526 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.
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.
The Geometrical Structure of 2d Bond-Orientational Order
We study the formulation of bond-orientational order in an arbitrary two
dimensional geometry. We find that bond-orientational order is properly
formulated within the framework of differential geometry with torsion. The
torsion reflects the intrinsic frustration for two-dimensional crystals with
arbitrary geometry. Within a Debye-Huckel approximation, torsion may be
identified as the density of dislocations. Changes in the geometry of the
system cause a reorganization of the torsion density that preserves
bond-orientational order. As a byproduct, we are able to derive several
identities involving the topology, defect density and geometric invariants such
as Gaussian curvature. The formalism is used to derive the general free energy
for a 2D sample of arbitrary geometry, both in the crystalline and hexatic
phases. Applications to conical and spherical geometries are briefly addressed.Comment: 22 pages, LaTeX, 4 eps figures Published versio
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
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
Spectroscopy, Interactions and Level Splittings in Au Nanoparticles
We have measured the electronic energy spectra of nm-scale Au particles using
a new tunneling spectroscopy configuration. The particle diameters ranged from
5nm to 9nm, and at low energies the spectrum is discrete, as expected by the
electron-in-a-box model. The density of tunneling resonances increases rapidly
with energy, and at higher energies the resonances overlap forming broad
resonances. Near the Thouless energy, the broad resonances merge into a
continuum. The tunneling resonances display Zeeman splitting in a magnetic
field. Surprisingly, the g-factors (~0.3) of energy levels in Au nano-particles
are much smaller than the g-factor (2.1) in bulk gold
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
The distribution of extremal points of Gaussian scalar fields
We consider the signed density of the extremal points of (two-dimensional)
scalar fields with a Gaussian distribution. We assign a positive unit charge to
the maxima and minima of the function and a negative one to its saddles. At
first, we compute the average density for a field in half-space with Dirichlet
boundary conditions. Then we calculate the charge-charge correlation function
(without boundary). We apply the general results to random waves and random
surfaces. Furthermore, we find a generating functional for the two-point
function. Its Legendre transform is the integral over the scalar curvature of a
4-dimensional Riemannian manifold.Comment: 22 pages, 8 figures, corrected published versio
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