We review recent theoretical progress in the physical understanding of far-from-equilibrium phenomena seen experimentally in epitaxial growth and erosion on crystal surfaces. The formation and dynamics of various interface structures (pyramids, ripples, etc.), and also kinetic phase transitions observed between these structures, can all be understood within a simple continuum model based on the mass conservation law and respecting the symmetries of the growing crystal surface. In particular, theoretical predictions and experimental results are compared for (001), (110) and (111) crystal surfaces.

Stress concentration at grain boundaries (GB), a phenomena arising from microstructural inhomogeneity, is an important factor in determining the mechanical properties of polycrystalline materials. In this study we use mesoscopic simulations to investigate characteristics of the deformation mechanism of grain-boundary diffusion creep (Coble creep) in a polycrystalline material. The stress distribution along the grain boundaries in a polycrystalline solid under externally applied stress is determined and the mechanism of how topological inhomogeneities introduce stress concentrations is investigated. Microstructures with inhomogeneities of various sizes and distributions are considered and their effect on the stress distribution and creep rate is quantified.

A mesoscopic simulation methodology has been used to investigate the effect of the initial grain size distribution and grain boundary (GB) mobilities on the development of abnormal grain growth in a single-phase polycrystalline material. Our studies show that regardless of the initial grain size distribution, in the absence of variability in GB properties, the system evolves by normal grain growth characterized by a uniform self-similar grain-size distribution, i.e. the presence of a few large grains in the initial microstructure does not promote abnormal grain growth. On the contrary, the presence of a limited set of grains having GBs with higher mobilities may lead to abnormal grain growth provided the biased GB mobility values are larger than certain threshold values. Kinetic and topological aspects of normal to abnormal grain growth transition are investigated.

We theoretically address epitaxial growth on (001) crystalline surfaces symmetry, in the regime when pyramids are formed across the growing interface due to Schwoebel step-edge barriers. We develop a kinetic scaling theory that analytically explains numerous experiments and simulations suggesting that pyramid size grows, via coarsening, as a fourth root of the deposition time. Pyramid dynamics is elucidated in terms of pyramid edges that form a growing self-organized square lattice across the growing interface. The edge lattice of pyramids is disordered by topological defects that are characterized here as dislocations. We show that pyramid coarsening is mediated by climb-motion of the dislocations of the edge lattice.

We investigate the dynamics of the classical Euler buckling of compressed solid membranes. We relate the membrane buckling dynamics to phase ordering phenomena. Membrane develops a wavelike pattern whose wavelength grows, via coarsening, as a power of time. Evolving membrane is similar to rough growing surfaces (“growing interfaces”) whose roughness grows as a power of time. Membrane buckling dynamics is characterized by a distinct scaling behavior not found in other coarsening phenomena

We study fluctuations of DNA-cationic lipid complexes in their lamellar membrane phases with DNA intercalated between lipid membranes. We theoretically elucidate this novel state of matter by characterizing it as the very first realization of a decoupled (unregistered) phase of strongly fluctuating 2-d smectic manifolds weakly interacting across membranes. Due to couplings between adjacent 2-d smectic Lx, × Ly planes, the experimentally observed ordinary 2-d smectic behavior [Salditt et al., Phys. Rev. Lett. 79, 2582 (1997)] of DNA in-plane undulations, with , must cross over, at the longest scales, to a novel fluctuation behavior, with < u2 > ˜ (logLy )2 ˜ (logLx.)2.

We use atomistic Monte-Carlo simulations to investigate the dynamics of cracks which sizes are smaller than the Griffith length. We demonstrate that such cracks can irreversibly grow proviso their size is larger than a certain critical length which is smaller than the Griffith length, as recently suggested [ L. Golubović and A. Peredera, Phys. Rev. E51, 2799 (1995)]. We show here that this thermally assisted creep crack growth is dominated by irreversible changes in the region of the crack tip, primarily in the form of dislocation emissions and nucleation of microcavities and voids. These processes act together during the crack growth: the crack tip region acts as a source for emissions of dislocations which subsequently serve as seeds for creation of vacancy clusters in a region away but still close to the crack tip. Eventually, passages between these vacancy clusters and the mother crack are formed and the crack thus increases in size. As this process repeats, the crack grows.

We use atomistic Monte-Carlo simulations to investigate the dynamics of cracks which sizes are smaller than the Griffith length. We demonstrate that such cracks can irreversibly grow proviso their size is larger than a certain critical length which is smaller than the Griffith length, as recently suggested [ L. Golubović and A. Peredera, Phys. Rev. E51, 2799 (1995)]. We show here that this thermally assisted creep crack growth is dominated by irreversible changes in the region of the crack tip, primarily in the form of dislocation emissions and nucleation of microcavities and voids. These processes act together during the crack growth: the crack tip region acts as a source for emissions of dislocations which subsequently serve as seeds for creation of vacancy clusters in a region away but still close to the crack tip. Eventually, passages between these vacancy clusters and the mother crack are formed and the crack thus increases in size. As this process repeats, the crack grows.