146 research outputs found
Sidebranching induced by external noise in solutal dendritic growth
We have studied sidebranching induced by fluctuations in dendritic growth.
The amplitude of sidebranching induced by internal (equilibrium) concentration
fluctuations in the case of solidification with solutal diffusion is computed.
This amplitude turns out to be significantly smaller than values reported in
previous experiments.The effects of other possible sources of fluctuations (of
an external origin)are examined by introducing non-conserved noise in a
phase-field model. This reproduces the characteristics of sidebranching found
in experiments. Results also show that sidebranching induced by external noise
is qualitatively similar to that of internal noise, and it is only
distinguished by its amplitude.Comment: 13 pages, 5 figure
Periodic forcing in viscous fingering of a nematic liquid crystal
We study viscous fingering of an air-nematic interface in a radial Hele-Shaw
cell when periodically switching on and off an electric field, which reorients
the nematic and thus changes its viscosity, as well as the surface tension and
its anisotropy (mainly enforced by a single groove in the cell). We observe
undulations at the sides of the fingers which correlate with the switching
frequency and with tip oscillations which give maximal velocity to smallest
curvatures. These lateral undulations appear to be decoupled from spontaneous
(noise-induced) side branching. We conclude that the lateral undulations are
generated by successive relaxations between two limiting finger widths. The
change between these two selected pattern scales is mainly due to the change in
the anisotropy. This scenario is confirmed by numerical simulations in the
channel geometry, using a phase-field model for anisotropic viscous fingering.Comment: completely rewritten version, more clear exposition of results (14
pages in Revtex + 7 eps figures
Phase-field model for Hele-Shaw flows with arbitrary viscosity contrast. II. Numerical study
We implement a phase-field simulation of the dynamics of two fluids with
arbitrary viscosity contrast in a rectangular Hele-Shaw cell. We demonstrate
the use of this technique in different situations including the linear regime,
the stationary Saffman-Taylor fingers and the multifinger competition dynamics,
for different viscosity contrasts. The method is quantitatively tested against
analytical predictions and other numerical results. A detailed analysis of
convergence to the sharp interface limit is performed for the linear dispersion
results. We show that the method may be a useful alternative to more
traditional methods.Comment: 13 pages in revtex, 5 PostScript figures. changes: 1 reference added,
figs. 4 and 5 rearrange
Dynamical Systems approach to Saffman-Taylor fingering. A Dynamical Solvability Scenario
A dynamical systems approach to competition of Saffman-Taylor fingers in a
channel is developed. This is based on the global study of the phase space
structure of the low-dimensional ODE's defined by the classes of exact
solutions of the problem without surface tension. Some simple examples are
studied in detail, and general proofs concerning properties of fixed points and
existence of finite-time singularities for broad classes of solutions are
given. The existence of a continuum of multifinger fixed points and its
dynamical implications are discussed. The main conclusion is that exact
zero-surface tension solutions taken in a global sense as families of
trajectories in phase space spanning a sufficiently large set of initial
conditions, are unphysical because the multifinger fixed points are
nonhyperbolic, and an unfolding of them does not exist within the same class of
solutions. Hyperbolicity (saddle-point structure) of the multifinger fixed
points is argued to be essential to the physically correct qualitative
description of finger competition. The restoring of hyperbolicity by surface
tension is discussed as the key point for a generic Dynamical Solvability
Scenario which is proposed for a general context of interfacial pattern
selection.Comment: 3 figures added, major rewriting of some sections, submitted to Phys.
Rev.
Dynamics of Turing patterns under spatio-temporal forcing
We study, both theoretically and experimentally, the dynamical response of
Turing patterns to a spatio-temporal forcing in the form of a travelling wave
modulation of a control parameter. We show that from strictly spatial
resonance, it is possible to induce new, generic dynamical behaviors, including
temporally-modulated travelling waves and localized travelling soliton-like
solutions. The latter make contact with the soliton solutions of P. Coullet
Phys. Rev. Lett. {\bf 56}, 724 (1986) and provide a general framework which
includes them. The stability diagram for the different propagating modes in the
Lengyel-Epstein model is determined numerically. Direct observations of the
predicted solutions in experiments carried out with light modulations in the
photosensitive CDIMA reaction are also reported.Comment: 6 pages, 5 figure
Phase-field model for Hele-Shaw flows with arbitrary viscosity contrast. I. Theoretical approach
We present a phase-field model for the dynamics of the interface between two
inmiscible fluids with arbitrary viscosity contrast in a rectangular Hele-Shaw
cell. With asymptotic matching techniques we check the model to yield the right
Hele-Shaw equations in the sharp-interface limit and compute the corrections to
these equations to first order in the interface thickness. We also compute the
effect of such corrections on the linear dispersion relation of the planar
interface. We discuss in detail the conditions on the interface thickness to
control the accuracy and convergence of the phase-field model to the limiting
Hele-Shaw dynamics. In particular, the convergence appears to be slower for
high viscosity contrasts.Comment: 17 pages in revtex. changes: 1 reference adde
The diffusion coefficient of propagating fronts with multiplicative noise
Recent studies have shown that in the presence of noise both fronts
propagating into a metastable state and so-called pushed fronts propagating
into an unstable state, exhibit diffusive wandering about the average position.
In this paper we derive an expression for the effective diffusion coefficient
of such fronts, which was motivated before on the basis of a multiple scale
ansatz. Our systematic derivation is based on the decomposition of the
fluctuating front into a suitably positioned average profile plus fluctuating
eigenmodes of the stability operator. While the fluctuations of the front
position in this particular decomposition are a Wiener process on all time
scales, the fluctuations about the time averaged front profile relax
exponentially.Comment: 4 page
Two-finger selection theory in the Saffman-Taylor problem
We find that solvability theory selects a set of stationary solutions of the
Saffman-Taylor problem with coexistence of two \it unequal \rm fingers
advancing with the same velocity but with different relative widths
and and different tip positions. For vanishingly small
dimensionless surface tension , an infinite discrete set of values of the
total filling fraction and of the relative
individual finger width are selected out of a
two-parameter continuous degeneracy. They scale as
and . The selected values of differ from
those of the single finger case. Explicit approximate expressions for both
spectra are given.Comment: 4 pages, 3 figure
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