101 research outputs found
Filamin cross-linked semiflexible networks: Fragility under strain
The semiflexible F-actin network of the cytoskeleton is cross-linked by a
variety of proteins including filamin, which contain Ig-domains that unfold
under applied tension. We examine a simple semiflexible network model
cross-linked by such unfolding linkers that captures the main mechanical
features of F-actin networks cross-linked by filamin proteins and show that
under sufficiently high strain the network spontaneously self-organizes so that
an appreciable fraction of the filamin cross-linkers are at the threshold of
domain unfolding. We propose an explanation of this organization based on a
mean-field model and suggest a qualitative experimental signature of this type
of network reorganization under applied strain that may be observable in
intracellular microrheology experiments of Crocker et al.Comment: 4 Pages, 3 figures, Revtex4, submitted to PR
Nonaffine Correlations in Random Elastic Media
Materials characterized by spatially homogeneous elastic moduli undergo
affine distortions when subjected to external stress at their boundaries, i.e.,
their displacements \uv (\xv) from a uniform reference state grow linearly
with position \xv, and their strains are spatially constant. Many materials,
including all macroscopically isotropic amorphous ones, have elastic moduli
that vary randomly with position, and they necessarily undergo nonaffine
distortions in response to external stress. We study general aspects of
nonaffine response and correlation using analytic calculations and numerical
simulations. We define nonaffine displacements \uv' (\xv) as the difference
between \uv (\xv) and affine displacements, and we investigate the
nonaffinity correlation function
and related functions. We introduce four model random systems with random
elastic moduli induced by locally random spring constants, by random
coordination number, by random stress, or by any combination of these. We show
analytically and numerically that scales as A |\xv|^{-(d-2)}
where the amplitude is proportional to the variance of local elastic moduli
regardless of the origin of their randomness. We show that the driving force
for nonaffine displacements is a spatial derivative of the random elastic
constant tensor times the constant affine strain. Random stress by itself does
not drive nonaffine response, though the randomness in elastic moduli it may
generate does. We study models with both short and long-range correlations in
random elastic moduli.Comment: 22 Pages, 18 figures, RevTeX
Diffusion and binding of finite-size particles in confined geometries
Describing the diffusion of particles through crowded, confined environments
with which they can interact is of considerable biological and technological
interest. Under conditions where the confinement dimensions become comparable
to the particle dimensions, steric interactions between particles, as well as
particle-wall interactions, will play a crucial role in determining transport
properties. To elucidate the effects of these interactions on particle
transport, we consider the diffusion and binding of finite-size particles
within a channel whose diameter is comparable to the size of the particles.
Using a simple lattice model of this process, we calculate the steady-state
current and density profiles of both bound and free particles in the channel.
We show that the system can exhibit qualitatively different behavior depending
on the ratio of the channel width to the particle size. We also perform
simulations of this system, and find excellent agreement with our analytic
results.Comment: 11 pages, 5 figures, Phys. Rev. E (accepted
Unfolding cross-linkers as rheology regulators in F-actin networks
We report on the nonlinear mechanical properties of a statistically
homogeneous, isotropic semiflexible network cross-linked by polymers containing
numerous small unfolding domains, such as the ubiquitous F-actin cross-linker
Filamin.
We show that the inclusion of such proteins has a dramatic effect on the
large strain behavior of the network. Beyond a strain threshold, which depends
on network density, the unfolding of protein domains leads to bulk shear
softening. Past this critical strain, the network spontaneously organizes
itself so that an appreciable fraction of the Filamin cross-linkers are at the
threshold of domain unfolding. We discuss via a simple mean-field model the
cause of this network organization and suggest that it may be the source of
power-law relaxation observed in in vitro and in intracellular microrheology
experiments. We present data which fully justifies our model for a simplified
network architecture.Comment: 11 pages, 4 figures. to appear in Physical Review
Scaling of the buckling transition of ridges in thin sheets
When a thin elastic sheet crumples, the elastic energy condenses into a
network of folding lines and point vertices. These folds and vertices have
elastic energy densities much greater than the surrounding areas, and most of
the work required to crumple the sheet is consumed in breaking the folding
lines or ``ridges''. To understand crumpling it is then necessary to understand
the strength of ridges. In this work, we consider the buckling of a single
ridge under the action of inward forcing applied at its ends. We demonstrate a
simple scaling relation for the response of the ridge to the force prior to
buckling. We also show that the buckling instability depends only on the ratio
of strain along the ridge to curvature across it. Numerically, we find for a
wide range of boundary conditions that ridges buckle when our forcing has
increased their elastic energy by 20% over their resting state value. We also
observe a correlation between neighbor interactions and the location of initial
buckling. Analytic arguments and numerical simulations are employed to prove
these results. Implications for the strength of ridges as structural elements
are discussed.Comment: 42 pages, latex, doctoral dissertation, to be submitted to Phys Rev
A Geometric Theory of Diblock Copolymer Phases
We analyze the energetics of sphere-like micellar phases in diblock
copolymers in terms of well-studied, geometric quantities for their lattices.
We argue that the A15 lattice with Pm3n symmetry should be favored as the
blocks become more symmetric and corroborate this through a self-consistent
field theory. Because phases with columnar or bicontinuous topologies
intervene, the A15 phase, though metastable, is not an equilibrium phase of
symmetric diblocks. We investigate the phase diagram of branched diblocks and
find thatthe A15 phase is stable.Comment: 4 pages, RevTeX, 3 eps figures include
Anomalous strength of membranes with elastic ridges
We report on a simulational study of the compression and buckling of elastic
ridges formed by joining the boundary of a flat sheet to itself. Such ridges
store energy anomalously: their resting energy scales as the linear size of the
sheet to the 1/3 power. We find that the energy required to buckle such a ridge
is a fixed multiple of the resting energy. Thus thin sheets with elastic ridges
such as crumpled sheets are qualitatively stronger than smoothly bent sheets.Comment: 4 pages, REVTEX, 3 figure
A Gradient-Based Approach for Breast DCE-MRI Analysis
Breast cancer is the main cause of female malignancy worldwide. Effective early detection by imaging studies remains critical to decrease mortality rates, particularly in women at high risk for developing breast cancer. Breast Magnetic Resonance Imaging (MRI) is a common diagnostic tool in the management of breast diseases, especially for high-risk women. However, during this examination, both normal and abnormal breast tissues enhance after contrast material administration. Specifically, the normal breast tissue enhancement is known as background parenchymal enhancement: it may represent breast activity and depends on several factors, varying in degree and distribution in different patients as well as in the same patient over time. While a light degree of normal breast tissue enhancement generally causes no interpretative difficulties, a higher degree may cause difficulty to detect and classify breast lesions at Magnetic Resonance Imaging even for experienced radiologists. In this work, we intend to investigate the exploitation of some statistical measurements to automatically characterize the enhancement trend of the whole breast area in both normal and abnormal tissues independently from the presence of a background parenchymal enhancement thus to provide a diagnostic support tool for radiologists in the MRI analysis
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