160 research outputs found
Experimental Measurement of the Persistence Exponent of the Planar Ising Model
Using a twisted nematic liquid crystal system exhibiting planar Ising model
dynamics, we have measured the scaling exponent which characterizes
the time evolution, , of the probability p(t) that the
local order parameter has not switched its state by the time t. For 0.4 seconds
to 200 seconds following the phase quench, the system exhibits scaling behavior
and, measured over this interval, , in good agreement
with theoretical analysis and numerical simulations.Comment: 4 pages RevTeX (multicol.sty and epsf.sty needed): 1 EPS figure.
Introduction and reference list modifie
Hydrodynamics of topological defects in nematic liquid crystals
We show that back-flow, the coupling between the order parameter and the
velocity fields, has a significant effect on the motion of defects in nematic
liquid crystals. In particular the defect speed can depend strongly on the
topological strength in two dimensions and on the sense of rotation of the
director about the core in three dimensions.Comment: 4 pages including two figure
Phase ordering in bulk uniaxial nematic liquid crystals
The phase-ordering kinetics of a bulk uniaxial nematic liquid crystal is
addressed using techniques that have been successfully applied to describe
ordering in the O(n) model. The method involves constructing an appropriate
mapping between the order-parameter tensor and a Gaussian auxiliary field. The
mapping accounts both for the geometry of the director about the dominant
charge 1/2 string defects and biaxiality near the string cores. At late-times t
following a quench, there exists a scaling regime where the bulk nematic liquid
crystal and the three-dimensional O(2) model are found to be isomorphic, within
the Gaussian approximation. As a consequence, the scaling function for
order-parameter correlations in the nematic liquid crystal is exactly that of
the O(2) model, and the length characteristic of the strings grows as
. These results are in accord with experiment and simulation. Related
models dealing with thin films and monopole defects in the bulk are presented
and discussed.Comment: 21 pages, 3 figures, REVTeX, submitted to Phys. Rev.
Hydrodynamics of domain growth in nematic liquid crystals
We study the growth of aligned domains in nematic liquid crystals. Results
are obtained solving the Beris-Edwards equations of motion using the lattice
Boltzmann approach. Spatial anisotropy in the domain growth is shown to be a
consequence of the flow induced by the changing order parameter field
(backflow). The generalization of the results to the growth of a cylindrical
domain, which involves the dynamics of a defect ring, is discussed.Comment: 12 revtex-style pages, including 12 figures; small changes before
publicatio
How Efficient Is The Langacker-Pi Mechanism of Monopole Annihilation?
We investigate the dynamics of monopole annihilation by the Langacker-Pi
mechanism. We find taht considerations of causality, flux-tube energetics and
the friction from Aharonov-Bohm scatteering suggest that the monopole
annihilation is most efficient if electromagnetism is spontaneously broken at
the lowest temperature () consistent with not having
the monopoles dominate the energy density of the universe.Comment: 10 page
Growth Laws for Phase Ordering
We determine the characteristic length scale, , in phase ordering
kinetics for both scalar and vector fields, with either short- or long-range
interactions, and with or without conservation laws. We obtain
consistently by comparing the global rate of energy change to the energy
dissipation from the local evolution of the order parameter. We derive growth
laws for O(n) models, and our results can be applied to other systems with
similar defect structures.Comment: 12 pages, LaTeX, second tr
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
Phase-ordering dynamics of the Gay-Berne nematic liquid crystal
Phase-ordering dynamics in nematic liquid crystals has been the subject of
much active investigation in recent years in theory, experiments and
simulations. With a rapid quench from the isotropic to nematic phase a large
number of topological defects are formed and dominate the subsequent
equilibration process. We present here the results of a molecular dynamics
simulation of the Gay-Berne model of liquid crystals after such a quench in a
system with 65536 molecules. Twist disclination lines as well as type-1 lines
and monopoles were observed. Evidence of dynamical scaling was found in the
behavior of the spatial correlation function and the density of disclination
lines. However, the behavior of the structure factor provides a more sensitive
measure of scaling, and we observed a crossover from a defect dominated regime
at small values of the wavevector to a thermal fluctuation dominated regime at
large wavevector.Comment: 18 pages, 16 figures, animations available at
http://www.physics.brown.edu/Users/faculty/pelcovits/lc/coarsening.htm
Dynamical Scaling: the Two-Dimensional XY Model Following a Quench
To sensitively test scaling in the 2D XY model quenched from
high-temperatures into the ordered phase, we study the difference between
measured correlations and the (scaling) results of a Gaussian-closure
approximation. We also directly compare various length-scales. All of our
results are consistent with dynamical scaling and an asymptotic growth law , though with a time-scale that depends on the
length-scale in question. We then reconstruct correlations from the
minimal-energy configuration consistent with the vortex positions, and find
them significantly different from the ``natural'' correlations --- though both
scale with . This indicates that both topological (vortex) and
non-topological (``spin-wave'') contributions to correlations are relevant
arbitrarily late after the quench. We also present a consistent definition of
dynamical scaling applicable more generally, and emphasize how to generalize
our approach to other quenched systems where dynamical scaling is in question.
Our approach directly applies to planar liquid-crystal systems.Comment: 10 pages, 10 figure
The Energy-Scaling Approach to Phase-Ordering Growth Laws
We present a simple, unified approach to determining the growth law for the
characteristic length scale, , in the phase ordering kinetics of a system
quenched from a disordered phase to within an ordered phase. This approach,
based on a scaling assumption for pair correlations, determines
self-consistently for purely dissipative dynamics by computing the
time-dependence of the energy in two ways. We derive growth laws for conserved
and non-conserved models, including two-dimensional XY models and
systems with textures. We demonstrate that the growth laws for other systems,
such as liquid-crystals and Potts models, are determined by the type of
topological defect in the order parameter field that dominates the energy. We
also obtain generalized Porod laws for systems with topological textures.Comment: LATeX 18 pages (REVTeX macros), one postscript figure appended,
REVISED --- rearranged and clarified, new paragraph on naive dimensional
analysis at end of section I
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