5,405 research outputs found
Algorithms for 3D rigidity analysis and a first order percolation transition
A fast computer algorithm, the pebble game, has been used successfully to
study rigidity percolation on 2D elastic networks, as well as on a special
class of 3D networks, the bond-bending networks. Application of the pebble game
approach to general 3D networks has been hindered by the fact that the
underlying mathematical theory is, strictly speaking, invalid in this case. We
construct an approximate pebble game algorithm for general 3D networks, as well
as a slower but exact algorithm, the relaxation algorithm, that we use for
testing the new pebble game. Based on the results of these tests and additional
considerations, we argue that in the particular case of randomly diluted
central-force networks on BCC and FCC lattices, the pebble game is essentially
exact. Using the pebble game, we observe an extremely sharp jump in the largest
rigid cluster size in bond-diluted central-force networks in 3D, with the
percolating cluster appearing and taking up most of the network after a single
bond addition. This strongly suggests a first order rigidity percolation
transition, which is in contrast to the second order transitions found
previously for the 2D central-force and 3D bond-bending networks. While a first
order rigidity transition has been observed for Bethe lattices and networks
with ``chemical order'', this is the first time it has been seen for a regular
randomly diluted network. In the case of site dilution, the transition is also
first order for BCC, but results for FCC suggest a second order transition.
Even in bond-diluted lattices, while the transition appears massively first
order in the order parameter (the percolating cluster size), it is continuous
in the elastic moduli. This, and the apparent non-universality, make this phase
transition highly unusual.Comment: 28 pages, 19 figure
Elastin is Localised to the Interfascicular Matrix of Energy Storing Tendons and Becomes Increasingly Disorganised With Ageing
Tendon is composed of fascicles bound together by the interfascicular matrix (IFM). Energy storing tendons are more elastic and extensible than positional tendons; behaviour provided by specialisation of the IFM to enable repeated interfascicular sliding and recoil. With ageing, the IFM becomes stiffer and less fatigue resistant, potentially explaining why older tendons become more injury-prone. Recent data indicates enrichment of elastin within the IFM, but this has yet to be quantified. We hypothesised that elastin is more prevalent in energy storing than positional tendons, and is mainly localised to the IFM. Further, we hypothesised that elastin becomes disorganised and fragmented, and decreases in amount with ageing, especially in energy storing tendons. Biochemical analyses and immunohistochemical techniques were used to determine elastin content and organisation, in young and old equine energy storing and positional tendons. Supporting the hypothesis, elastin localises to the IFM of energy storing tendons, reducing in quantity and becoming more disorganised with ageing. These changes may contribute to the increased injury risk in aged energy storing tendons. Full understanding of the processes leading to loss of elastin and its disorganisation with ageing may aid in the development of treatments to prevent age related tendinopathy
Rigidity and intermediate phases in glasses driven by speciation
The rigid to floppy transitions and the associated intermediate phase in
glasses are studied in the case where the local structure is not fully
determined from the macroscopic concentration. The approach uses size
increasing cluster approximations and constraint counting algorithms. It is
shown that the location and the width of the intermediate phase and the
corresponding structural, mechanical and energetical properties of the network
depend crucially on the way local structures are selected at a given
concentration. The broadening of the intermediate phase is obtained for
networks combining a large amount of flexible local structural units and a high
rate of medium range order.Comment: 4 pages, 4 figure
Kinetic glass behavior in a diffusive model
Three properties of the Edwards-Anderson model with mobile bonds are
investigated which are characteristic of kinetic glasses. First is two-time
relaxation in aged systems, where a significant difference is observed between
spin and bond autocorrelation functions. The spin subsystem does not show
two-time behavior, and the relaxation is stretched exponential. The bond
subsystem shows two-time behavior, with the first relaxation nearly exponential
and the second similar to the spin one. Second is the two-temperature behavior,
which can be tuned by bond dilution through the full range reported in the
literature. Third is the rigid-to-floppy transition, identified as a function
of bond dilution. Simple Glauber Monte Carlo evolution without extraneous
constraints reproduces the behavior of classical kinetic simulations, with the
bond (spin) degree of freedom corresponding to configurational (orientational)
disorder.Comment: 4 pages, 3 figures, minimal corrections, to appear in Phys. Rev. B
(RC
Floppy modes and the free energy: Rigidity and connectivity percolation on Bethe Lattices
We show that negative of the number of floppy modes behaves as a free energy
for both connectivity and rigidity percolation, and we illustrate this result
using Bethe lattices. The rigidity transition on Bethe lattices is found to be
first order at a bond concentration close to that predicted by Maxwell
constraint counting. We calculate the probability of a bond being on the
infinite cluster and also on the overconstrained part of the infinite cluster,
and show how a specific heat can be defined as the second derivative of the
free energy. We demonstrate that the Bethe lattice solution is equivalent to
that of the random bond model, where points are joined randomly (with equal
probability at all length scales) to have a given coordination, and then
subsequently bonds are randomly removed.Comment: RevTeX 11 pages + epsfig embedded figures. Submitted to Phys. Rev.
Stressed backbone and elasticity of random central-force systems
We use a new algorithm to find the stress-carrying backbone of ``generic''
site-diluted triangular lattices of up to 10^6 sites. Generic lattices can be
made by randomly displacing the sites of a regular lattice. The percolation
threshold is Pc=0.6975 +/- 0.0003, the correlation length exponent \nu =1.16
+/- 0.03 and the fractal dimension of the backbone Db=1.78 +/- 0.02. The number
of ``critical bonds'' (if you remove them rigidity is lost) on the backbone
scales as L^{x}, with x=0.85 +/- 0.05. The Young's modulus is also calculated.Comment: 5 pages, 5 figures, uses epsfi
Sediment Sorting and Rounding in a Basaltic Glacio-Fluvio-Aeolian Environment: hrisjkull Glacier, Iceland
Sediments and sedimentary rocks preserve a rich history of environment and climate. Identifying these signals requires an understanding of the physical and chemical processes that have affected sedimentary deposits [1]. Such processes include sorting and rounding during transport and chemical alteration through weathering and diagenesis. Although these processes have long been studied in quartz-dominated sedimentary systems [2], a lack of studies of basaltic sedimentary systems limits our interpretations of the environment and climate where mafic source rocks dominate, such as on Mars [3,4]. As part of the SAND-E: Semi-Autonomous Navigation for Detrital Environments project [5], which uses robotic operations to examine physical and chemical changes to sediments in basaltic glacio-fluvialaeolian environments, this research studies changes in sorting and rounding of fluvial-aeolian sediments along a glacier-proximal-to-glacier-distal transect in the outwash-plain of the risjkull glacier in SW Iceland (Fig. 1
Gas permeation through a polymer network
We study the diffusion of gas molecules through a two-dimensional network of
polymers with the help of Monte Carlo simulations. The polymers are modeled as
non-interacting random walks on the bonds of a two-dimensional square lattice,
while the gas particles occupy the lattice cells. When a particle attempts to
jump to a nearest-neighbor empty cell, it has to overcome an energy barrier
which is determined by the number of polymer segments on the bond separating
the two cells. We investigate the gas current as a function of the mean
segment density , the polymer length and the probability
for hopping across segments. Whereas decreases monotonically with
for fixed , its behavior for fixed and increasing
depends strongly on . For small, non-zero , appears to increase
slowly with . In contrast, for , it is dominated by the underlying
percolation problem and can be non-monotonic. We provide heuristic arguments to
put these interesting phenomena into context.Comment: Dedicated to Lothar Schaefer on the occasion of his 60th birthday. 11
pages, 3 figure
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