Geometry dependence in linear interface growth
arXiv:1908.10892 · doi:10.1103/PhysRevE.100.042107
Abstract
The effect of geometry in the statistics of \textit{nonlinear} universality classes for interface growth has been widely investigated in recent years and it is well known to yield a split of them into subclasses. In this work, we investigate this for the \textit{linear} classes of Edwards-Wilkinson (EW) and of Mullins-Herring (MH) in one- and two-dimensions. From comparison of analytical results with extensive numerical simulations of several discrete models belonging to these classes, as well as numerical integrations of the growth equations on substrates of fixed size (flat geometry) or expanding linearly in time (radial geometry), we verify that the height distributions (HDs), the spatial and the temporal covariances are universal, but geometry-dependent. In fact, the HDs are always Gaussian and, when defined in terms of the so-called "KPZ ansatz" , their probability density functions have mean null, so that all their cumulants are null, except by their variances, which assume different values in the flat and radial cases. The shape of the (rescaled) covariance curves is analyzed in detail and compared with some existing analytical results for them. Overall, these results demonstrate that the splitting of such university classes is quite general, being not restricted to the nonlinear ones.
References in corpus (34)
- Probability Distribution of the Free Energy of the Continuum Directed Random Polymer in 1+1 dimensions
- Universal Distributions for Growth Processes in 1+1 Dimensions and Random Matrices
- The one-dimensional KPZ equation: an exact solution and its universality
- Universal Fluctuations of Growing Interfaces: Evidence in Turbulent Liquid Crystals
- Growing interfaces uncover universal fluctuations behind scale invariance
- A KPZ Cocktail- Shaken, not stirred: Toasting 30 years of kinetically roughened surfaces
- An exact solution for the KPZ equation with flat initial conditions
- Persistence exponents for fluctuating interfaces
- Spatial correlations of the 1D KPZ surface on a flat substrate
- Large time asymptotics of growth models on space-like paths II: PNG and parallel TASEP
- Universal fluctuations in the growth of semiconductor thin films
- Universal correlators and distributions as experimental signatures of 2+1 Kardar-Parisi-Zhang growth
- Persistence of Kardar-Parisi-Zhang Interfaces
- Kardar-Parisi-Zhang universality class in 2+1 dimensions: Universal geometry-dependent distributions and finite-time corrections
- Kinetic roughening of surfaces: Derivation, solution and application of linear growth equations
- Universal aspects of curved, flat & stationary-state Kardar-Parisi-Zhang statistics
- Universal fluctuations in radial growth models belonging to the KPZ universality class
- Universal fluctuations in KPZ growth on one-dimensional flat substrates
- Mapping of 2+1-dimensional Kardar-Parisi-Zhang growth onto a driven lattice gas model of dimer
- Universality and dependence on initial conditions in the class of the nonlinear molecular beam epitaxy equation
- Non-universal parameters, corrections and universality in Kardar-Parisi-Zhang growth
- Interface fluctuations for deposition on enlarging flat substrates
- Initial pseudo-steady state & asymptotic KPZ universality in semiconductor on polymer deposition
- Temperature effect on (2+1) experimental Kardar-Parisi-Zhang growth
- Kardar-Parisi-Zhang Interfaces with Inward Growth
- Topology and the Kardar-Parisi-Zhang universality class
- Substrate effects and diffusion dominated roughening in Cu2O electrodeposition
- A pseudo-spectral approach to inverse problems in interface dynamics
- Kardar-Parisi-Zhang growth on one-dimensional decreasing substrates
- Stochastic growth equations on growing domains
- Stochastic models for tumoral growth
- Circular Kardar-Parisi-Zhang interfaces evolving out of the plane
- Dynamics of curved interfaces
- Geometrical approach to tumor growth
Cited by in corpus (13)
- Nonequilibrium criticality driven by Kardar-Parisi-Zhang fluctuations in the synchronization of oscillator lattices
- Spreading fronts of wetting liquid droplets: microscopic simulations and universal fluctuations
- Transition between chaotic and stochastic universality classes of kinetic roughening
- Kardar-Parisi-Zhang universality class in the synchronization of oscillator lattices with time-dependent noise
- Height fluctuations in homoepitaxial thin film growth: A numerical study
- Surface growth on treelike lattices and the upper critical dimension of the KPZ class
- Kardar-Parisi-Zhang growth on square domains that enlarge nonlinearly in time
- Microscopic fluctuations in the spreading fronts of circular wetting liquid droplets
- Height distributions in interface growth: The role of the averaging process
- Universal interface fluctuations in the contact process
- Numerical Integration of the KPZ and Related Equations on Networks: The Case of the Cayley Tree
- Exponents and front fluctuations in the quenched Kardar-Parisi-Zhang universality class of one- and two- dimensional interfaces
- Dimensional crossover in surface growth on rectangular substrates