Related papers: Dynamic Scaling in Epitaxial Growth
Optimal growth of structures governed by spatially stochastic dynamics arises in many scientific settings, for example in processes such as solution-based crystallization and the formation of microbial biofilms on patterned substrates or…
A new model of crystal growth is presented that describes the phenomena on atomic length and diffusive time scales. The former incorporates elastic and plastic deformation in a natural manner, and the latter enables access to times scales…
We study the kinetics of domain growth of fluid mixtures quenched from a disordered to a lamellar phase. At low viscosities, in two dimensions, when hydrodynamic modes become important, dynamical scaling is verified in the form $C(\vec k,…
We present a novel computational method to simulate accurately a wide range of interfacial patterns whose growth is limited by a large scale diffusion field. To illustrate the computational power of this method, we demonstrate that it can…
Using extensive molecular dynamics simulations, we have performed finite-size scaling (FSS) in the aging regime of a model glass-forming liquid to investigate how the length scales associated with amorphous order (static length) and dynamic…
This is a brief survey of recent experimental studies on out-of-equilibrium scaling laws, focusing on two prominent situations where non-trivial universality classes have been identified theoretically: absorbing-state phase transitions and…
At a continuous transition into a nonunique absorbing state, particle systems may exhibit nonuniversal critical behavior, in apparent violation of hyperscaling. We propose a generalized scaling theory for dynamic critical behavior at a…
In order to elucidate the role of surfaces at nonequilibrium phase transitions we consider kinetic Ising models with surfaces subjected to a periodic oscillating magnetic field. Whereas the corresponding bulk system undergoes a continuous…
Step meandering due to a deterministic morphological instability on vicinal surfaces during growth is studied. We investigate nonlinear dynamics of a step model with asymmetric step kinetics, terrace and line diffusion, by means of a…
The universal behaviour of the directed percolation universality class is well understood, both the critical scaling as well as finite size scaling. This article focuses on the block (finite size) scaling of the order parameter and its…
In this pedagogical study, carried out by adopting standard mathematical methods of nonlinear dynamics, we have presented some simple analytical models to understand terminal behaviour in industrial growth. This issue has also been…
Ballistic deposition is one of the many models of interface growth that are believed to be in the KPZ universality class, but have so far proved to be largely intractable mathematically. In this model, blocks of size one fall independently…
Nonequilibrium statistical mechanics exhibit a variety of complex phenomena far from equilibrium. It inherits challenges of equilibrium, including accurately describing the joint distribution of a large number of configurations, and also…
A number of recent experiments have showed that surfactants can modify the growth mode of an epitaxial film, suppressing islanding and promoting layer-by-layer growth. Here I introduce a set of coupled equations to describe the…
Stochastic interface dynamics serve as mathematical models for diverse time-dependent physical phenomena: the evolution of boundaries between thermodynamic phases, crystal growth, random deposition... Interesting limits arise at large…
Dynamical scaling and ageing in disordered systems far from equilibrium is reviewed. Particular attention is devoted to the question to what extent a recently introduced generalization of dynamical scaling to local scale-invariance can…
We introduce super exponential inflation ($\omega < -1$) from a 5D Riemann-flat canonical metric on which we make a dynamical foliation. The resulting metric describes a super accelerated expansion for the early universe well-known as super…
The dynamics of fluctuating radially growing interfaces is approached using the formalism of stochastic growth equations on growing domains. This framework reveals a number of dynamic features arising during surface growth. For fast growth,…
In this paper, we introduce the concept of Developmental Partial Differential Equation (DPDE), which consists of a Partial Differential Equation (PDE) on a time-varying manifold with complete coupling between the PDE and the manifold's…
We introduce an approach for calculating non-universal properties of rough surfaces. The technique uses concepts of distinct surface-configuration classes, defined by the surface growth rule. The key idea is a mapping between discrete…