Related papers: Finite-time scaling for kinetic rough interfaces
We show that time dependent couplings may lead to nontrivial scaling properties of the surface fluctuations of the asymptotic regime in non-equilibrium kinetic roughening models . Three typical situations are studied. In the case of a…
We argue that the spatiotemporal dynamics of bred vectors in chaotic extended systems are related to a kinetic roughening process in the Kardar-Parisi-Zhang universality class. This implies that there exists a characteristic length scale…
We study a generalized Blume-Capel model on the simple cubic lattice. In addition to the nearest neighbor coupling there is a next to next to nearest neighbor coupling. In order to quantify spatial anisotropy, we determine the correlation…
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…
We study the phase turbulence of the one-dimensional complex Ginzburg-Landau equation, in which the defect-free chaotic dynamics of the order parameter maps to a phase equation well approximated by the Kuramoto-Sivashinsky model. In this…
Interfaces in two-dimensional systems exhibit unexpected complex dynamical behaviors, the dynamics of a border connecting a stripe pattern and a uniform state is studied. Numerical simulations of a prototype isotropic model, the subcritical…
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…
We consider the evolution of interfaces with a diffusive term and a generalized Kardar-Parisi-Zhang (KPZ) non-linearity, which results in a propagation velocity that depends periodically on the tilt of the interface. Using large scale…
We consider an infinite spatial inhomogeneous random graph model with an integrable connection kernel that interpolates nicely between existing spatial random graph models. Key examples are versions of the weight-dependent random connection…
In the 1960's, four famous scaling relations were developed which relate the six standard critical exponents describing continuous phase transitions in the thermodynamic limit of statistical physics models. They are well understood at a…
We study the pinning phase transition for discrete surface dynamics in random environments. A renormalization procedure is devised to prove that the interface moves with positive velocity under a finite size condition. This condition is…
We study a class of close-packed dimer models on the square lattice, in the presence of small but extensive perturbations that make them non-determinantal. Examples include the 6-vertex model close to the free-fermion point, and the dimer…
The curve time series framework provides a convenient vehicle to accommodate some nonstationary features into a stationary setup. We propose a new method to identify the dimensionality of curve time series based on the dynamical dependence…
The pinning-depinning phase transitions of interfaces for two classes of discrete elastic-string models are investigated numerically. In the (1+1)-dimensions, we revisit these two elastic-string models with slight modification to growth…
We use a discrete-time formulation to study the asymmetric avalanche process [Phys. Rev. Lett. vol. 87, 084301 (2001)] on a finite ring and obtain an exact expression for the average avalanche size of particles as a function of toppling…
We investigate the behavior of discrete interface growth models belonging to the Edwards--Wilkinson (EW) and Kardar--Parisi--Zhang (KPZ) universality classes, when defined on a complete graph, a topology commonly used to probe the…
We study the local scaling properties of driven interfaces in disordered media modeled by the Edwards-Wilkinson equation with quenched noise. We find that, due to the super-rough character of the interface close to the depinning transition,…
Recently, the concept of geometric renormalization group provides a good approach for studying the structural symmetry and functional invariance of complex networks. Along this line, we systematically investigate the finite-size scaling of…
Ferroic domain walls are known to display the characteristic scaling properties of self-affine rough interfaces. Different methods have been used to extract roughness information in ferroelectric and ferromagnetic materials. Here, we review…
The short-time evolution of a growing interface is studied within the framework of the dynamic renormalization group approach for the Kadar-Parisi-Zhang (KPZ) equation and for an idealized continuum model of molecular beam epitaxy (MBE).…