Related papers: Dynamic Scaling in Epitaxial Growth
The existence of exponential dichotomies has been well-established as a powerful tool to study existence, stability, and bifurcations of coherent structures. Currently, the application of exponential dichotomies to elliptic problems posed…
Motivated by a controversy over the correct results derived from the dynamic renormalization group (DRG) analysis of the non linear molecular beam epitaxy (MBE) equation, a self-consistent expansion (SCE) for the non linear MBE theory is…
In this work, the out-of-equilibrium dynamics of the Kardar-Parisi-Zhang equation in (1+1) dimensions is studied by means of numerical simulations, focussing on the two-times evolution of an interface in the absence of any disordered…
The approach to equilibrium, from a nonequilibrium initial state, in a system at its critical point is usually described by a scaling theory with a single growing length scale, $\xi(t) \sim t^{1/z}$, where z is the dynamic exponent that…
We study in detail the dynamic scaling of the three-dimensional (3D) Ising model driven through its critical point on finite-size lattices and show that a series of new critical exponents are needed to account for the anomalous scalings…
We experimentally and numerically investigate the expansion of initially localized ultracold bosons in homogeneous one- and two-dimensional optical lattices. We find that both dimensionality and interaction strength crucially influence…
The non-modal transient growth of perturbations in horizontal and inclined channel flows of two immiscible fluids is studied. 3D perturbations are examined in order to find the optimal perturbations that attain the maximum amplification of…
We introduce a general theoretical framework to study the shape dynamics of actively growing and remodeling surfaces. Using this framework we develop a physical model for growing bacterial cell walls and study the interplay of cell shape…
Alternative approach for description of the non-equilibrium phenomena arising in solids at a severe external loading is analyzed. The approach is based on the new form of kinetic equations in terms of the internal and modified free energy.…
In this work we survey selected theoretical developments for models of deposition of extended particles, with and without surface diffusion, on linear and planar substrates, of interest in colloid, polymer, and certain biological systems.
We consider a family of stochastic models of evolving two-dimensional Young diagrams, given in terms of certain energies, with Gibbs invariant measures. `Static' scaling limits of the shape functions, under these Gibbs measures, have been…
Tissue growth kinetics and interface dynamics depend on the properties of the tissue environment and cell-cell interactions. In cellular environments, substrate heterogeneity and geometry arise from a variety factors, such as the structure…
Ballistic deposition is a classical model for interface growth in which unit blocks fall down vertically at random on the different sites of $\mathbb{Z}$ and stick to the interface at the first point of contact, causing it to grow. We…
The scaling properties of the maximal height of a growing self-affine surface with a lateral extent $L$ are considered. In the late-time regime its value measured relative to the evolving average height scales like the roughness: $h^{*}_{L}…
We propose a simple discrete model to study the nonequilibrium fluctuations of two locally coupled 1+1 dimensional systems (interfaces). Measuring numerically the tilt-dependent velocity we construct a set of stochastic continuum equations…
We propose a dual scale drift-diffusion model for interfacial growth and etching processes. The two scales are: (i) a depletion layer width surrounding the aggregate and (ii) a drift length.The interplay between these two antithetical…
Recent theory and experiments have shown how the buildup of a high-concentration polymer layer at a one-dimensional solvent-air interface can lead to an evaporation rate that scales with time as $t^{-1/2}$ and that is insensitive to the…
We study the depinning transition for models representative of each of the two universality classes of interface roughening with quenched disorder. For one of the universality classes, the roughness exponent changes value at the transition,…
As a canonical model for wetting far from thermal equilibrium we study a Kardar-Parisi-Zhang interface growing on top of a hard-core substrate. Depending on the average growth velocity the model exhibits a non-equilibrium wetting transition…
We present a sharp-interface model of two-dimensional ramified growth during quasi-steady electrodeposition. Our model differs from previous modeling methods in that it includes the important effects of extended space-charge regions and…