177 research outputs found
Directed force chain networks and stress response in static granular materials
A theory of stress fields in two-dimensional granular materials based on
directed force chain networks is presented. A general equation for the
densities of force chains in different directions is proposed and a complete
solution is obtained for a special case in which chains lie along a discrete
set of directions. The analysis and results demonstrate the necessity of
including nonlinear terms in the equation. A line of nontrivial fixed point
solutions is shown to govern the properties of large systems. In the vicinity
of a generic fixed point, the response to a localized load shows a crossover
from a single, centered peak at intermediate depths to two propagating peaks at
large depths that broaden diffusively.Comment: 18 pages, 12 figures. Minor corrections to one figur
Local growth of icosahedral quasicrystalline tilings
Icosahedral quasicrystals (IQCs) with extremely high degrees of translational
order have been produced in the laboratory and found in naturally occurring
minerals, yet questions remain about how IQCs form. In particular, the
fundamental question of how locally determined additions to a growing cluster
can lead to the intricate long-range correlations in IQCs remains open. In
answer to this question, we have developed an algorithm that is capable of
producing a perfectly ordered IQC, yet relies exclusively on local rules for
sequential, face-to-face addition of tiles to a cluster. When the algorithm is
seeded with a special type of cluster containing a defect, we find that growth
is forced to infinity with high probability and that the resultant IQC has a
vanishing density of defects. The geometric features underlying this algorithm
can inform analyses of experimental systems and numerical models that generate
highly ordered quasicrystals.Comment: 13 pages, 15 figures, 1 tabl
Hyperuniformity of Quasicrystals
Hyperuniform systems, which include crystals, quasicrystals and special
disordered systems, have attracted considerable recent attention, but rigorous
analyses of the hyperuniformity of quasicrystals have been lacking because the
support of the spectral intensity is dense and discontinuous. We employ the
integrated spectral intensity, , to quantitatively characterize the
hyperuniformity of quasicrystalline point sets generated by projection methods.
The scaling of as tends to zero is computed for one-dimensional
quasicrystals and shown to be consistent with independent calculations of the
variance, , in the number of points contained in an interval of
length . We find that one-dimensional quasicrystals produced by projection
from a two-dimensional lattice onto a line of slope fall into distinct
classes determined by the width of the projection window. For a countable dense
set of widths, ; for all others, . This
distinction suggests that measures of hyperuniformity define new classes of
quasicrystals in higher dimensions as well.Comment: 12 pages, 14 figure
Network growth models and genetic regulatory networks
We study a class of growth algorithms for directed graphs that are candidate
models for the evolution of genetic regulatory networks. The algorithms involve
partial duplication of nodes and their links, together with innovation of new
links, allowing for the possibility that input and output links from a newly
created node may have different probabilities of survival. We find some
counterintuitive trends as parameters are varied, including the broadening of
indegree distribution when the probability for retaining input links is
decreased. We also find that both the scaling of transcription factors with
genome size and the measured degree distributions for genes in yeast can be
reproduced by the growth algorithm if and only if a special seed is used to
initiate the process.Comment: 8 pages with 7 eps figures; uses revtex4. Added references, cleaner
figure
Controlling extended systems with spatially filtered, time-delayed feedback
We investigate a control technique for spatially extended systems combining
spatial filtering with a previously studied form of time-delay feedback. The
scheme is naturally suited to real-time control of optical systems. We apply
the control scheme to a model of a transversely extended semiconductor laser in
which a desirable, coherent traveling wave state exists, but is a member of a
nowhere stable family. Our scheme stabilizes this state, and directs the system
towards it from realistic, distant and noisy initial conditions. As confirmed
by numerical simulation, a linear stability analysis about the controlled state
accurately predicts when the scheme is successful, and illustrates some key
features of the control including the individual merit of, and interplay
between, the spatial and temporal degrees of freedom in the control.Comment: 9 pages REVTeX including 7 PostScript figures. To appear in Physical
Review
Force distribution in a scalar model for non-cohesive granular material
We study a scalar lattice model for inter-grain forces in static,
non-cohesive, granular materials, obtaining two primary results. (i) The
applied stress as a function of overall strain shows a power law dependence
with a nontrivial exponent, which moreover varies with system geometry. (ii)
Probability distributions for forces on individual grains appear Gaussian at
all stages of compression, showing no evidence of exponential tails. With
regard to both results, we identify correlations responsible for deviations
from previously suggested theories.Comment: 16 pages, 9 figures, Submitted to PR
Jamming Transition In Non-Spherical Particle Systems: Pentagons Versus Disks
We investigate the jamming transition in a quasi-2D granular material composed of regular pentagons or disks subjected to quasistatic uniaxial compression. We report six major findings based on experiments with monodisperse photoelastic particles with static friction coefficient μ≈1. (1) For both pentagons and disks, the onset of rigidity occurs when the average coordination number of non-rattlers, Znr, reaches 3, and the dependence of Znr on the packing fraction ϕ changes again when Znr reaches 4. (2) Though the packing fractions ϕc1 and ϕc2 at these transitions differ from run to run, for both shapes the data from all runs with different initial configurations collapses when plotted as a function of the non-rattler fraction. (3) The averaged values of ϕc1 and ϕc2 for pentagons are around 1% smaller than those for disks. (4) Both jammed pentagons and disks show Gamma distribution of the Voronoi cell area with same parameters. (5) The jammed pentagons have similar translational order for particle centers but slightly less orientational order for contacting pairs compared to jammed disks. (6) For jammed pentagons, the angle between edges at a face-to-vertex contact point shows a uniform distribution and the size of a cluster connected by face-to-face contacts shows a power-law distribution
Jamming Transition In Non-Spherical Particle Systems: Pentagons Versus Disks
We investigate the jamming transition in a quasi-2D granular material composed of regular pentagons or disks subjected to quasistatic uniaxial compression. We report six major findings based on experiments with monodisperse photoelastic particles with static friction coefficient μ≈1. (1) For both pentagons and disks, the onset of rigidity occurs when the average coordination number of non-rattlers, Znr, reaches 3, and the dependence of Znr on the packing fraction ϕ changes again when Znr reaches 4. (2) Though the packing fractions ϕc1 and ϕc2 at these transitions differ from run to run, for both shapes the data from all runs with different initial configurations collapses when plotted as a function of the non-rattler fraction. (3) The averaged values of ϕc1 and ϕc2 for pentagons are around 1% smaller than those for disks. (4) Both jammed pentagons and disks show Gamma distribution of the Voronoi cell area with same parameters. (5) The jammed pentagons have similar translational order for particle centers but slightly less orientational order for contacting pairs compared to jammed disks. (6) For jammed pentagons, the angle between edges at a face-to-vertex contact point shows a uniform distribution and the size of a cluster connected by face-to-face contacts shows a power-law distribution
Growing Perfect Decagonal Quasicrystals by Local Rules
A local growth algorithm for a decagonal quasicrystal is presented. We show
that a perfect Penrose tiling (PPT) layer can be grown on a decapod tiling
layer by a three dimensional (3D) local rule growth. Once a PPT layer begins to
form on the upper layer, successive 2D PPT layers can be added on top resulting
in a perfect decagonal quasicrystalline structure in bulk with a point defect
only on the bottom surface layer. Our growth rule shows that an ideal
quasicrystal structure can be constructed by a local growth algorithm in 3D,
contrary to the necessity of non-local information for a 2D PPT growth.Comment: 4pages, 2figure
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