We propose a mean field theory for interfaces growing according to the Kardar-Parisi-Zhang (KPZ) equation in 1+1 dimensions. The mean field equations are formulated in terms of densities at different heights, taking surface tension and the influence of the nonlinear term in the KPZ equation into account. Although spatial correlations are neglected, the mean field equations still reflect the spa...

A stable numerical solution to the unsolved problem of nonequilibrium growth/evaporation at long time step of multiple dissociating acids (e.g., nitric acid, hydrochloric acid, carbonic acid, sulfuric acid, etc.) and a base (ammonia) is discussed. The solution eliminates most oscillatory behavior observed in previous solutions at long time step. The solution is applicable across the entire rela...

Time-dependent simulations of two-dimensional isothermal Ni-Cu dendrites are simulated using a phase-field model solved with a finite-difference adaptive mesh refinement technique. Dendrite tip velocity selection is examined and found to exhibit a transition between two markedly different regimes as undercooling is increased. At low undercooling, the dendrite tip growth rate is consistent with ...

Strain has significance for both the growth characteristics and material properties of thin epitaxial films. In this work, the method of lattice statics is applied to an epitaxial system with cubic symmetry, using harmonic potentials. The energy density and force balance equations are written using a finite difference formalism that clearly shows their consistency with continuum elasticity. For...

Numerical analysis of hypersonic continuum and rarefied gas flows near blunt probes is presented under conditions of intensive gas blowing from the surface. Nonequilibrium parameters in the multicomponent flows were evaluated for slot and uniform injections of air, helium, and hydrogen. Numerical results indicate that the most effective cooling of the probe surface occurs at moderate uniform in...

Understanding fundamental growth processes is key to the control of nonequilibrium structure formation for a wide range of materials on all length scales, from atomic to molecular and even colloidal systems. While atomic systems are relatively well studied, molecular and colloidal growth are currently moving more into the focus. This poses the question to what extent growth laws are size scalab...

– We elucidate the mechanism underlying the continuous nonequilibrium phase transition of the Pair Contact Process with Diffusion (PCPD). We compute its scaling exponents to second order in an ε-expansion around the upper critical dimension dc = 2 within a simple functional renormalization group (RG) approach. In particular, we establish that the PCPD is not in the directed percolation universa...

The quantitative knowledge of interface anisotropy in lattice models is a major issue, both for the parametrization continuum models, and analysis experimental observations. In this paper, we focus on line tension stiffness, which plays role equilibrium shapes fluctuations, selection nonequilibrium growth patterns. We consider 2D Ising Hamiltonian square with first second-nearest-neighbor inter...

We find that studying the simplest of the coupled nonequilibrium growth equations of Barabasi by self-consistent mode coupling requires the use of dressed vertices. Using the vertex renormalization, we find a roughening exponent which already in the leading order is quite close to the numerical value.

This paper deals with the derivation of the Gibbs equation for a nonviscous gas in the presence of heat flux. The analysis aims to shed some light on the physical interpretation of thermodynamic potentials far from equilibrium. Two different definitions for the chemical potential and thermodynamic pressure far from equilibrium are introduced: nonequilibrium chemical potential and nonequilibrium...