Publications (53)
Anomalous scaling in a non local growth model in the Kardar-Parisi-Zhang universality class
Mario Castro, Rodolfo Cuerno, Angel S\anchez +1
We study the interface dynamics of a discrete model to quantitatively describe electrochemical deposition experiments. Extensive numerical simulations indicate that the interface d…
Nonequilibrium criticality driven by Kardar-Parisi-Zhang fluctuations in the synchronization of oscillator lattices
Ricardo Gutiérrez, Rodolfo Cuerno
The synchronization of oscillator ensembles is pervasive throughout nonlinear science, from classical or quantum mechanics to biology, to human assemblies. Traditionally, the main…
Non-universality of front fluctuations for compact colonies of non-motile bacteria
Silvia N. Santalla, Javier RodrÃguez-Laguna, José P. Abad +5
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), uni…
Symmetry of surface nanopatterns induced by ion-beam sputtering: the role of anisotropic surface diffusion
Javier Renedo, Javier Muñoz-GarcÃa, Mario Castro +1
Ion Beam Sputtering (IBS) is a cost-effective technique able to produce ordered nanopatterns on the surfaces of different materials. To date, most theoretical studies of this proce…
Strong anisotropy in surface kinetic roughening: analysis and experiments
Edoardo Vivo, Matteo Nicoli, Martin Engler +3
We report an experimental assessment of surface kinetic roughening properties that are anisotropic in space. Working for two specific instances of silicon surfaces irradiated by io…
Exponents and front fluctuations in the quenched Kardar-Parisi-Zhang universality class of one- and two- dimensional interfaces
Ãngela Tajuelo-Valbuena, Jara Trujillo-Mulero, Juan J. Meléndez +2
We have simulated an automaton version of the quenched Kardar-Parisi-Zhang (qKPZ) equation in one and two dimensions in order to study the scaling properties of the interface at th…
Strong anisotropy in two-dimensional surfaces with generic scale invariance: Gaussian and related models
Edoardo Vivo, Matteo Nicoli, Rodolfo Cuerno
Among systems that display generic scale invariance, those whose asymptotic properties are anisotropic in space (strong anisotropy, SA) have received a relatively smaller attention…
Non-linear ripple dynamics on amorphous surfaces patterned by ion-beam sputtering
Javier Muñoz-GarcÃa, Mario Castro, Rodolfo Cuerno
Erosion by ion-beam sputtering (IBS) of amorphous targets at off-normal incidence frequently produces a (nanometric) rippled surface pattern, strongly resembling macroscopic ripple…
Topology and the Kardar-Parisi-Zhang universality class
Silvia N. Santalla, Javier Rodriguez-Laguna, Alessio Celi +1
We study the role of the topology of the background space on the one-dimensional Kardar-Parisi-Zhang (KPZ) universality class. To do so, we study the growth of balls on disordered…
Multiparticle Biased DLA with surface diffusion: a comprehensive model of electrodeposition
Mario Castro, Rodolfo Cuerno, Angel Sanchez +1
We present a complete study of the Multiparticle Biased Diffusion-Limited Aggregation (MBDLA) model supplemented with surface difussion (SD), focusing on the relevance and effects…
A microscopic model for thin film spreading
Douglas B. Abraham, Rodolfo Cuerno, Esteban Moro
A microscopic, driven lattice gas model is proposed for the dynamics and spatio-temporal fluctuations of the precursor film observed in spreading experiments. Matter is transported…
Single tensionless transition in the Laplacian roughening model
Juan Jesus Ruiz-Lorenzo, Esteban Moro, Rodolfo Cuerno
We report large scale Monte Carlo simulations of the equilibrium discrete Laplacian roughening (dLr) model, originally introduced as the simplest one accommodating the hexatic phas…
Noisy Kuramoto-Sivashinsky equation for an erosion model
Kent Baekgaard Lauritsen, Rodolfo Cuerno, Hernan A. Makse
We derive the continuum equation for a discrete model for ion sputtering. We follow an approach based on the master equation, and discuss how it can be truncated to a Fokker-Planck…
Dynamical phase diagram of synchronization in one dimension: universal behavior from Edwards-Wilkinson to random deposition through Kardar-Parisi-Zhang
Ricardo Gutierrez, Rodolfo Cuerno
Synchronization in one dimension displays generic scale invariance with universal properties previously observed in surface kinetic roughening and the wider context of the Kardar-P…
Universality of cauliflower-like fronts: from nanoscale thin films to macroscopic plants
Mario Castro, Rodolfo Cuerno, Matteo Nicoli +2
Chemical vapor deposition (CVD) is a widely used technique to grow solid materials with accurate control of layer thickness and composition. Under mass-transport-limited conditions…
Universality Classes with Strong Coupling in Conserved Surface Roughening: Explicit vs Emergent Symmetries
Pedro Gatón-Pérez, Enrique Rodriguez-Fernandez, Rodolfo Cuerno
The occurrence of strong coupling or nonlinear scaling behavior for kinetically rough interfaces whose dynamics are conserved, but not necessarily variational, remains to be fully…
Influence of coupling symmetries and noise on the critical dynamics of synchronizing oscillator lattices
Ricardo Gutierrez, Rodolfo Cuerno
Recent work has shown that the synchronization process in lattices of self-sustained (phase and limit-cycle) oscillators displays universal scale-invariant behavior previously stud…
Renormalization Group Analysis of a Noisy Kuramoto-Sivashinsky Equation
Rodolfo Cuerno, Kent Baekgaard Lauritsen
We have analyzed the Kuramoto-Sivashinsky equation with a stochastic noise term through a dynamic renormalization group calculation. For a system in which the lattice spacing is sm…
Shape effects in the fluctuations of random isochrones on a square lattice
Iván Ãlvarez Domenech, Javier RodrÃguez-Laguna, Rodolfo Cuerno +2
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 c…
Dynamic effects induced by renormalization in anisotropic pattern forming systems
Adrian Keller, Matteo Nicoli, Stefan Facsko +1
The dynamics of patterns in large two-dimensional domains remains a challenge in non-equilibrium phenomena. Often it is addressed through mild extensions of one-dimensional equatio…
Dynamic renormalization group study of a generalized continuum model of crystalline surfaces
Rodolfo Cuerno, Esteban Moro
We apply the Nozieres-Gallet dynamic renormalization group (RG) scheme to a continuum equilibrium model of a d-dimensional surface relaxing by linear surface tension and linear sur…
Universal fluctuations of global geometrical measurements in planar clusters
Silvia N. Santalla, Iván Ãlvarez Domenech, Daniel Villarrubia +2
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 g…
Gaussian statistics as an emergent symmetry of the stochastic Burgers equation
Enrique Rodriguez-Fernandez, Rodolfo Cuerno
Symmetries play a conspicuous role in the large-scale behavior of critical systems. While in equilibrium they allow to classify asymptotics into different universality classes, out…
Nonconserved critical dynamics of the two-dimensional Ising model as a surface kinetic roughening process
Héctor Vaquero del Pino, Rodolfo Cuerno
We have revisited the non-conserved (or model A) critical dynamics of the two-dimensional Ising model through numerical simulations of its lattice and continuum formulations --Glau…
Transients due to instabilities hinder Kardar-Parisi-Zhang scaling: a unified derivation for surface growth by electrochemical and chemical vapor deposition
Rodolfo Cuerno, Mario Castro
We propose a unified moving boundary problem for surface growth by electrochemical and chemical vapor deposition, which is derived from constitutive equations into which stochastic…
Kardar-Parisi-Zhang Universality in First-Passage Percolation: the Role of Geodesic Degeneracy
Pedro Córdoba-Torres, Silvia N. Santalla, Rodolfo Cuerno +1
We have characterized the scaling behavior of the first-passage percolation (FPP) model on two types of discrete networks, the regular square lattice and the disordered Delaunay la…
Stochastic Model for Surface Erosion Via Ion-Sputtering: Dynamical Evolution from Ripple Morphology to Rough Morphology
Rodolfo Cuerno, Hernan A. Makse, Silvina Tomassone +2
Surfaces eroded by ion-sputtering are sometimes observed to develop morphologies which are either ripple (periodic), or rough (non-periodic). We introduce a discrete stochastic mod…
Hydrodynamic approach to surface pattern formation by ion beams
Mario Castro, Rodolfo Cuerno
On the proper timescale, amorphous solids can flow. Solid flow can be observed macroscopically in glaciers or lead pipes, but it can also be artificially enhanced by creating defec…
Coupling of morphology to surface transport in ion-beam irradiated surfaces. I. Oblique incidence
Javier Muñoz-GarcÃa, Rodolfo Cuerno, Mario Castro
We propose and study a continuum model for the dynamics of amorphizable surfaces undergoing ion-beam sputtering (IBS) at intermediate energies and oblique incidence. After consider…
Dynamics of Rough Interfaces in Chemical Vapor Deposition: Experiments and a Model for Silica Films
Fernando Ojeda, Rodolfo Cuerno, Roberto Salvarezza +1
We study the surface dynamics of silica films grown by low pressure chemical vapor deposition. Atomic force microscopy measurements show that the surface reaches a scale invariant…
Production of ordered silicon nanocrystals by low-energy ion sputtering
Raul Gago, Luis Vazquez, Rodolfo Cuerno +3
We report on the production of ordered assemblies of silicon nanostructures by means of irradiation of a Si(100) substrate with 1.2 keV Ar ions at normal incidence. Atomic Force an…
Spectrum of an Elliptic Free Fermionic Corner Transfer Matrix Hamiltonian
Rodolfo Cuerno
The eigenvalues of the Corner Transfer Matrix Hamiltonian associated to the elliptic matrix of the eight vertex free fermion model are computed in the anisotropic case for magn…
Unified moving boundary model with fluctuations for unstable diffusive growth
Matteo Nicoli, Mario Castro, Rodolfo Cuerno
We study a moving boundary model of non-conserved interface growth that implements the interplay between diffusive matter transport and aggregation kinetics at the interface. Consp…
Dimensional fragility of the Kardar-Parisi-Zhang universality class
Matteo Nicoli, Rodolfo Cuerno, Mario Castro
We assess the dependence on substrate dimensionality of the asymptotic scaling behavior of a whole family of equations that feature the basic symmetries of the Kardar-Parisi-Zhang…
Kardar-Parisi-Zhang universality class in the synchronization of oscillator lattices with time-dependent noise
Ricardo Gutierrez, Rodolfo Cuerno
Systems of oscillators subject to time-dependent noise typically achieve synchronization for long times when their mutual coupling is sufficiently strong. The dynamical process whe…
Short-range stationary patterns and long-range disorder in an evolution equation for one-dimensional interfaces
Javier Muñoz-GarcÃa, Rodolfo Cuerno, Mario Castro
A novel local evolution equation for one-dimensional interfaces is derived in the context of erosion by ion beam sputtering. We present numerical simulations of this equation which…
Super-roughening versus intrinsic anomalous scaling of surfaces
Juan M. Lopez, Miguel A. Rodriguez, Rodolfo Cuerno
In this paper we study kinetically rough surfaces which display anomalous scaling in their local properties such as roughness, or height-height correlation function. By studying th…
Morphology of Ion-Sputtered Surfaces
Maxim Makeev, Rodolfo Cuerno, Albert-László Barabási
We derive a stochastic nonlinear continuum theory to describe the morphological evolution of amorphous surfaces eroded by ion bombardment. Starting from Sigmund's theory of sputter…
Self-Organized Ordering of Nanostructures Produced by Ion-Beam Sputtering
Mario Castro, Rodolfo Cuerno, Luiz Vazquez +1
We study the self-organized ordering of nanostructures produced by ion-beam sputtering (IBS) of targets amorphizing under irradiation. By introducing a model akin to models of patt…
Random geometry and the Kardar-Parisi-Zhang universality class
Silvia N. Santalla, Javier Rodriguez-Laguna, Tom LaGatta +1
We consider a model of a quenched disordered geometry in which a random metric is defined on , which is flat on average and presents short-range correlations. We foc…
Self-organized surface nanopatterning by ion beam sputtering
Javier Muñoz-GarcÃa, Luis Vázquez, Rodolfo Cuerno +3
The production of nanopatterns on the surfaces of targets irradiated by ion beams at low and intermediate energies has developed during the present decade to a salient degree of co…
Ion induced solid flow
Mario Castro, Rodolfo Cuerno
Amorphous solids can flow over very long periods of time. Solid flow can also be artificially enhanced by creating defects, as by Ion Beam Sputtering (IBS) in which collimated ions…
Analytical results for a continuum model of crystalline tensionless surfaces. I. Variational mean field study
Esteban Moro, Rodolfo Cuerno
We study analytically the equilibrium and near-equilibrium properties of a model of surfaces relaxing via linear surface diffusion and subject to a lattice potential. We employ the…
Universality issues in surface kinetic roughening of thin solid films
Rodolfo Cuerno, Luis Vazquez
Since publication of the main contributions on the theory of kinetic roughening more than fifteen years ago, many works have been reported on surface growth or erosion that employ…
Strong anisotropy in two-dimensional surfaces with generic scale invariance: Non-linear effects
Edoardo Vivo, Matteo Nicoli, Rodolfo Cuerno
We expand a previous study [Phys. Rev. E 86, 051611 (2012)] on the conditions for occurrence of strong anisotropy (SA) in the scaling properties of two-dimensional surfaces display…
The circular Kardar-Parisi-Zhang equation as an inflating, self-avoiding ring polymer
Silvia N. Santalla, Javier Rodriguez-Laguna, Rodolfo Cuerno
We consider the Kardar-Parisi-Zhang (KPZ) equation for a circular interface in two dimensions, unconstrained by the standard small-slopes and no-overhang approximations. Numerical…
Dynamic Scaling of Ion-Sputtered Surfaces
Rodolfo Cuerno, Albert-Laszlo Barabasi
We derive a stochastic nonlinear equation to describe the evolution and scaling properties of surfaces eroded by ion bombardment. The coefficients appearing in the equation can be…
Intrinsic geometry approach to surface kinetic roughening
Javier Rodriguez-Laguna, Silvia N. Santalla, Rodolfo Cuerno
A model for kinetic roughening of one-dimensional interfaces is presented within an intrinsic geometry framework that is free from the standard small-slope and no-overhang approxim…
Kinetic roughening in a realistic model of non-conserved interface growth
Matteo Nicoli, Mario Castro, Rodolfo Cuerno
We provide a quantitative picture of non-conserved interface growth from a diffusive field making special emphasis on two main issues, the range of validity of the effective small-…
Dynamical Renormalization Group Study for a Class of Non-local Interface Equations
Matteo Nicoli, Rodolfo Cuerno, Mario Castro
We provide a detailed Dynamic Renormalization Group study for a class of stochastic equations that describe non-conserved interface growth mediated by non-local interactions. We co…
Kardar-Parisi-Zhang asymptotics for the two-dimensional noisy Kuramoto-Sivashinsky equation
Matteo Nicoli, Edoardo Vivo, Rodolfo Cuerno
We study numerically the Kuramoto-Sivashinsky (KS) equation forced by external white noise in two space dimensions, that is a generic model for e.g. surface kinetic roughening in t…
Kardar-Parisi-Zhang fluctuations in the synchronization dynamics of limit-cycle oscillators
Ricardo Gutiérrez, Rodolfo Cuerno
The time-dependent process whereby one-dimensional systems of self-sustained oscillators synchronize is shown to display scale invariance in space and time, akin to that found in t…
Anomalous ballistic scaling in the tensionless or inviscid Kardar-Parisi-Zhang equation
Enrique Rodriguez-Fernandez, Silvia N. Santalla, Mario Castro +1
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…