36 research outputs found
Defect Statistics in the Two Dimensional Complex Ginsburg-Landau Model
The statistical correlations between defects in the two dimensional complex
Ginsburg-Landau model are studied in the defect-coarsening regime. In
particular the defect-velocity probability distribution is determined and has
the same high velocity tail found for the purely dissipative time-dependent
Ginsburg-Landau (TDGL) model. The spiral arms of the defects lead to a very
different behavior for the order parameter correlation function in the scaling
regime compared to the results for the TDGL model.Comment: 24 page
Multiscaling to Standard Scaling Crossover in the Bray-Humayun Model for Phase Ordering Kinetics
The Bray-Humayun model for phase ordering dynamics is solved numerically in
one and two space dimensions with conserved and non conserved order parameter.
The scaling properties are analysed in detail finding the crossover from
multiscaling to standard scaling in the conserved case. Both in the
nonconserved case and in the conserved case when standard scaling holds the
novel feature of an exponential tail in the scaling function is found.Comment: 21 pages, 10 Postscript figure
Response Functions in Phase Ordering Kinetics
We discuss the behavior of response functions in phase ordering kinetics
within the perturbation theory approach developed earlier. At zeroth order the
results agree with previous gaussian theory calculations. At second order the
nonequilibrium exponents \lambda and \lambda_{R} are changed but remain equal.Comment: 29 page
Theory of Phase Ordering Kinetics
The theory of phase ordering dynamics -- the growth of order through domain
coarsening when a system is quenched from the homogeneous phase into a
broken-symmetry phase -- is reviewed, with the emphasis on recent developments.
Interest will focus on the scaling regime that develops at long times after the
quench. How can one determine the growth laws that describe the time-dependence
of characteristic length scales, and what can be said about the form of the
associated scaling functions? Particular attention will be paid to systems
described by more complicated order parameters than the simple scalars usually
considered, e.g. vector and tensor fields. The latter are needed, for example,
to describe phase ordering in nematic liquid crystals, on which there have been
a number of recent experiments. The study of topological defects (domain walls,
vortices, strings, monopoles) provides a unifying framework for discussing
coarsening in these different systems.Comment: To appear in Advances in Physics. 85 pages, latex, no figures. For a
hard copy with figures, email [email protected]
Nonequilibrium Dynamics in the Complex Ginzburg-Landau Equation
We present results from a comprehensive analytical and numerical study of
nonequilibrium dynamics in the 2-dimensional complex Ginzburg-Landau (CGL)
equation. In particular, we use spiral defects to characterize the domain
growth law and the evolution morphology. An asymptotic analysis of the
single-spiral correlation function shows a sequence of singularities --
analogous to those seen for time-dependent Ginzburg-Landau (TDGL) models with
O(n) symmetry, where is even.Comment: 11 pages, 5 figure
Domain Growth and Finite-Size-Scaling in the Kinetic Ising Model
This paper describes the application of finite-size scaling concepts to
domain growth in systems with a non-conserved order parameter. A finite-size
scaling ansatz for the time-dependent order parameter distribution function is
proposed, and tested with extensive Monte-Carlo simulations of domain growth in
the 2-D spin-flip kinetic Ising model. The scaling properties of the
distribution functions serve to elucidate the configurational self-similarity
that underlies the dynamic scaling picture. Moreover, it is demonstrated that
the application of finite-size-scaling techniques facilitates the accurate
determination of the bulk growth exponent even in the presence of strong
finite-size effects, the scale and character of which are graphically exposed
by the order parameter distribution function. In addition it is found that one
commonly used measure of domain size--the scaled second moment of the
magnetisation distribution--belies the full extent of these finite-size
effects.Comment: 13 pages, Latex. Figures available on request. Rep #9401
Renormalized kinetic theory of classical fluids in and out of equilibrium
We present a theory for the construction of renormalized kinetic equations to
describe the dynamics of classical systems of particles in or out of
equilibrium. A closed, self-consistent set of evolution equations is derived
for the single-particle phase-space distribution function , the correlation
function , the retarded and advanced density response
functions to an external potential , and
the associated memory functions . The basis of the theory is an
effective action functional of external potentials that
contains all information about the dynamical properties of the system. In
particular, its functional derivatives generate successively the
single-particle phase-space density and all the correlation and density
response functions, which are coupled through an infinite hierarchy of
evolution equations. Traditional renormalization techniques are then used to
perform the closure of the hierarchy through memory functions. The latter
satisfy functional equations that can be used to devise systematic
approximations. The present formulation can be equally regarded as (i) a
generalization to dynamical problems of the density functional theory of fluids
in equilibrium and (ii) as the classical mechanical counterpart of the theory
of non-equilibrium Green's functions in quantum field theory. It unifies and
encompasses previous results for classical Hamiltonian systems with any initial
conditions. For equilibrium states, the theory reduces to the equilibrium
memory function approach. For non-equilibrium fluids, popular closures (e.g.
Landau, Boltzmann, Lenard-Balescu) are simply recovered and we discuss the
correspondence with the seminal approaches of Martin-Siggia-Rose and of
Rose.and we discuss the correspondence with the seminal approaches of
Martin-Siggia-Rose and of Rose.Comment: 63 pages, 10 figure
Scaling and Crossover in the Large-N Model for Growth Kinetics
The dependence of the scaling properties of the structure factor on space
dimensionality, range of interaction, initial and final conditions, presence or
absence of a conservation law is analysed in the framework of the large-N model
for growth kinetics. The variety of asymptotic behaviours is quite rich,
including standard scaling, multiscaling and a mixture of the two. The
different scaling properties obtained as the parameters are varied are
controlled by a structure of fixed points with their domains of attraction.
Crossovers arising from the competition between distinct fixed points are
explicitely obtained. Temperature fluctuations below the critical temperature
are not found to be irrelevant when the order parameter is conserved. The model
is solved by integration of the equation of motion for the structure factor and
by a renormalization group approach.Comment: 48 pages with 6 figures available upon request, plain LaTe
Interface fluctuations, bulk fluctuations and dimensionality in the off-equilibrium response of coarsening systems
The relationship between statics and dynamics proposed by Franz, Mezard,
Parisi and Peliti (FMPP) for slowly relaxing systems [Phys.Rev.Lett. {\bf 81},
1758 (1998)] is investigated in the framework of non disordered coarsening
systems. Separating the bulk from interface response we find that for statics
to be retrievable from dynamics the interface contribution must be
asymptotically negligible. How fast this happens depends on dimensionality.
There exists a critical dimensionality above which the interface response
vanishes like the interface density and below which it vanishes more slowly. At
the interface response does not vanish leading to the violation of the
FMPP scheme. This behavior is explained in terms of the competition between
curvature driven and field driven interface motion.Comment: 11 pages, 3 figures. Significantly improved version of the paper with
new results, new numerical simulations and new figure
Boundary Effects in Local Inflation and Spectrum of Density Perturbations
We observe that when a local patch in a radiation filled Robertson-Walker
universe inflates by some reason, outside perturbations can enter into the
inflating region. Generally, the physical wavelengths of these perturbations
become larger than the Hubble radius as they cross into the inflating space and
their amplitudes freeze out immediately. It turns out that the corresponding
power spectrum is not scale invariant. Although these perturbations cannot
reach out to a distance inner observer shielded by a de Sitter horizon, they
still indicate a curious boundary effect in local inflationary scenarios.Comment: 11 pages, 8 figures, revtex4, v4: minor typos corrected, twocolumn
versio