17,978 research outputs found
Multicellular rosettes drive fluid-solid transition in epithelial tissues
Models for confluent biological tissues often describe the network formed by
cells as a triple-junction network, similar to foams. However, higher order
vertices or multicellular rosettes are prevalent in developmental and {\it in
vitro} processes and have been recognized as crucial in many important aspects
of morphogenesis, disease, and physiology. In this work, we study the influence
of rosettes on the mechanics of a confluent tissue. We find that the existence
of rosettes in a tissue can greatly influence its rigidity. Using a generalized
vertex model and effective medium theory we find a fluid-to-solid transition
driven by rosette density and intracellular tensions. This transition exhibits
several hallmarks of a second-order phase transition such as a growing
correlation length and a universal critical scaling in the vicinity a critical
point. Further, we elucidate the nature of rigidity transitions in dense
biological tissues and other cellular structures using a generalized Maxwell
constraint counting approach. This answers a long-standing puzzle of the origin
of solidity in these systems.Comment: 11 pages, 5 figures + 8 pages, 7 figures in Appendix. To be appear in
PR
Adaptive Elastic Networks as models of supercooled liquids
The thermodynamics and dynamics of supercooled liquids correlate with their
elasticity. In particular for covalent networks, the jump of specific heat is
small and the liquid is {\it strong} near the threshold valence where the
network acquires rigidity. By contrast, the jump of specific heat and the
fragility are large away from this threshold valence. In a previous work [Proc.
Natl. Acad. Sci. U.S.A., 110, 6307 (2013)], we could explain these behaviors by
introducing a model of supercooled liquids in which local rearrangements
interact via elasticity. However, in that model the disorder characterizing
elasticity was frozen, whereas it is itself a dynamic variable in supercooled
liquids. Here we study numerically and theoretically adaptive elastic network
models where polydisperse springs can move on a lattice, thus allowing for the
geometry of the elastic network to fluctuate and evolve with temperature. We
show numerically that our previous results on the relationship between
structure and thermodynamics hold in these models. We introduce an
approximation where redundant constraints (highly coordinated regions where the
frustration is large) are treated as an ideal gas, leading to analytical
predictions that are accurate in the range of parameters relevant for real
materials. Overall, these results lead to a description of supercooled liquids,
in which the distance to the rigidity transition controls the number of
directions in phase space that cost energy and the specific heat.Comment: 12 pages, 14 figure
A model for the erosion onset of a granular bed sheared by a viscous fluid
We study theoretically the erosion threshold of a granular bed forced by a
viscous fluid. We first introduce a novel model of interacting particles driven
on a rough substrate. It predicts a continuous transition at some threshold
forcing , beyond which the particle current grows linearly , in agreement with experiments. The stationary state is
reached after a transient time which diverges near the
transition as with .
The model also makes quantitative testable predictions for the drainage
pattern: the distribution of local current is found to be extremely
broad with , spatial correlations for the current are
negligible in the direction transverse to forcing, but long-range parallel to
it. We explain some of these features using a scaling argument and a mean-field
approximation that builds an analogy with -models. We discuss the
relationship between our erosion model and models for the depinning transition
of vortex lattices in dirty superconductors, where our results may also apply.Comment: 5 pages, 6 figure
Hessian spectrum at the global minimum of high-dimensional random landscapes
Using the replica method we calculate the mean spectral density of the
Hessian matrix at the global minimum of a random dimensional
isotropic, translationally invariant Gaussian random landscape confined by a
parabolic potential with fixed curvature . Simple landscapes with
generically a single minimum are typical for , and we show that
the Hessian at the global minimum is always {\it gapped}, with the low spectral
edge being strictly positive. When approaching from above the transitional
point separating simple landscapes from 'glassy' ones, with
exponentially abundant minima, the spectral gap vanishes as .
For the Hessian spectrum is qualitatively different for 'moderately
complex' and 'genuinely complex' landscapes. The former are typical for
short-range correlated random potentials and correspond to 1-step
replica-symmetry breaking mechanism. Their Hessian spectra turn out to be again
gapped, with the gap vanishing on approaching from below with a larger
critical exponent, as . At the same time in the 'most complex'
landscapes with long-ranged power-law correlations the replica symmetry is
completely broken. We show that in that case the Hessian remains gapless for
all values of , indicating the presence of 'marginally stable'
spatial directions. Finally, the potentials with {\it logarithmic} correlations
share both 1RSB nature and gapless spectrum. The spectral density of the
Hessian always takes the semi-circular form, up to a shift and an amplitude
that we explicitly calculate.Comment: 28 pages, 1 figure; a brief summary of main results is added to the
introductio
- …