Related papers: Dynamic Scaling of Non-Euclidean Interfaces
We study the role of the quench temperature $T_f$ in the phase-ordering kinetics of the Ising model with single spin flip in $d=2,3$. Equilibrium interfaces are flat at $T_f=0$, whereas at $T_f>0$ they are curved and rough (above the…
Using coarse grained models we investigate the behavior of water adjacent to an extended hydrophobic surface peppered with various fractions of hydrophilic patches of different sizes. We study the spatial dependence of the mean interface…
We study the dynamic scaling hypothesis in invariant surface growth. We show that the existence of power-law scaling of the correlation functions (scale invariance) does not determine a unique dynamic scaling form of the correlation…
We report numerical and analytic results for the spatial survival probability for fluctuating one-dimensional interfaces with Edwards-Wilkinson or Kardar-Parisi-Zhang dynamics in the steady state. Our numerical results are obtained from…
We present and analyze a model of an evolving sandpile surface in (2 + 1) dimensions where the dynamics of mobile grains ({\rho}(x, t)) and immobile clusters (h(x, t)) are coupled. Our coupling models the situation where the sandpile is…
Dynamical scaling arises naturally in various many-body systems far from equilibrium. After a short historical overview, the elements of possible extensions of dynamical scaling to a local scale-invariance will be introduced.…
We present a simple one dimensional stochastic model with three control parameters and a surprisingly rich zoo of phase transitions. At each (discrete) site $x$ and time $t$, an integer $n(x,t)$ satisfies a linear interface equation with…
The coarsening process in a class of driven systems exhibiting striped structures is studied. The dynamics is governed by the motion of the driven interfaces between the stripes. When two interfaces meet they coalesce thus giving rise to a…
There are three fundamental physical processes that gives rise to the morphology of a surface: deposition, surface diffusion and desorption. The characteristics of the interfaces generated by the combination of deposition and surface…
We consider the two-dimensional (2D) flow in a flat free-slip surface that bounds a three-dimensional (3D) volume in which the flow is turbulent. The equations of motion for the two-dimensional flow in the surface are neither compressible…
Interfaces of phase-separated systems roughen in time due to capillary waves. Because of fluxes in the bulk, their dynamics is nonlocal in real space and is not described by the Edwards-Wilkinson or Kardar-Parisi-Zhang (KPZ) equations, nor…
We develop a new approach to characterizing the morphology of rough surfaces based on the analysis of the scaling properties of contour loops, i.e. loops of constant height. Given a height profile of the surface we perform independent…
We investigate scaling and universality in nonequilibrium spin correlation functions in the presence of uncorrelated noise. In the absence of noise, spin correlation functions exhibit a crossover from monotonic decay at fast sweep…
Interlocking interfaces are commonly employed to mitigate relative sliding under shear.Indeed, Their geometry is typically selected on grounds of fabrication convenience rather than analytical optimality. There is no reason to suppose that…
Roughening of interfaces implies the divergence of the interface width $w$ with the system size $L$. For two-dimensional systems the divergence of $w^2$ is linear in $L$. In the framework of a detailed capillary wave approximation and of…
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 model that allows us to interpret these experimental…
We study statistical scale invariance and dynamic scaling in a simple solid-on-solid 2+1 - dimensional limited mobility discrete model of nonequilibrium surface growth, which we believe should describe the low temperature kinetic roughening…
Equilibrium crystal surfaces, constrained to equilibrate by means of dissociative dimer deposition and evaporation, have anomalous global surface roughness. We generalize earlier results for one dimensional interfaces to two dimensions. The…
The surface tension of rough interfaces between coexisting phases in 2D and 3D Ising models are discussed in view of the known results and some original calculations presented in this paper. The results are summarised in a formula, which…
We study numerically the depinning transition of driven elastic interfaces in a random-periodic medium with localized periodic-correlation peaks in the direction of motion. The analysis of the moving interface geometry reveals the existence…