78 research outputs found
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
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
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
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
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
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
Direct observation of the effective bending moduli of a fluid membrane: Free-energy cost due to the reference-plane deformations
Effective bending moduli of a fluid membrane are investigated by means of the
transfer-matrix method developed in our preceding paper. This method allows us
to survey various statistical measures for the partition sum. The role of the
statistical measures is arousing much attention, since Pinnow and Helfrich
claimed that under a suitable statistical measure, that is, the local mean
curvature, the fluid membranes are stiffened, rather than softened, by thermal
undulations. In this paper, we propose an efficient method to observe the
effective bending moduli directly: We subjected a fluid membrane to a curved
reference plane, and from the free-energy cost due to the reference-plane
deformations, we read off the effective bending moduli. Accepting the
mean-curvature measure, we found that the effective bending rigidity gains even
in the case of very flexible membrane (small bare rigidity); it has been rather
controversial that for such non-perturbative regime, the analytical prediction
does apply. We also incorporate the Gaussian-curvature modulus, and calculated
its effective rigidity. Thereby, we found that the effective Gaussian-curvature
modulus stays almost scale-invariant. All these features are contrasted with
the results under the normal-displacement measure
Symmetries and Elasticity of Nematic Gels
A nematic liquid-crystal gel is a macroscopically homogeneous elastic medium
with the rotational symmetry of a nematic liquid crystal. In this paper, we
develop a general approach to the study of these gels that incorporates all
underlying symmetries. After reviewing traditional elasticity and clarifying
the role of broken rotational symmetries in both the reference space of points
in the undistorted medium and the target space into which these points are
mapped, we explore the unusual properties of nematic gels from a number of
perspectives. We show how symmetries of nematic gels formed via spontaneous
symmetry breaking from an isotropic gel enforce soft elastic response
characterized by the vanishing of a shear modulus and the vanishing of stress
up to a critical value of strain along certain directions. We also study the
phase transition from isotropic to nematic gels. In addition to being fully
consistent with approaches to nematic gels based on rubber elasticity, our
description has the important advantages of being independent of a microscopic
model, of emphasizing and clarifying the role of broken symmetries in
determining elastic response, and of permitting easy incorporation of spatial
variations, thermal fluctuations, and gel heterogeneity, thereby allowing a
full statistical-mechanical treatment of these novel materials.Comment: 21 pages, 4 eps figure
Kinetic roughening of surfaces: Derivation, solution and application of linear growth equations
We present a comprehensive analysis of a linear growth model, which combines
the characteristic features of the Edwards--Wilkinson and noisy Mullins
equations. This model can be derived from microscopics and it describes the
relaxation and growth of surfaces under conditions where the nonlinearities can
be neglected. We calculate in detail the surface width and various correlation
functions characterizing the model. In particular, we study the crossover
scaling of these functions between the two limits described by the combined
equation. Also, we study the effect of colored and conserved noise on the
growth exponents, and the effect of different initial conditions. The
contribution of a rough substrate to the surface width is shown to decay
universally as , where is
the time--dependent correlation length associated with the growth process,
is the initial roughness and the correlation length of the
substrate roughness, and is the surface dimensionality. As a second
application, we compute the large distance asymptotics of the height
correlation function and show that it differs qualitatively from the functional
forms commonly used in the intepretation of scattering experiments.Comment: 28 pages with 4 PostScript figures, uses titlepage.sty; to appear in
Phys. Rev.
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