250 research outputs found
Pattern formation in inclined layer convection
We report experiments on thermally driven convection in an inclined layer of
large aspect ratio in a fluid of Prandtl number . We observed
a number of new nonlinear, mostly spatio-temporally chaotic, states. At small
angles of inclination we found longitudinal rolls, subharmonic oscillations,
Busse oscillations, undulation chaos, and crawling rolls. At larger angles, in
the vicinity of the transition from buoyancy- to shear-driven instability, we
observed drifting transverse rolls, localized bursts, and drifting bimodals.
For angles past vertical, when heated from above, we found drifting transverse
rolls and switching diamond panes.Comment: For MPEG movies, see http://milou.msc.cornell.edu/ILCmovie
Percolation-dependent Reaction Rates in the Etching of Disordered Solids
A prototype statistical model for the etching of a random solid is
investigated in order to assess the influence of disorder and temperature on
the dissolution kinetics. At low temperature, the kinetics is dominated by
percolation phenomena, and the percolation threshold determines the global
reaction time. At high temperature, the fluctuations of the reaction rate are
Gaussian, whereas at low temperature they exhibit a power law tail due to
chemical avalanches. This is an example where microscopic disorder directly
induces non-classical chemical kinetics.Comment: Revtex, 4 pages, 5 figure
Stability of hexagonal solidification patterns
We investigate the dynamics of cellular solidification patterns using
three-dimensional phase-field simulations. The cells can organize into stable
hexagonal patterns or exhibit unsteady evolutions. We identify the relevant
secondary instabilities of regular hexagonal arrays and find that the stability
boundaries depend significantly on the strength of crystalline anisotropy. We
also find multiplet states that can be reached by applying well-defined
perturbations to a pre-existing hexagonal array.Comment: Minor changes, mainly in introduction and conclusion, one reference
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Eutectic colony formation: A phase field study
Eutectic two-phase cells, also known as eutectic colonies, are commonly
observed during the solidification of ternary alloys when the composition is
close to a binary eutectic valley. In analogy with the solidification cells
formed in dilute binary alloys, colony formation is triggered by a
morphological instability of a macroscopically planar eutectic solidification
front due to the rejection by both solid phases of a ternary impurity that
diffuses in the liquid. Here we develop a phase-field model of a binary
eutectic with a dilute ternary impurity and we investigate by dynamical
simulations both the initial linear regime of this instability, and the
subsequent highly nonlinear evolution of the interface that leads to fully
developed two-phase cells with a spacing much larger than the lamellar spacing.
We find a good overall agreement with our recent linear stability analysis [M.
Plapp and A. Karma, Phys. Rev. E 60, 6865 (1999)], which predicts a
destabilization of the front by long-wavelength modes that may be stationary or
oscillatory. A fine comparison, however, reveals that the assumption commonly
attributed to Cahn that lamella grow perpendicular to the envelope of the
solidification front is weakly violated in the phase-field simulations. We show
that, even though weak, this violation has an important quantitative effect on
the stability properties of the eutectic front. We also investigate the
dynamics of fully developed colonies and find that the large-scale envelope of
the composite eutectic front does not converge to a steady state, but exhibits
cell elimination and tip-splitting events up to the largest times simulated.Comment: 18 pages, 18 EPS figures, RevTeX twocolumn, submitted to Phys. Rev.
Phase-Field Formulation for Quantitative Modeling of Alloy Solidification
A phase-field formulation is introduced to simulate quantitatively
microstructural pattern formation in alloys. The thin-interface limit of this
formulation yields a much less stringent restriction on the choice of interface
thickness than previous formulations and permits to eliminate non-equilibrium
effects at the interface. Dendrite growth simulations with vanishing solid
diffusivity show that both the interface evolution and the solute profile in
the solid are well resolved
Dynamics and Selection of Giant Spirals in Rayleigh-Benard Convection
For Rayleigh-Benard convection of a fluid with Prandtl number \sigma \approx
1, we report experimental and theoretical results on a pattern selection
mechanism for cell-filling, giant, rotating spirals. We show that the pattern
selection in a certain limit can be explained quantitatively by a
phase-diffusion mechanism. This mechanism for pattern selection is very
different from that for spirals in excitable media
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