6,599 research outputs found
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
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
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
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 C high-velocity
shape-preserving growth is observed. These data indicate that the needle tip
assumes an effective radius} which is nearly independent of both
supersaturation and the applied potential. The small scale of 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
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