143 research outputs found
Free Energies of Isolated 5- and 7-fold Disclinations in Hexatic Membranes
We examine the shapes and energies of 5- and 7-fold disclinations in
low-temperature hexatic membranes. These defects buckle at different values of
the ratio of the bending rigidity, , to the hexatic stiffness constant,
, suggesting {\em two} distinct Kosterlitz-Thouless defect proliferation
temperatures. Seven-fold disclinations are studied in detail numerically for
arbitrary . We argue that thermal fluctuations always drive
into an ``unbuckled'' regime at long wavelengths, so that
disclinations should, in fact, proliferate at the {\em same} critical
temperature. We show analytically that both types of defects have power law
shapes with continuously variable exponents in the ``unbuckled'' regime.
Thermal fluctuations then lock in specific power laws at long wavelengths,
which we calculate for 5- and 7-fold defects at low temperatures.Comment: LaTeX format. 17 pages. To appear in Phys. Rev.
Orientational order on curved surfaces - the high temperature region
We study orientational order, subject to thermal fluctuations, on a fixed
curved surface. We derive, in particular, the average density of zeros of
Gaussian distributed vector fields on a closed Riemannian manifold. Results are
compared with the density of disclination charges obtained from a Coulomb gas
model. Our model describes the disordered state of two dimensional objects with
orientational degrees of freedom, such as vector ordering in Langmuir
monolayers and lipid bilayers above the hexatic to fluid transition.Comment: final version, 13 Pages, 2 figures, uses iopart.cl
Disclination Asymmetry in Two-Dimensional Nematic Liquid Crystals with Unequal Frank Constants
The behavior of a thin film of nematic liquid crystal with unequal Frank
constants is discussed. Distinct Frank constants are found to imply unequal
core energies for and disclinations. Even so, a topological
constraint is shown to ensure that the bulk densities of the two types of
disclinations are the same. For a system with free boundary conditions, such as
a liquid membrane, unequal core energies simply renormalize the Gaussian
rigidity and line tension.Comment: RevTex forma
Signed zeros of Gaussian vector fields-density, correlation functions and curvature
We calculate correlation functions of the (signed) density of zeros of
Gaussian distributed vector fields. We are able to express correlation
functions of arbitrary order through the curvature tensor of a certain abstract
Riemann-Cartan or Riemannian manifold. As an application, we discuss one- and
two-point functions. The zeros of a two-dimensional Gaussian vector field model
the distribution of topological defects in the high-temperature phase of
two-dimensional systems with orientational degrees of freedom, such as
superfluid films, thin superconductors and liquid crystals.Comment: 14 pages, 1 figure, uses iopart.cls, improved presentation, to appear
in J. Phys.
Ergodic properties of a model for turbulent dispersion of inertial particles
We study a simple stochastic differential equation that models the dispersion
of close heavy particles moving in a turbulent flow. In one and two dimensions,
the model is closely related to the one-dimensional stationary Schroedinger
equation in a random delta-correlated potential. The ergodic properties of the
dispersion process are investigated by proving that its generator is
hypoelliptic and using control theory
Light Induced Melting of Colloidal Crystals in Two Dimensions
We demonstrate that particles confined to two dimensions (2d) and subjected
to a one-dimensional (1d) periodic potential exhibit a rich phase diagram, with
both ``locked floating solids'' and smectic phases. The resulting phases and
phase transitions are studied as a function of temperature and potential
strength. We find reentrant melting as a function of the potential strength.
Our results lead to universal predictions consistent with recent experiments on
2d colloids in the presence of a laser-induced 1d periodic potential.Comment: 4 pages, 3 figures, also available at http://cmtw.harvard.edu/~fre
Heterogeneity and Disorder: Contributions of Rolf Landauer
Rolf Landauer made important contributions to many branches of science.
Within the broad area of transport in disordered media, he wrote seminal papers
on electrical conduction in macroscopically inhomogeneous materials, as well as
fundamental analyses of electron transport in quantum mechanical systems with
disorder on the atomic scale. We review here some of these contributions. We
also briefly describe some main events in his personal and scientific life.Comment: 10 pages, 3 figures; presented on the occasion when Rolf Landauer was
awarded, posthumously, the inaugural ETOPIM Medal at the ETOPIM 8 Conference,
which took place during 7--12 June, 2009 in Rethymnon, Cret
Novel Phases and Reentrant Melting of Two Dimensional Colloidal Crystals
We investigate two-dimensional (2d) melting in the presence of a
one-dimensional (1d) periodic potential as, for example, realized in recent
experiments on 2d colloids subjected to two interfering laser beams. The
topology of the phase diagram is found to depend primarily on two factors: the
relative orientation of the 2d crystal and the periodic potential troughs,
which select a set of Bragg planes running parallel to the troughs, and the
commensurability ratio p= a'/d of the spacing a' between these Bragg planes to
the period d of the periodic potential. The complexity of the phase diagram
increases with the magnitude of the commensurabilty ratio p. Rich phase
diagram, with ``modulated liquid'', ``floating'' and ``locked floating'' solid
and smectic phases are found. Phase transitions between these phases fall into
two broad universality classes, roughening and melting, driven by the
proliferation of discommensuration walls and dislocations, respectively. We
discuss correlation functions and the static structure factor in these phases
and make detailed predictions of the universal features close to the phase
boundaries. We predict that for charged systems with highly screened
short-range interactions these melting transitions are generically reentrant as
a function of the strength of the periodic potential, prediction that is in
accord with recent 2d colloid experiments. Implications of our results for
future experiments are also discussed.Comment: 37 pages, 24 figure
On the origin of the large scale structures of the universe
We revise the statistical properties of the primordial cosmological density
anisotropies that, at the time of matter radiation equality, seeded the
gravitational development of large scale structures in the, otherwise,
homogeneous and isotropic Friedmann-Robertson-Walker flat universe. Our
analysis shows that random fluctuations of the density field at the same
instant of equality and with comoving wavelength shorter than the causal
horizon at that time can naturally account, when globally constrained to
conserve the total mass (energy) of the system, for the observed scale
invariance of the anisotropies over cosmologically large comoving volumes.
Statistical systems with similar features are generically known as glass-like
or lattice-like. Obviously, these conclusions conflict with the widely accepted
understanding of the primordial structures reported in the literature, which
requires an epoch of inflationary cosmology to precede the standard expansion
of the universe. The origin of the conflict must be found in the widespread,
but unjustified, claim that scale invariant mass (energy) anisotropies at the
instant of equality over comoving volumes of cosmological size, larger than the
causal horizon at the time, must be generated by fluctuations in the density
field with comparably large comoving wavelength.Comment: New section added; final version to appear in Physical Review D;
discussion extended and detailed with new calculations to support the claims
of the paper; statistical properties of vacuum fluctuations now discussed in
the context of FRW flat universe; new important conclussions adde
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