42 research outputs found
1D Cahn-Hilliard dynamics : coarsening and interrupted coarsening
Many systems exhibit a phase where the order parameter is spatially
modulated. These patterns can be the result of a frustration caused by the
competition between interaction forces with opposite effects. In all models
with local interactions, these ordered phases disappear in the strong
segregation regime (low temperature). It is expected however that these phases
should persist in the case of long range interactions, which can't be correctly
described by a Ginzburg-Landau type model with only a finite number of spatial
derivatives of the order parameter. An alternative approach is to study the
dynamics of the phase transition or pattern formation. While, in the usual
process of Ostwald ripening, succession of doubling of the domain size leads to
a total segregation, or macro-segregation, C. Misbah and P. Politi have shown
that long-range interactions could cause an interruption of this coalescence
process, stabilizing a pattern which then remains in a micro-structured state
or super-crystal. We show that this is the case for a modified Cahn-Hilliard
dynamics due to Oono which includes a non local term and which is particularly
well suited to describe systems with a modulated phase
The Lamellar-Disorder Interface : One-Dimensional Modulated Profiles
We study interfacial behavior of a lamellar (stripe) phase coexisting with a
disordered phase. Systematic analytical expansions are obtained for the
interfacial profile in the vicinity of a tricritical point. They are
characterized by a wide interfacial region involving a large number of
lamellae. Our analytical results apply to systems with one dimensional symmetry
in true thermodynamical equilibrium and are of relevance to metastable
interfaces between lamellar and disordered phases in two and three dimensions.
In addition, good agreement is found with numerical minimization schemes of the
full free energy functional having the same one dimensional symmetry. The
interfacial energy for the lamellar to disordered transition is obtained in
accord with mean field scaling laws of tricritical points.Comment: 12 pages, 8 figure
Tails of Localized Density of States of Two-dimensional Dirac Fermions
The density of states of Dirac fermions with a random mass on a
two-dimensional lattice is considered. We give the explicit asymptotic form of
the single-electron density of states as a function of both energy and
(average) Dirac mass, in the regime where all states are localized. We make use
of a weak-disorder expansion in the parameter g/m^2, where g is the strength of
disorder and m the average Dirac mass for the case in which the evaluation of
the (supersymmetric) integrals corresponds to non-uniform solutions of the
saddle point equation. The resulting density of states has tails which deviate
from the typical pure Gaussian form by an analytic prefactor.Comment: 8 pages, REVTeX, 1 eps figure; to appear in Annalen der Physi
1D Cahn-Hilliard equation: Ostwald ripening and modulated phase systems
Using an approximate analytical solution of the Cahn-Hilliard equation
describing the coalescence during a first order phase transition, we compute
the characteristic time for one step of period doubling in Langer's self
similar scenario for Ostwald ripening. As an application, we compute the
thermodynamically stable period of a 1D modulated phase pattern
Coalescence in the 1D Cahn-Hilliard model
We present an approximate analytical solution of the Cahn-Hilliard equation
describing the coalescence during a first order phase transition. We have
identified all the intermediate profiles, stationary solutions of the noiseless
Cahn-Hilliard equation. Using properties of the soliton lattices, periodic
solutions of the Ginzburg-Landau equation, we have construct a family of ansatz
describing continuously the processus of destabilization and period doubling
predicted in Langer's self similar scenario
1D Cahn-Hilliard dynamics : coarsening and interrupted coarsening
Many systems exhibit a phase where the order parameter is spatially modulated. These patterns can be the result of a frustration caused by the competition between interaction forces with opposite effects. In all models with local interactions, these ordered phases disappear in the strong segregation regime (low temperature). It is expected however that these phases should persist in the case of long range interactions, which can't be correctly described by a Ginzburg-Landau type model with only a finite number of spatial derivatives of the order parameter. An alternative approach is to study the dynamics of the phase transition or pattern formation. While, in the usual process of Ostwald ripening, succession of doubling of the domain size leads to a total segregation, or macro-segregation, C. Misbah and P. Politi have shown that long-range interactions could cause an interruption of this coalescence process, stabilizing a pattern which then remains in a micro-structured state or super-crystal. We show that this is the case for a modified Cahn-Hilliard dynamics due to Oono which includes a non local term and which is particularly well suited to describe systems with a modulated phase
1D Cahn-Hilliard dynamics : coarsening and interrupted coarsening
Many systems exhibit a phase where the order parameter is spatially modulated. These patterns can be the result of a frustration caused by the competition between interaction forces with opposite effects. In all models with local interactions, these ordered phases disappear in the strong segregation regime (low temperature). It is expected however that these phases should persist in the case of long range interactions, which can't be correctly described by a Ginzburg-Landau type model with only a finite number of spatial derivatives of the order parameter. An alternative approach is to study the dynamics of the phase transition or pattern formation. While, in the usual process of Ostwald ripening, succession of doubling of the domain size leads to a total segregation, or macro-segregation, C. Misbah and P. Politi have shown that long-range interactions could cause an interruption of this coalescence process, stabilizing a pattern which then remains in a micro-structured state or super-crystal. We show that this is the case for a modified Cahn-Hilliard dynamics due to Oono which includes a non local term and which is particularly well suited to describe systems with a modulated phase
Modulated phases and Cahn-Hilliard dynamics
L'objet de ce mémoire est de rendre compte de travaux portant sur les phases spatialement modulées ou phases lamellaires, leur thermodynamique (diagramme de phases, profil des interfaces) et la dynamique des transitions de phase qui les font apparaître. En particulier, je me suis intéressé aux non-linéarités de cette dynamique de transition de phase particulière en me basant sur les modèles de Swift-Hohenberg, Cahn-Hilliard et Oono, d'après les noms de leurs auteurs
Phases modulées et dynamique de Cahn-Hilliard
L'objet de ce mémoire est de rendre compte de travaux portant sur les phases spatialement modulées ou phases lamellaires, leur thermodynamique (diagramme de phases, profil des interfaces) et la dynamique des transitions de phase qui les font apparaître. En particulier, je me suis intéressé aux non-linéarités de cette dynamique de transition de phase particulière en me basant sur les modèles de Swift-Hohenberg, Cahn-Hilliard et Oono, d'après les noms de leurs auteurs