We introduce a model of two coupled reaction–diffusion equations to describe the dynamics and propagation of flame fronts in random media. The model incorporates heat diffusion, its dissipation, and its production through coupling to the background reactant density. We first show analytically and numerically that there is a finite critical value of the background density, below which the front ...

Deformation mechanisms involving mass transport by stress driven diffusion influence a large number of technological problems. We study the formation of undulations on surfaces of stressed films at high temperature by exploring the deformation kinetics governed by volume and surface diffusion. A governing equation is derived that gives the amplitude change of such surfaces as a function of time...

Recent observations of the growth of protein crystals have identified two different growth regimes. At low supersaturation, the surface of the crystal is smooth and increasing in size due to the nucleation of steps at defects and the subsequent growth of the steps. At high supersaturation, nucleation occurs at many places simultaneously, the crystal surface becomes rough, and the growth velocit...

We report large scale Monte Carlo simulations of the equilibrium discrete Laplacian roughening (dLr) model, originally introduced as the simplest one accommodating the hexatic phase in two-dimensional melting. The dLr model is also relevant to surface roughening in molecular beam epitaxy (MBE). Our data suggest a single phase transition, possibly of the Kosterlitz-Thouless type, between a flat ...

We study front propagation when an invading species competes with a resident; we assume nearest-neighbor preemptive competition for resources in an individual-based, two-dimensional lattice model. The asymptotic front velocity exhibits an effective power-law dependence on the difference between the two species' clonal propagation rates (key ecological parameters). The mean-field approximation b...

We use in situ real-time X-ray reflectivity and complementary atomic force microscopy to monitor crystallinity and roughness evolution during growth of organic heterostructures, i.e. perfluoropentacene (PFP) on diindenoperylene (DIP) and pentacene (PEN) on PFP. For both systems, surface smoothing during thermal evaporation of the second material on top of the first is observed. The smoothing ca...

The influence of the Cu current collector grade (cold-rolled, annealed, or textured) and ink solid fraction (SF) on performance Si-based electrodes for Li-ion batteries is investigated. Two binders are considered this study: one carboxymethyl cellulose citric acid other which consists same organic components with added Zn(II) cations. These ones cross-link carboxylate moieties through coordinat...

A theory for surface transitions in the presence of a disordered pinning potential is presented. Arbitrary disorder correlations are treated in the framework of a dynamical functional renormalization group. The roughening transition, where surface roughness and mobility behave discontinuously, is shown to turn smoothly into the continuous superroughening transition, when the range of disorder c...