10,254 research outputs found
Jamming Mechanisms and Density Dependence in a Kinetically-Constrained Model
We add relaxation mechanisms that mimic the effect of temperature and
non-equilibrium driving to the recently-proposed spiral model which jams at a
critical density rho_c < 1. This enables us to explore unjamming by temperature
or driving at rho_c < rho < 1. We numerically calculate the relaxation time of
the persistence function and its spatial heterogeneity. We disentangle the
three different relaxation mechanisms responsible for unjamming when varying
density, temperature, and driving strength, respectively. We show that the
spatial scale of dynamic heterogeneity depends on density much more strongly
than on temperature and driving
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
Universal Jamming Phase Diagram in the Hard-Sphere Limit
We present a new formulation of the jamming phase diagram for a class of
glass-forming fluids consisting of spheres interacting via finite-ranged
repulsions at temperature , packing fraction or pressure , and
applied shear stress . We argue that the natural choice of axes for the
phase diagram are the dimensionless quantities ,
, and , where is the temperature, is the
pressure, is the stress, is the sphere diameter,
is the interaction energy scale, and is the sphere mass. We demonstrate
that the phase diagram is universal at low ; at low
pressure, observables such as the relaxation time are insensitive to details of
the interaction potential and collapse onto the values for hard spheres,
provided the observables are non-dimensionalized by the pressure. We determine
the shape of the jamming surface in the jamming phase diagram, organize
previous results in relation to the jamming phase diagram, and discuss the
significance of various limits.Comment: 8 pages, 5 figure
Revealing structure-function relationships in functional flow networks via persistent homology
Complex networks encountered in biology are often characterized by
significant structural diversity. Whether it be differences in the
three-dimensional structure of allosteric proteins, or the variation among the
micro-scale structures of organisms' cerebral vasculature systems, identifying
relationships between structure and function often poses a difficult challenge.
Here we showcase an approach to characterizing structure-function relationships
in complex networks applied in the context of flow networks tuned to perform
specific functions. Using persistent homology, we analyze flow networks tuned
to perform complex multifunctional tasks, answering the question of how local
changes in the network structure coordinate to create functionality at at the
scale of the entire network. We find that the response of such networks encodes
hidden topological features - sectors of uniform pressure - that are not
apparent in the underlying network architectures, Regardless of differences in
local connectivity, these features provide a universal topological description
for all networks that perform these types of functions. We show that these
features correlate strongly with the tuned response, providing a clear
topological relationship between structure and function and structural insight
into the limits of multifunctionality.Comment: 22 pages (double column), 12 figure
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