68 research outputs found
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.
Diamagnetic interactions in superheated-superconducting microgranules under an external magnetic field
L'estudi de les transicions produĂŻdes en conjunts de grĂ nuls superconductors metastables tĂ© nterès tant per a la fĂsica fonamental com per a aplicacions com ara els detectors de partĂcules. L'estudi teòric d'aquest problema ha estat obstaculitzat per la dificultat del tractament de les interaccions diamagnètiques entre grĂ nuls. En aquesta revisiĂł descrivim el comportament d'aquests sistemes, desenvolupem el mètode numèric del tractament i presentem uns quants resultats experimentals i numèrics.The study of the phase transitions produced in ensembles of metastable superconducting granules by magnetic field variations is important both for fundamental physics and for applications in particle detectors. Theoretical study of the problem has long been hampered by the difficulty in dealing with the diamagnetic interactions between granules. In this review we describe the behaviour of such systems, develop numerical procedures to deal with them, and present some experimental and numerical results
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from the tip of the dendrite, where linear theories are no longer valid.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.
A blue sky catastrophe in double-diffusive convection
A global bifurcation of the blue sky catastrophe type has been found in a
small Prandtl number binary mixture contained in a laterally heated cavity. The
system has been studied numerically applying the tools of bifurcation theory.
The catastrophe corresponds to the destruction of an orbit which, for a large
range of Rayleigh numbers, is the only stable solution. This orbit is born in a
global saddle-loop bifurcation and becomes chaotic in a period doubling cascade
just before its disappearance at the blue sky catastrophe.Comment: 4 pages, 6 figures, REVTeX, To be published in Physical Review
Letter
Speeding chemical reactions by focusing
We present numerical results for a chemical reaction of colloidal particles which are transported by
a laminar fluid and are focused by periodic obstacles in such a way that the two components are well
mixed and consequently the chemical reaction is speeded up. The roles of the various system param-
eters (diffusion coefficients, reaction rate, and obstacles sizes) are studied. We show that focusing
speeds up the reaction from the diffusion limited rate, ~t-1/2 to very close to the perfect mixing rate,
~t1/2~t-1Postprint (published version
Ballistic and diffusive corrections to front propagation in the presence of multiplicative noise
We study the dynamics of reaction-diffusion fronts under the influence of multiplicative noise. An approximate theoretical scheme is introduced to compute the velocity of the front and its diffusive wandering due to the presence of noise. The theoretical approach is based on a multiple scale analysis rather than on a small noise expansion and is confirmed with numerical simulations for a wide range of the noise intensity. We report on the possibility of noise sustained solutions with a continuum of possible velocities, in situations where only a single velocity is allowed without noise. Í“S1063-651XÍ‘98Í’03611-3
Fronts dynamics in the presence of spatio-temporal structured noises
Front dynamics modeled by a reaction-diffusion equation are studied under the
influence of spatio-temporal structured noises. An effective deterministic
model is analytical derived where the noise parameters, intensity, correlation
time and correlation length appear explicitely. The different effects of these
parameters are discussed for the Ginzburg-Landau and Schl\"ogl models. We
obtain an analytical expression for the front velocity as a function of the
noise parameters. Numerical simulations results are in a good agreement with
the theoretical predictions.Comment: 11 pages, 6 figures; REVTEX; to be published in Phys.Rev.E, july 200
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
External Fluctuations in a Pattern-Forming Instability
The effect of external fluctuations on the formation of spatial patterns is
analysed by means of a stochastic Swift-Hohenberg model with multiplicative
space-correlated noise. Numerical simulations in two dimensions show a shift of
the bifurcation point controlled by the intensity of the multiplicative noise.
This shift takes place in the ordering direction (i.e. produces patterns), but
its magnitude decreases with that of the noise correlation length. Analytical
arguments are presented to explain these facts.Comment: 11 pages, Revtex, 10 Postscript figures added with psfig style
(included). To appear in Physical Review
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