36 research outputs found
Phase Field Modeling of Fast Crack Propagation
We present a continuum theory which predicts the steady state propagation of
cracks. The theory overcomes the usual problem of a finite time cusp
singularity of the Grinfeld instability by the inclusion of elastodynamic
effects which restore selection of the steady state tip radius and velocity. We
developed a phase field model for elastically induced phase transitions; in the
limit of small or vanishing elastic coefficients in the new phase, fracture can
be studied. The simulations confirm analytical predictions for fast crack
propagation.Comment: 5 pages, 11 figure
Amplitude equations for systems with long-range interactions
We derive amplitude equations for interface dynamics in pattern forming
systems with long-range interactions. The basic condition for the applicability
of the method developed here is that the bulk equations are linear and solvable
by integral transforms. We arrive at the interface equation via long-wave
asymptotics. As an example, we treat the Grinfeld instability, and we also give
a result for the Saffman-Taylor instability. It turns out that the long-range
interaction survives the long-wave limit and shows up in the final equation as
a nonlocal and nonlinear term, a feature that to our knowledge is not shared by
any other known long-wave equation. The form of this particular equation will
then allow us to draw conclusions regarding the universal dynamics of systems
in which nonlocal effects persist at the level of the amplitude description.Comment: LaTeX source, 12 pages, 4 figures, accepted for Physical Review
Influence of external flows on crystal growth: numerical investigation
We use a combined phase-field/lattice-Boltzmann scheme [D. Medvedev, K.
Kassner, Phys. Rev. E {\bf 72}, 056703 (2005)] to simulate non-facetted crystal
growth from an undercooled melt in external flows. Selected growth parameters
are determined numerically.
For growth patterns at moderate to high undercooling and relatively large
anisotropy, the values of the tip radius and selection parameter plotted as a
function of the Peclet number fall approximately on single curves. Hence, it
may be argued that a parallel flow changes the selected tip radius and growth
velocity solely by modifying (increasing) the Peclet number. This has
interesting implications for the availability of current selection theories as
predictors of growth characteristics under flow.
At smaller anisotropy, a modification of the morphology diagram in the plane
undercooling versus anisotropy is observed. The transition line from dendrites
to doublons is shifted in favour of dendritic patterns, which become faster
than doublons as the flow speed is increased, thus rendering the basin of
attraction of dendritic structures larger.
For small anisotropy and Prandtl number, we find oscillations of the tip
velocity in the presence of flow. On increasing the fluid viscosity or
decreasing the flow velocity, we observe a reduction in the amplitude of these
oscillations.Comment: 10 pages, 7 figures, accepted for Physical Review E; size of some
images had to be substantially reduced in comparison to original, resulting
in low qualit
Correlated Persistent Tunneling Currents in Glasses
Low temperature properties of glasses are derived within a generalized
tunneling model, considering the motion of charged particles on a closed path
in a double-well potential. The presence of a magnetic induction field B
violates the time reversal invariance due to the Aharonov-Bohm phase, and leads
to flux periodic energy levels. At low temperature, this effect is shown to be
strongly enhanced by dipole-dipole and elastic interactions between tunneling
systems and becomes measurable. Thus, the recently observed strong sensitivity
of the electric permittivity to weak magnetic fields can be explained. In
addition, superimposed oscillations as a function of the magnetic field are
predicted.Comment: 4 page