2,129 research outputs found
Numerical study of the shape and integral parameters of a dendrite
We present a numerical study of sidebranching of a solidifying dendrite by
means of a phase--field model. Special attention is paid to the regions far
from the tip of the dendrite, where linear theories are no longer valid. Two
regions have been distinguished outside the linear region: a first one in which
sidebranching is in a competition process and a second one further down where
branches behave as independent of each other. The shape of the dendrite and
integral parameters characterizing the whole dendrite (contour length and area
of the dendrite) have been computed and related to the characteristic tip
radius for both surface tension and kinetic dominated dendrites. Conclusions
about the different behaviors observed and comparison with available
experiments and theoretical predictions are presented.Comment: 10 pages, 7 figures, Accepted for publication in Phys. Rev.
Sharp-Interface Limit of a Fluctuating Phase-Field Model
We present a derivation of the sharp-interface limit of a generic fluctuating
phase-field model for solidification. As a main result, we obtain a
sharp-interface projection which presents noise terms in both the diffusion
equation and in the moving boundary conditions. The presented procedure does
not rely on the fluctuation-dissipation theorem, and can therefore be applied
to account for both internal and external fluctuations in either variational or
non-variational phase-field formulations. In particular, it can be used to
introduce thermodynamical fluctuations in non-variational formulations of the
phase-field model, which permit to reach better computational efficiency and
provide more flexibility for describing some features of specific physical
situations. This opens the possibility of performing quantitative phase-field
simulations in crystal growth while accounting for the proper fluctuations of
the system.Comment: 21 pages, 1 figure, submitted to Phys. Rev.
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
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
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
Viscous fingering in liquid crystals: Anisotropy and morphological transitions
We show that a minimal model for viscous fingering with a nematic liquid
crystal in which anisotropy is considered to enter through two different
viscosities in two perpendicular directions can be mapped to a two-fold
anisotropy in the surface tension. We numerically integrate the dynamics of the
resulting problem with the phase-field approach to find and characterize a
transition between tip-splitting and side-branching as a function of both
anisotropy and dimensionless surface tension. This anisotropy dependence could
explain the experimentally observed (reentrant) transition as temperature and
applied pressure are varied. Our observations are also consistent with previous
experimental evidence in viscous fingering within an etched cell and
simulations of solidification.Comment: 12 pages, 3 figures. Submitted to PR
Non-isothermal model for the direct isotropic/smectic-A liquid crystalline transition
An extension to a high-order model for the direct isotropic/smectic-A liquid
crystalline phase transition was derived to take into account thermal effects
including anisotropic thermal diffusion and latent heat of phase-ordering.
Multi-scale multi-transport simulations of the non-isothermal model were
compared to isothermal simulation, showing that the presented model extension
corrects the standard Landau-de Gennes prediction from constant growth to
diffusion-limited growth, under shallow quench/undercooling conditions.
Non-isothermal simulations, where meta-stable nematic pre-ordering precedes
smectic-A growth, were also conducted and novel non-monotonic
phase-transformation kinetics observed.Comment: First revision: 20 pages, 7 figure
Kinematic reduction of reaction-diffusion fronts with multiplicative noise: Derivation of stochastic sharp-interface equations
We study the dynamics of generic reaction-diffusion fronts, including pulses
and chemical waves, in the presence of multiplicative noise. We discuss the
connection between the reaction-diffusion Langevin-like field equations and the
kinematic (eikonal) description in terms of a stochastic moving-boundary or
sharp-interface approximation. We find that the effective noise is additive and
we relate its strength to the noise parameters in the original field equations,
to first order in noise strength, but including a partial resummation to all
orders which captures the singular dependence on the microscopic cutoff
associated to the spatial correlation of the noise. This dependence is
essential for a quantitative and qualitative understanding of fluctuating
fronts, affecting both scaling properties and nonuniversal quantities. Our
results predict phenomena such as the shift of the transition point between the
pushed and pulled regimes of front propagation, in terms of the noise
parameters, and the corresponding transition to a non-KPZ universality class.
We assess the quantitative validity of the results in several examples
including equilibrium fluctuations, kinetic roughening, and the noise-induced
pushed-pulled transition, which is predicted and observed for the first time.
The analytical predictions are successfully tested against rigorous results and
show excellent agreement with numerical simulations of reaction-diffusion field
equations with multiplicative noise.Comment: 17 pages, 6 figure
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