61 research outputs found
Normal stress anisotropy and marginal stability in athermal elastic networks
Hydrogels of semiflexible biopolymers such as collagen have been shown to
contract axially under shear strain, in contrast to the axial dilation observed
for most elastic materials. Recent work has shown that this behavior can be
understood in terms of the porous, two-component nature and consequent
time-dependent compressibility of hydrogels. The apparent normal stress
measured by a torsional rheometer reflects only the tensile contribution of the
axial component on long (compressible) timescales, crossing over
to the first normal stress difference, at short
(incompressible) times. While the behavior of is well understood for
isotropic viscoelastic materials undergoing affine shear deformation,
biopolymer networks are often anisotropic and deform nonaffinely. Here, we
numerically study the normal stresses that arise under shear in subisostatic,
athermal semiflexible polymer networks. We show that such systems exhibit
strong deviations from affine behavior and that these anomalies are controlled
by a rigidity transition as a function of strain
Budding and Domain Shape Transformations in Mixed Lipid Films and Bilayer Membranes
We study the stability and shapes of domains with spontaneous curvature in
fluid films and membranes, embedded in a surrounding membrane with zero
spontaneous curvature. These domains can result from the inclusion of an
impurity in a fluid membrane, or from phase separation within the membrane. We
show that for small but finite line and surface tensions and for finite
spontaneous curvatures, an equilibrium phase of protruding circular domains is
obtained at low impurity concentrations. At higher concentrations, we predict a
transition from circular domains, or "caplets", to stripes. In both cases, we
calculate the shapes of these domains within the Monge representation for the
membrane shape. With increasing line tension, we show numerically that there is
a budding transformation from stable protruding circular domains to spherical
buds. We calculate the full phase diagram, and demonstrate a two triple points,
of respectively bud-flat-caplet and flat-stripe-caplet coexistence.Comment: 14 pages, to appear in Phys Rev
Fluctuation-stabilized marginal networks and anomalous entropic elasticity
We study the elastic properties of thermal networks of Hookean springs. In
the purely mechanical limit, such systems are known to have vanishing rigidity
when their connectivity falls below a critical, isostatic value. In this work
we show that thermal networks exhibit a non-zero shear modulus well below
the isostatic point, and that this modulus exhibits an anomalous, sublinear
dependence on temperature . At the isostatic point, increases as the
square-root of , while we find below the isostatic
point, where . We show that this anomalous dependence
is entropic in origin.Comment: 9 pages, 7 figure
A symmetrical method to obtain shear moduli from microrheology
Passive microrheology typically deduces shear elastic loss and storage moduli
from displacement time series or mean-squared displacement (MSD) of thermally
fluctuating probe particles in equilibrium materials. Common data analysis
methods use either Kramers-Kronig (KK) transformations or functional fitting to
calculate frequency-dependent loss and storage moduli. We propose a new
analysis method for passive microrheology that avoids the limitations of both
of these approaches. In this method, we determine both real and imaginary
components of the complex, frequency-dependent response function as direct integral
transforms of the MSD of thermal particle motion. This procedure significantly
improves the high-frequency fidelity of relative to the use of
KK transformation, which has been shown to lead to artifacts in
. We test our method on both model data and experimental
data. Experiments were performed on solutions of worm-like micelles and dilute
collagen solutions. While the present method agrees well with established
KK-based methods at low frequencies, we demonstrate significant improvement at
high frequencies using our symmetric analysis method, up to almost the
fundamental Nyquist limit.Comment: 8 pages, 4 figure
On-site residence time in a driven diffusive system: violation and recovery of mean-field
We investigate simple one-dimensional driven diffusive systems with open
boundaries. We are interested in the average on-site residence time defined as
the time a particle spends on a given site before moving on to the next site.
Using mean-field theory, we obtain an analytical expression for the on-site
residence times. By comparing the analytic predictions with numerics, we
demonstrate that the mean-field significantly underestimates the residence time
due to the neglect of time correlations in the local density of particles. The
temporal correlations are particularly long-lived near the average shock
position, where the density changes abruptly from low to high. By using Domain
wall theory (DWT), we obtain highly accurate estimates of the residence time
for different boundary conditions. We apply our analytical approach to
residence times in a totally asymmetric exclusion process (TASEP), TASEP
coupled to Langmuir kinetics (TASEP + LK), and TASEP coupled to mutually
interactive LK (TASEP + MILK). The high accuracy of our predictions is verified
by comparing these with detailed Monte Carlo simulations
Field theory for mechanical criticality in disordered fiber networks
Strain-controlled criticality governs the elasticity of jamming and fiber
networks. While the upper critical dimension of jamming is believed to be
=2, non mean-field exponents are observed in numerical studies of 2D and
3D fiber networks. The origins of this remains unclear. In this study we
propose a minimal mean-field model for strain-controlled criticality of fiber
networks. We then extend this to a phenomenological field theory, in which non
mean-field behavior emerges as a result of the disorder in the network
structure. We predict that the upper critical dimension for such systems is
=4 using a Gaussian approximation. Moreover, we identify an order
parameter for the phase transition, which has been lacking for fiber networks
to date
Effective Medium Theory for Mechanical Phase Transitions of Fiber Networks
Networks of stiff fibers govern the elasticity of biological structures such
as the extracellular matrix of collagen. These networks are known to stiffen
nonlinearly under shear or extensional strain. Recently, it has been shown that
such stiffening is governed by a strain-controlled athermal but critical phase
transition, from a floppy phase below the critical strain to a rigid phase
above the critical strain. While this phase transition has been extensively
studied numerically and experimentally, a complete analytical theory for this
transition remains elusive. Here, we present an effective medium theory (EMT)
for this mechanical phase transition of fiber networks. We extend a previous
EMT appropriate for linear elasticity to incorporate nonlinear effects via an
anharmonic Hamiltonian. The mean-field predictions of this theory, including
the critical exponents, scaling relations and non-affine fluctuations
qualitatively agree with previous experimental and numerical results
Stress-stabilized sub-isostatic fiber networks in a rope-like limit
The mechanics of disordered fibrous networks such as those that make up the
extracellular matrix are strongly dependent on the local connectivity or
coordination number. For biopolymer networks this coordination number is
typically between three and four. Such networks are sub-isostatic and linearly
unstable to deformation with only central force interactions, but exhibit a
mechanical phase transition between floppy and rigid states under strain.
Introducing weak bending interactions stabilizes these networks and suppresses
the critical signatures of this transition. We show that applying external
stress can also stabilize sub-isostatic networks with only tensile central
force interactions, i.e., a rope-like potential. Moreover, we find that the
linear shear modulus shows a power law scaling with the external normal stress,
with a non-mean-field exponent. For networks with finite bending rigidity, we
find that the critical stain shifts to lower values under prestress
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