface fluctuations in the contact process.

We study the interface representation of the contact process at its directed-percolation critical point, where the scaling properties of the interface can be related to those of the original particle model. Interestingly, such a behavior happens to be intrinsically anomalous and more complex than that described by the standard Family-Vicsek dynamic scaling Ansatz of surface kinetic roughening. We expand on a previous numerical study by Dickman and Muñoz [Phys.

Large-scale kinetic roughening behavior of coffee-ring fronts.

We have studied the kinetic roughening behavior of the fronts of coffee-ring aggregates via extensive numerical simulations of the off-lattice model considered for this context [Dias et al., Soft Matter 14, 1903 (2018)1744-683X10.1039/C7SM02136D].

Anomalous ballistic scaling in the tensionless or inviscid Kardar-Parisi-Zhang equation.

The one-dimensional Kardar-Parisi-Zhang (KPZ) equation is becoming an overarching paradigm for the scaling of nonequilibrium, spatially extended, classical and quantum systems with strong correlations. Recent analytical solutions have uncovered a rich structure regarding its scaling exponents and fluctuation statistics. However, the zero surface tension or zero viscosity case eludes such analytical solutions and has remained ill-understood.

Spreading fronts of wetting liquid droplets: Microscopic simulations and universal fluctuations.

We have used kinetic Monte Carlo (kMC) simulations of a lattice gas to study front fluctuations in the spreading of a nonvolatile liquid droplet onto a solid substrate. Our results are consistent with a diffusive growth law for the radius of the precursor layer, R∼t^{δ}, with δ≈1/2 in all the conditions considered for temperature and substrate wettability, in good agreement with previous studies. The fluctuations of the front exhibit kinetic roughening properties with exponent values which depend on temperature T, but become T independent for sufficiently high T.

Surface nanopatterning by ion beam irradiation: compositional effects.

Surface nanopatterning induced by ion beam irradiation (IBI) has emerged as an effective nanostructuring technique since it induces patterns on large areas of a wide variety of materials, in short time, and at low cost. Nowadays, two main subfields can be distinguished within IBI nanopatterning depending on the irrelevant or relevant role played by the surface composition. In this review, we give an up-dated account of the progress reached when surface composition plays a relevant role, with a main focus on IBI surface patterning with simultaneous co-deposition of foreign atoms.

Non-KPZ fluctuations in the derivative of the Kardar-Parisi-Zhang equation or noisy Burgers equation.

The Kardar-Parisi-Zhang (KPZ) equation is a paradigmatic model of nonequilibrium low-dimensional systems with spatiotemporal scale invariance, recently highlighting universal behavior in fluctuation statistics. Its space derivative, namely the noisy Burgers equation, has played a very important role in its study, predating the formulation of the KPZ equation proper, and being frequently held as an equivalent system. We show that, while differences in the scaling exponents for the two equations are indeed due to a mere space derivative, the field statistics behave in a remarkably different way: while the KPZ equation follows the Tracy-Widom distribution, its derivative displays Gaussian behavior, hence being in a different universality class.

Gaussian statistics as an emergent symmetry of the stochastic scalar Burgers equation.

Symmetries play a conspicuous role in the large-scale behavior of critical systems. In equilibrium they allow us to classify asymptotics into different universality classes, and out of equilibrium, they sometimes emerge as collective properties which are not explicit in the "bare" interactions. Here we elucidate the emergence of an up-down symmetry in the asymptotic behavior of the stochastic scalar Burgers equation in one and two dimensions, manifested by the occurrence of Gaussian fluctuations even within the time regime controlled by nonlinearities.

Nonuniversality of front fluctuations for compact colonies of nonmotile bacteria.

The front of a compact bacterial colony growing on a Petri dish is a paradigmatic instance of non-equilibrium fluctuations in the celebrated Eden, or Kardar-Parisi-Zhang (KPZ), universality class. While in many experiments the scaling exponents crucially differ from the expected KPZ values, the source of this disagreement has remained poorly understood. We have performed growth experiments with B.

Concurrent segregation and erosion effects in medium-energy iron beam patterning of silicon surfaces.

We have bombarded crystalline silicon targets with a 40 keV Fe ion beam at different incidence angles. The resulting surfaces have been characterized by atomic force, current-sensing and magnetic force microscopies, scanning electron microscopy, and x-ray photoelectron spectroscopy. We have found that there is a threshold angle smaller than 40° for the formation of ripple patterns, which is definitely lower than those frequently reported for noble gas ion beams.

Morphological stabilization and KPZ scaling by electrochemically induced co-deposition of nanostructured NiW alloy films.

We have assessed the stabilizing role that induced co-deposition has in the growth of nanostructured NiW alloy films by electrodeposition on polished steel substrates, under pulsed galvanostatic conditions. We have compared the kinetic roughening properties of NiW films with those of Ni films deposited under the same conditions, as assessed by Atomic Force Microscopy. The surface morphologies of both systems are super-rough at short times, but differ at long times: while a cauliflower-like structure dominates for Ni, the surfaces of NiW films display a nodular morphology consistent with more stable, conformal growth, whose height fluctuations are in the Kardar-Parisi-Zhang universality class of rough two-dimensional interfaces.

Universal behavior of crystalline membranes: Crumpling transition and Poisson ratio of the flat phase.

We revisit the universal behavior of crystalline membranes at and below the crumpling transition, which pertains to the mechanical properties of important soft and hard matter materials, such as the cytoskeleton of red blood cells or graphene. Specifically, we perform large-scale Monte Carlo simulations of a triangulated two-dimensional phantom network which is freely fluctuating in three-dimensional space. We obtain a continuous crumpling transition characterized by critical exponents which we estimate accurately through the use of finite-size techniques.

Fully nonlinear dynamics of stochastic thin-film dewetting.

The spontaneous formation of droplets via dewetting of a thin fluid film from a solid substrate allows materials nanostructuring. Often, it is crucial to be able to control the evolution, and to produce patterns characterized by regularly spaced droplets. While thermal fluctuations are expected to play a role in the dewetting process, their relevance has remained poorly understood, particularly during the nonlinear stages of evolution that involve droplet formation.

Macroscopic response to microscopic intrinsic noise in three-dimensional Fisher fronts.

We study the dynamics of three-dimensional Fisher fronts in the presence of density fluctuations. To this end we simulate the Fisher equation subject to stochastic internal noise, and study how the front moves and roughens as a function of the number of particles in the system, N. Our results suggest that the macroscopic behavior of the system is driven by the microscopic dynamics at its leading edge where number fluctuations are dominated by rare events.

Strong anisotropy in two-dimensional surfaces with generic scale invariance: nonlinear effects.

We expand a previous study [Phys. Rev. E 86, 051611 (2012)] on the conditions for occurrence of strong anisotropy in the scaling properties of two-dimensional surfaces displaying generic scale invariance.

Pattern-wavelength coarsening from topological dynamics in silicon nanofoams.

We report the experimental observation of a submicron cellular structure on the surface of silicon targets eroded by an ion plasma. Analysis by atomic force microscopy allows us to assess the time evolution and show that the system can be described quantitatively by the convective Cahn-Hilliard equation, found in the study of domain coarsening for a large class of driven systems. The space-filling trait of the ensuing pattern relates it to evolving foams.

Circular Kardar-Parisi-Zhang equation as an inflating, self-avoiding ring polymer.

We consider the Kardar-Parisi-Zhang equation for a circular interface in two dimensions, unconstrained by the standard small-slope and no-overhang approximations. Numerical simulations using an adaptive scheme allow us to elucidate the complete time evolution as a crossover between a short-time regime with the interface fluctuations of a self-avoiding ring or two-dimensional vesicle, and a long-time regime governed by the Tracy-Widom distribution expected for this geometry. For small-noise amplitudes, scaling behavior is only of the latter type.

Strong anisotropy in two-dimensional surfaces with generic scale invariance: Gaussian and related models.

Among systems that display generic scale invariance, those whose asymptotic properties are anisotropic in space (strong anisotropy, SA) have received relatively less attention, especially in the context of kinetic roughening for two-dimensional surfaces. This is in contrast with their experimental ubiquity, e.g.

Independence of interrupted coarsening on initial system order: ion-beam nanopatterning of amorphous versus crystalline silicon targets.

Interrupted coarsening (IC) has recently been identified as an important feature for the dynamics of the typical length-scale in pattern-forming systems on surfaces. In practice, it can be beneficial to improve pattern ordering since it combines a certain degree of defect suppression with a limited increase in the typical pattern wavelength. However, little is known about its robustness with respect to changes in the preparation of the initial system for cases with potential applications.

Pattern formation in stromatolites: insights from mathematical modelling.

To this day, computer models for stromatolite formation have made substantial use of the Kardar-Parisi-Zhang (KPZ) equation. Oddly enough, these studies yielded mutually exclusive conclusions about the biotic or abiotic origin of such structures. We show in this paper that, at our current state of knowledge, a purely biotic origin for stromatolites can neither be proved nor disproved by means of a KPZ-based model.