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We study the dynamics of an exactly solvable lattice model for inhomogeneous interface growth. The interface grows deterministically with constant velocity except along a defect line where the growth process is random. We obtain exact…

Condensed Matter · Physics 2009-10-28 Gunter M. Schütz

We report on an extensive numerical investigation of the Kardar-Parisi-Zhang equation describing non-equilibrium interfaces. Attention is paid to the dependence of the growth exponents on the details of the distribution of the noise. All…

Statistical Mechanics · Physics 2009-10-30 T. J. Newman , Michael R. Swift

Until very recently, the asymptotic occurrence of intrinsic anomalous scaling has been expected to require concomitant effects for kinetically rough interfaces, like quenched disorder or morphological instabilities. However, counterexamples…

Statistical Mechanics · Physics 2024-05-15 E. Rodriguez-Fernandez , S. N. Santalla , M. Castro , R. Cuerno

A diffused interface model describing the evolution of two conterminous incompressible fluids in a porous medium is discussed. The system consists of the Cahn-Hilliard equation with Flory-Huggins logarithmic potential, coupled via surface…

Analysis of PDEs · Mathematics 2024-07-24 Nitu Lakhmara , Hari Shankar Mahato

We report on a linear Langevin model that describes the evolution of the roughness of two interfaces that move towards each other and are coupled by a diffusion field. This model aims at describing the closing of the gap between two…

Materials Science · Physics 2022-07-27 Bastien Marguet , F. D. A. Aarão Reis , Olivier Pierre-Louis

The dynamics of linear stochastic growth equations on growing substrates is studied. The substrate is assumed to grow in time following the power law $t^\gamma$, where the growth index $\gamma$ is an arbitrary positive number. Two different…

Statistical Mechanics · Physics 2015-05-13 Carlos Escudero

According to recent numerical results from lattice models, the critical exponents of systems with many absorbing states and an order parameter coupled to a non-diffusive conserved field coincide with those of the linear interface depinning…

Condensed Matter · Physics 2016-08-31 Mikko Alava , Miguel A. Munoz

We study the motion of phase interfaces in a diffusive lattice equation with bistable nonlinearity and derive a free boundary problem with hysteresis to describe the macroscopic evolution in the parabolic scaling limit. The first part of…

Analysis of PDEs · Mathematics 2015-03-03 Michael Helmers , Michael Herrmann

A stochastic partial differential equation along the lines of the Kardar-Parisi-Zhang equation is introduced for the evolution of a growing interface in a radial geometry. Regular polygon solutions as well as radially symmetric solutions…

Statistical Mechanics · Physics 2015-06-25 M. T. Batchelor , B. I. Henry , S. D. Watt

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 show interrupted coarsening in which an ordered cell…

Statistical Mechanics · Physics 2009-11-13 Javier Muñoz-García , Rodolfo Cuerno , Mario Castro

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-slopes (interfacial) theories and the interplay between the…

Statistical Mechanics · Physics 2009-11-13 Matteo Nicoli , Mario Castro , Rodolfo Cuerno

We study effects of turbulent mixing on the random growth of an interface in the problem of the deposition of a substance on a substrate. The growth is modelled by the well-known Kardar--Parisi--Zhang model. The turbulent advecting velocity…

Statistical Mechanics · Physics 2015-11-06 N. V. Antonov , P. I. Kakin

We discuss the behavior of bounded slope quenched noise invasion models in high dimensions. We first observe that the roughness of such a steady state interface is generated by the combination of the roughness of the invasion process…

Condensed Matter · Physics 2008-02-03 Omri Gat , Zeev Olami

A limited mobility nonequilibrium solid-on-solid dynamical model for kinetic surface growth is introduced as a simple description for the morphological evolution of a growing interface under random vapor deposition and surface diffusion…

Statistical Mechanics · Physics 2009-10-31 S. Das Sarma , P. Punyindu

The dynamics of a one dimensional growth model involving attachment and detachment of particles is studied in the presence of a localized growth inhomogeneity along with anchored boundary conditions. At large times, the latter enforce an…

Statistical Mechanics · Physics 2007-05-23 M. D. Grynberg

We study the forced fluid invasion of an air-filled model porous medium at constant flow rate, in 1+1 dimensions, both experimentally and theoretically. We focus on the non-local character of the interface dynamics, due to liquid…

Condensed Matter · Physics 2009-11-07 A. Hernandez-Machado , J. Soriano , A. M. Lacasta , M. A. Rodriguez , L. Ramirez-Piscina , J. Ortin

The growth of stochastic interfaces in the vicinity of a boundary and the non-trivial crossover towards the behaviour deep in the bulk is analysed. The causal interactions of the interface with the boundary lead to a roughness larger near…

Statistical Mechanics · Physics 2014-10-16 Nicolas Allegra , Jean-Yves Fortin , Malte Henkel

We generalize a model of growth over a disordered environment, to a large class of It\=o processes. In particular, we study how the microscopic properties of the noise influence the macroscopic growth rate. The present model can account for…

Populations and Evolution · Quantitative Biology 2017-04-26 Thomas Gueudré

By analytically solving some simple models of phase-ordering kinetics, we suggest a mechanism for the onset of non-equilibrium behaviour in colloid-polymer mixtures. These mixtures can function as models of atomic systems; their physics…

Soft Condensed Matter · Physics 2016-08-31 R. M. L. Evans , W. C. K. Poon

The effects of a randomly moving environment on a randomly growing interface are studied by the field theoretic renormalization group analysis. The kinetic growth of an interface (kinetic roughening) is described by the Kardar-Parisi-Zhang…

Statistical Mechanics · Physics 2020-01-28 N. V. Antonov , P. I. Kakin , N. M. Lebedev