156 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
Tuning Jammed Frictionless Disk Packings from Isostatic to Hyperstatic
We perform extensive computational studies of two-dimensional static
bidisperse disk packings using two distinct packing-generation protocols. The
first involves thermally quenching equilibrated liquid configurations to zero
temperature over a range of thermal quench rates and initial packing
fractions followed by compression and decompression in small steps to reach
packing fractions at jamming onset. For the second, we seed the system
with initial configurations that promote micro- and macrophase-separated
packings followed by compression and decompression to . We find that
amorphous, isostatic packings exist over a finite range of packing fractions
from in the large-system limit,
with . In agreement with previous calculations,
we obtain for , where is the rate
above which is insensitive to rate. We further compare the structural
and mechanical properties of isostatic versus hyperstatic packings. The
structural characterizations include the contact number, bond orientational
order, and mixing ratios of the large and small particles. We find that the
isostatic packings are positionally and compositionally disordered, whereas
bond-orientational and compositional order increase with contact number for
hyperstatic packings. In addition, we calculate the static shear modulus and
normal mode frequencies of the static packings to understand the extent to
which the mechanical properties of amorphous, isostatic packings are different
from partially ordered packings. We find that the mechanical properties of the
packings change continuously as the contact number increases from isostatic to
hyperstatic.Comment: 11 pages, 15 figure
Entropy and Temperature of a Static Granular Assembly
Granular matter is comprised of a large number of particles whose collective
behavior determines macroscopic properties such as flow and mechanical
strength. A comprehensive theory of the properties of granular matter,
therefore, requires a statistical framework. In molecular matter, equilibrium
statistical mechanics, which is founded on the principle of conservation of
energy, provides this framework. Grains, however, are small but macroscopic
objects whose interactions are dissipative since energy can be lost through
excitations of the internal degrees of freedom. In this work, we construct a
statistical framework for static, mechanically stable packings of grains, which
parallels that of equilibrium statistical mechanics but with conservation of
energy replaced by the conservation of a function related to the mechanical
stress tensor. Our analysis demonstrates the existence of a state function that
has all the attributes of entropy. In particular, maximizing this state
function leads to a well-defined granular temperature for these systems.
Predictions of the ensemble are verified against simulated packings of
frictionless, deformable disks. Our demonstration that a statistical ensemble
can be constructed through the identification of conserved quantities other
than energy is a new approach that is expected to open up avenues for
statistical descriptions of other non-equilibrium systems.Comment: 5 pages, 4 figure
Elastic Correlations in Nucleosomal DNA Structure
The structure of DNA in the nucleosome core particle is studied using an
elastic model that incorporates anisotropy in the bending energetics and
twist-bend coupling. Using the experimentally determined structure of
nucleosomal DNA [T.J. Richmond and C.A. Davey, Nature {\bf 423}, 145 (2003)],
it is shown that elastic correlations exist between twist, roll, tilt, and
stretching of DNA, as well as the distance between phosphate groups. The
twist-bend coupling term is shown to be able to capture these correlations to a
large extent, and a fit to the experimental data yields a new estimate of G=25
nm for the value of the twist-bend coupling constant
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
A minimal model for kinetic arrest
To elucidate slow dynamics in glassy materials, we introduce the {\it
Figure-8 model} in which hard blocks undergo Brownian motion around a
circuit in the shape of a figure-8. This system undergoes kinetic arrest at a
critical packing fraction , and for
long-time diffusion is controlled by rare, cooperative `junction-crossing'
particle rearrangements. We find that the average time between junction
crossings , and hence the structural relaxation time, does not
simply scale with the configurational volume \OmegaLow of transition states,
because also depends on the time to complete a junction crossing.
The importance of these results in understanding cage-breaking dynamics in
glassy systems is discussed.Comment: 4 pages, 4 figure
Jamming transition in emulsions and granular materials
We investigate the jamming transition in packings of emulsions and granular
materials via molecular dynamics simulations. The emulsion model is composed of
frictionless droplets interacting via nonlinear normal forces obtained using
experimental data acquired by confocal microscopy of compressed emulsions
systems. Granular materials are modeled by Hertz-Mindlin deformable spherical
grains with Coulomb friction. In both cases, we find power-law scaling for the
vanishing of pressure and excess number of contacts as the system approaches
the jamming transition from high volume fractions. We find that the
construction history parametrized by the compression rate during the
preparation protocol has a strong effect on the micromechanical properties of
granular materials but not on emulsions. This leads the granular system to jam
at different volume fractions depending on the histories. Isostaticity is found
in the packings close to the jamming transition in emulsions and in granular
materials at slow compression rates and infinite friction. Heterogeneity of
interparticle forces increases as the packings approach the jamming transition
which is demonstrated by the exponential tail in force distributions and the
small values of the participation number measuring spatial localization of the
forces. However, no signatures of the jamming transition are observed in
structural properties, like the radial distribution functions and the
distributions of contacts.Comment: Submitted to PR
Organization of atomic bond tensions in model glasses
In order to understand whether internal stresses in glasses are correlated or
randomly distributed, we study the organization of atomic bond tensions (normal
forces between pairs of atoms). Measurements of the invariants of the atomic
bond tension tensor in simulated 2D and 3D binary Lennard-Jones glasses, reveal
new and unexpected correlations and provide support for Alexander's conjecture
about the non-random character of internal stresses in amorphous solids
Effective Temperatures of a Driven System Near Jamming
Fluctuations in a model of a sheared, zero-temperature foam are studied
numerically. Five different quantities that reduce to the true temperature in
an equilibrium thermal system are calculated. All five have the same shear-rate
dependence, and three have the same value. Near the onset of jamming, the
relaxation time is the same function of these three temperatures in the sheared
system as of the true temperature in an unsheared system. These results imply
that statistical mechanics is useful for the system and provide strong support
for the concept of jamming.Comment: 4 pages, 4 postscript figure
Effect of boundaries on the force distributions in granular media
The effect of boundaries on the force distributions in granular media is
illustrated by simulations of 2D packings of frictionless, Hertzian spheres. To
elucidate discrepancies between experimental observations and theoretical
predictions, we distinguish between the weight distribution {\cal P} (w)
measured in experiments and analyzed in the q-model, and the distribution of
interparticle forces P(f). The latter one is robust, while {\cal P}(w) can be
obtained once the local packing geometry and P(f) are known. By manipulating
the (boundary) geometry, we show that {\cal P}(w) can be varied drastically.Comment: 4 pages, 4 figure
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