105 research outputs found
Structural Properties of the Sliding Columnar Phase in Layered Liquid Crystalline Systems
Under appropriate conditions, mixtures of cationic and neutral lipids and DNA
in water condense into complexes in which DNA strands form local 2D smectic
lattices intercalated between lipid bilayer membranes in a lamellar stack.
These lamellar DNA-cationic-lipid complexes can in principle exhibit a variety
of equilibrium phases, including a columnar phase in which parallel DNA strands
from a 2D lattice, a nematic lamellar phase in which DNA strands align along a
common direction but exhibit no long-range positional order, and a possible new
intermediate phase, the sliding columnar (SC) phase, characterized by a
vanishing shear modulus for relative displacement of DNA lattices but a
nonvanishing modulus for compressing these lattices. We develop a model capable
of describing all phases and transitions among them and use it to calculate
structural properties of the sliding columnar phase. We calculate displacement
and density correlation functions and x-ray scattering intensities in this
phase and show, in particular, that density correlations within a layer have an
unusual dependence on separation r. We
investigate the stability of the SC phase with respect to shear couplings
leading to the columnar phase and dislocation unbinding leading to the lamellar
nematic phase. For models with interactions only between nearest neighbor
planes, we conclude that the SC phase is not thermodynamically stable.
Correlation functions in the nematic lamellar phase, however, exhibit SC
behavior over a range of length scalesComment: 28 pages, 4 figure
Sliding Columnar Phase of DNA-Lipid Complexes
We introduce a simple model for DNA-cationic-lipid complexes in which
galleries between planar bilayer lipid lamellae contain DNA 2D smectic lattices
that couple orientationally and positionally to lattices in neighboring
galleries. We identify a new equilibrium phase in which there are long-range
orientational but not positional correlations between DNA lattices. We discuss
properties of this new phase such as its X-ray structure factor S(r), which
exhibits unusual exp(- const.ln^2 r) behavior as a function of in-plane
separation r.Comment: This file contains 4 pages of double column text and one postscript
figure. This version includes interactions between dislocations in a given
gallery and presents an improved estimate of the decoupling temperature. It
is the published versio
Coarsening scenarios in unstable crystal growth
Crystal surfaces may undergo thermodynamical as well kinetic,
out-of-equilibrium instabilities. We consider the case of mound and pyramid
formation, a common phenomenon in crystal growth and a long-standing problem in
the field of pattern formation and coarsening dynamics. We are finally able to
attack the problem analytically and get rigorous results. Three dynamical
scenarios are possible: perpetual coarsening, interrupted coarsening, and no
coarsening. In the perpetual coarsening scenario, mound size increases in time
as L=t^n, where the coasening exponent is n=1/3 when faceting occurs, otherwise
n=1/4.Comment: Changes in the final part. Accepted for publication in Phys. Rev.
Let
Nonlinear Elasticity of the Sliding Columnar Phase
The sliding columnar phase is a new liquid-crystalline phase of matter
composed of two-dimensional smectic lattices stacked one on top of the other.
This phase is characterized by strong orientational but weak positional
correlations between lattices in neighboring layers and a vanishing shear
modulus for sliding lattices relative to each other. A simplified elasticity
theory of the phase only allows intralayer fluctuations of the columns and has
three important elastic constants: the compression, rotation, and bending
moduli, , , and . The rotationally invariant theory contains
anharmonic terms that lead to long wavelength renormalizations of the elastic
constants similar to the Grinstein-Pelcovits renormalization of the elastic
constants in smectic liquid crystals. We calculate these renormalizations at
the critical dimension and find that , where is a wavenumber. The behavior of
, , and in a model that includes fluctuations perpendicular to the
layers is identical to that of the simple model with rigid layers. We use
dimensional regularization rather than a hard-cutoff renormalization scheme
because ambiguities arise in the one-loop integrals with a finite cutoff.Comment: This file contains 18 pages of double column text in REVTEX format
and 6 postscript figure
The 0 and the pi phase Josephson coupling through an insulating barrier with magnetic impurities
We have studied temperature and field dependencies of the critical current
in the Nb-FeSi-Nb Josephson junction with tunneling
barrier formed by paramagnetic insulator. We demonstrate that in these
junctions the co-existence of both the 0 and the states within one tunnel
junction takes place which leads to the appearance of a sharp cusp in the
temperature dependence similar to the cusp found for the
transition in metallic junctions. This cusp is not related to the
temperature induced transition itself, but is caused by the different
temperature dependencies of the opposing 0 and supercurrents through the
barrier.Comment: Accepted in Physical Review
Stochastic Model for Surface Erosion Via Ion-Sputtering: Dynamical Evolution from Ripple Morphology to Rough Morphology
Surfaces eroded by ion-sputtering are sometimes observed to develop
morphologies which are either ripple (periodic), or rough (non-periodic). We
introduce a discrete stochastic model that allows us to interpret these
experimental observations within a unified framework. We find that a periodic
ripple morphology characterizes the initial stages of the evolution, whereas
the surface displays self-affine scaling in the later time regime. Further, we
argue that the stochastic continuum equation describing the surface height is a
noisy version of the Kuramoto-Sivashinsky equation.Comment: 4 pages, 7 postscript figs., Revtex, to appear in Phys. Rev. Let
Dynamics of folding in Semiflexible filaments
We investigate the dynamics of a single semiflexible filament, under the
action of a compressing force, using numerical simulations and scaling
arguments. The force is applied along the end to end vector at one extremity of
the filament, while the other end is held fixed. We find that, unlike in
elastic rods the filament folds asymmetrically with a folding length which
depends only on the bending stiffness and the applied force. It is shown that
this behavior can be attributed to the exponentially falling tension profile in
the filament. While the folding time depends on the initial configuration, at
late time, the distance moved by the terminal point of the filament and the
length of the fold shows a power law dependence on time with an exponent 1/2.Comment: 13 pages, Late
Sliding Phases in XY-Models, Crystals, and Cationic Lipid-DNA Complexes
We predict the existence of a totally new class of phases in weakly coupled,
three-dimensional stacks of two-dimensional (2D) XY-models. These ``sliding
phases'' behave essentially like decoupled, independent 2D XY-models with
precisely zero free energy cost associated with rotating spins in one layer
relative to those in neighboring layers. As a result, the two-point spin
correlation function decays algebraically with in-plane separation. Our
results, which contradict past studies because we include higher-gradient
couplings between layers, also apply to crystals and may explain recently
observed behavior in cationic lipid-DNA complexes.Comment: 4 pages of double column text in REVTEX format and 1 postscript
figur
Classical motion in force fields with short range correlations
We study the long time motion of fast particles moving through time-dependent
random force fields with correlations that decay rapidly in space, but not
necessarily in time. The time dependence of the averaged kinetic energy and
mean-squared displacement is shown to exhibit a large degree of universality;
it depends only on whether the force is, or is not, a gradient vector field.
When it is, p^{2}(t) ~ t^{2/5} independently of the details of the potential
and of the space dimension. Motion is then superballistic in one dimension,
with q^{2}(t) ~ t^{12/5}, and ballistic in higher dimensions, with q^{2}(t) ~
t^{2}. These predictions are supported by numerical results in one and two
dimensions. For force fields not obtained from a potential field, the power
laws are different: p^{2}(t) ~ t^{2/3} and q^{2}(t) ~ t^{8/3} in all dimensions
d\geq 1
Fast coarsening in unstable epitaxy with desorption
Homoepitaxial growth is unstable towards the formation of pyramidal mounds
when interlayer transport is reduced due to activation barriers to hopping at
step edges. Simulations of a lattice model and a continuum equation show that a
small amount of desorption dramatically speeds up the coarsening of the mound
array, leading to coarsening exponents between 1/3 and 1/2. The underlying
mechanism is the faster growth of larger mounds due to their lower evaporation
rate.Comment: 4 pages, 4 PostScript figure
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