Nonlinear Two-Dimensional Green's Function in Smectics

The problem of the strain of smectics subjected to a force distributed over a line in the basal plane has been solved

Interface kinetics in phase field models: isothermal transformations in binary alloys and steps dynamics in molecular-beam-epitaxy

We present a unified description of interface kinetic effects in phase field models for isothermal transformations in binary alloys and steps dynamics in molecular-beam-epitaxy. The phase field equations of motion incorporate a kinetic cross-coupling between the phase field and the concentration field. This cross coupling generalizes the phenomenology of kinetic effects and was omitted until recently in classical phase field models. We derive general expressions (independent of the details of the phase field model) for the kinetic coefficients within the corresponding macroscopic approach using a physically motivated reduction procedure. The latter is equivalent to the so-called thin interface limit but is technically simpler. It involves the calculation of the effective dissipation that can be ascribed to the interface in the phase field model. We discuss in details the possibility of a non positive definite matrix of kinetic coefficients, i.e. a negative effective interface dissipation, although being in the range of stability of the underlying phase field model. Numerically, we study the step-bunching instability in molecular-beam-epitaxy due to the Ehrlich-Schwoebel effect, present in our model due to the cross-coupling. Using the reduction procedure we compare the results of the phase field simulations with the analytical predictions of the macroscopic approach

Fast crack propagation by surface diffusion

We present a continuum theory which describes the fast growth of a crack by surface diffusion. This mechanism overcomes the usual cusp singularity by a self-consistent selection of the crack tip radius. It predicts the saturation of the steady state crack velocity appreciably below the Rayleigh speed and tip blunting. Furthermore, it includes the possibility of a tip splitting instability for high applied tensions

Electrically Enhanced Free Dendrite Growth in Polar and Non-polar Systems

We describe the electrically enhanced growth of needle crystals from the vapor phase, for which there exists a morphological instability above a threshold applied potential. Our improved theoretical treatment of this phenomenon shows that the instability is present in both polar and non-polar systems, and we provide an extension of solvability theory to include electrical effects. We present extensive experimental data for ice needle growth above the electrical threshold, where at $T=-5$C high-velocity shape-preserving growth is observed. These data indicate that the needle tip assumes an effective radius} $R^{\ast}$ which is nearly independent of both supersaturation and the applied potential. The small scale of $R^{\ast}$ and its response to chemical additives suggest that the needle growth rate is being limited primarily by structural instabilities, possibly related to surface melting. We also demonstrate experimentally that non-polar systems exhibit this same electrically induced morphological instability

Achieving realistic interface kinetics in phase field models with a diffusional contrast

Phase field models are powerful tools to tackle free boundary problems. For phase transformations involving diffusion, the evolution of the non conserved phase field is coupled to the evolution of the conserved diffusion field. Introducing the kinetic cross coupling between these two fields [E. A. Brener, G. Boussinot, Phys. Rev. E {\bf 86}, 060601(R) (2012)], we solve the long-standing problem of a realistic description of interface kinetics when a diffusional contrast between the phases is taken into account. Using the case of the solidification of a pure substance, we show how to eliminate the temperature jump at the interface and to recover full equilibrium boundary conditions. We confirm our results by numerical simulations

Viscoelastic Fracture of Biological Composites

Soft constituent materials endow biological composites, such as bone, dentin and nacre, with viscoelastic properties that may play an important role in their remarkable fracture resistance. In this paper we calculate the scaling properties of the quasi-static energy release rate and the viscoelastic contribution to the fracture energy of various biological composites, using both perturbative and non-perturbative approaches. We consider coarse-grained descriptions of three types of anisotropic structures: (i) Liquid-crystal-like composites (ii) Stratified composites (iii) Staggered composites, for different crack orientations. In addition, we briefly discuss the implications of anisotropy for fracture criteria. Our analysis highlights the dominant lengthscales and scaling properties of viscoelastic fracture of biological composites. It may be useful for evaluating crack velocity toughening effects and structure-dissipation relations in these materials.Comment: 18 pages, 3 figure

Melting of alloys along the inter-phase boundaries in eutectic and peritectic systems

We discuss a simple model of the melting kinetics along the solid-solid interface in eutectic and peritectic systems. The process is controlled by the diffusion inside the liquid phase and the existence of a triple junction is crucial for the velocity selection problem. Using the lubrication approximation for the diffusion field in the liquid phase we obtain scaling results for the steady-state velocity of the moving pattern depending on the overheating above the equilibrium temperature and on the material parameters of the system, including the dependences on the angles at the triple junction

Frictional shear cracks

We discuss crack propagation along the interface between two dissimilar materials. The crack edge separates two states of the interface, ``stick'' and ``slip''. In the slip region we assume that the shear stress is proportional to the sliding velocity, i.e. the linear viscous friction law. In this picture the static friction appears as the Griffith threshold for crack propagation. We calculate the crack velocity as a function of the applied shear stress and find that the main dissipation comes from the macroscopic region and is mainly due to the friction at the interface. The relevance of our results to recent experiments, Baumberger et al, Phys. Rev. Lett. 88, 075509 (2002), is discussed

Comment on ``Solidification of a Supercooled Liquid in a Narrow Channel''

Comment on PRL v. 86, p. 5084 (2001) [cond-mat/0101016]. We point out that the authors' simulations are consistent with the known theory of steady-state solutions in this system