465 research outputs found
A geometrically controlled rigidity transition in a model for confluent 3D tissues
The origin of rigidity in disordered materials is an outstanding open problem
in statistical physics. Previously, a class of 2D cellular models has been
shown to undergo a rigidity transition controlled by a mechanical parameter
that specifies cell shapes. Here, we generalize this model to 3D and find a
rigidity transition that is similarly controlled by the preferred surface area:
the model is solid-like below a dimensionless surface area of
, and fluid-like above this value. We demonstrate that,
unlike jamming in soft spheres, residual stresses are necessary to create
rigidity. These stresses occur precisely when cells are unable to obtain their
desired geometry, and we conjecture that there is a well-defined minimal
surface area possible for disordered cellular structures. We show that the
behavior of this minimal surface induces a linear scaling of the shear modulus
with the control parameter at the transition point, which is different from the
scaling observed in particulate matter. The existence of such a minimal surface
may be relevant for biological tissues and foams, and helps explain why cell
shapes are a good structural order parameter for rigidity transitions in
biological tissues.Comment: 6 pages main text + 13 pages appendix, 3 main text figures + 6
appendix figure
A random matrix definition of the boson peak
The density of vibrational states for glasses and jammed solids exhibits
universal features, including an excess of modes above the Debye prediction
known as the boson peak located at a frequency . We show that the
eigenvector statistics for boson peak modes are universal, and develop a new
definition of the boson peak based on this universality that displays the
previously observed characteristic scaling . We
identify a large new class of random matrices that obey a generalized global
tranlational invariance constraint and demonstrate that members of this class
also have a boson peak with precisely the same universal eigenvector
statistics. We denote this class as boson peak random matrices, and conjecture
it comprises a new universality class. We characterize the eigenvector
statistics as a function of coordination number, and find that one member of
this new class reproduces the scaling of with coordination number
that is observed near the jamming transition.Comment: 6 pages, 4 figures, Supplementary Figures available at
https://mmanning.expressions.syr.edu/epl2015
Motility-driven glass and jamming transitions in biological tissues
Cell motion inside dense tissues governs many biological processes, including
embryonic development and cancer metastasis, and recent experiments suggest
that these tissues exhibit collective glassy behavior. To make quantitative
predictions about glass transitions in tissues, we study a self-propelled
Voronoi (SPV) model that simultaneously captures polarized cell motility and
multi-body cell-cell interactions in a confluent tissue, where there are no
gaps between cells. We demonstrate that the model exhibits a jamming transition
from a solid-like state to a fluid-like state that is controlled by three
parameters: the single-cell motile speed, the persistence time of single-cell
tracks, and a target shape index that characterizes the competition between
cell-cell adhesion and cortical tension. In contrast to traditional particulate
glasses, we are able to identify an experimentally accessible structural order
parameter that specifies the entire jamming surface as a function of model
parameters. We demonstrate that a continuum Soft Glassy Rheology model
precisely captures this transition in the limit of small persistence times, and
explain how it fails in the limit of large persistence times. These results
provide a framework for understanding the collective solid-to-liquid
transitions that have been observed in embryonic development and cancer
progression, which may be associated with Epithelial-to-Mesenchymal transition
in these tissues.Comment: accepted for publication in Physical Review X, 201
- β¦