Self-organized criticality in the intermediate phase of rigidity percolation

Experimental results for covalent glasses have highlighted the existence of a new self-organized phase due to the tendency of glass networks to minimize internal stress. Recently, we have shown that an equilibrated self-organized two-dimensional lattice-based model also possesses an intermediate phase in which a percolating rigid cluster exists with a probability between zero and one, depending on the average coordination of the network. In this paper, we study the properties of this intermediate phase in more detail. We find that microscopic perturbations, such as the addition or removal of a single bond, can affect the rigidity of macroscopic regions of the network, in particular, creating or destroying percolation. This, together with a power-law distribution of rigid cluster sizes, suggests that the system is maintained in a critical state on the rigid/floppy boundary throughout the intermediate phase, a behavior similar to self-organized criticality, but, remarkably, in a thermodynamically equilibrated state. The distinction between percolating and non-percolating networks appears physically meaningless, even though the percolating cluster, when it exists, takes up a finite fraction of the network. We point out both similarities and differences between the intermediate phase and the critical point of ordinary percolation models without self-organization. Our results are consistent with an interpretation of recent experiments on the pressure dependence of Raman frequencies in chalcogenide glasses in terms of network homogeneity.Comment: 20 pages, 18 figure

Self-organization with equilibration: a model for the intermediate phase in rigidity percolation

Recent experimental results for covalent glasses suggest the existence of an intermediate phase attributed to the self-organization of the glass network resulting from the tendency to minimize its internal stress. However, the exact nature of this experimentally measured phase remains unclear. We modify a previously proposed model of self-organization by generating a uniform sampling of stress-free networks. In our model, studied on a diluted triangular lattice, an unusual intermediate phase appears, in which both rigid and floppy networks have a chance to occur, a result also observed in a related model on a Bethe lattice by Barre et al. [Phys. Rev. Lett. 94, 208701 (2005)]. Our results for the bond-configurational entropy of self-organized networks, which turns out to be only about 2% lower than that of random networks, suggest that a self-organized intermediate phase could be common in systems near the rigidity percolation threshold.Comment: 9 pages, 6 figure

Time Domain Simulations of Arm Locking in LISA

Arm locking is a technique that has been proposed for reducing laser frequency fluctuations in the Laser Interferometer Space Antenna (LISA), a gravitational-wave observatory sensitive in the milliHertz frequency band. Arm locking takes advantage of the geometric stability of the triangular constellation of three spacecraft that comprise LISA to provide a frequency reference with a stability in the LISA measurement band that exceeds that available from a standard reference such as an optical cavity or molecular absorption line. We have implemented a time-domain simulation of arm locking including the expected limiting noise sources (shot noise, clock noise, spacecraft jitter noise, and residual laser frequency noise). The effect of imperfect a priori knowledge of the LISA heterodyne frequencies and the associated 'pulling' of an arm locked laser is included. We find that our implementation meets requirements both on the noise and dynamic range of the laser frequency.Comment: Revised to address reviewer comments. Accepted by Phys. Rev.

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

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.

Energy landscape and rigidity

The effects of floppy modes in the thermodynamical properties of a system are studied. From thermodynamical arguments, we deduce that floppy modes are not at zero frequency and thus a modified Debye model is used to take into account this effect. The model predicts a deviation from the Debye law at low temperatures. Then, the connection between the topography of the energy landscape, the topology of the phase space and the rigidity of a glass is explored. As a result, we relate the number of constraints and floppy modes with the statistics of the landscape. We apply these ideas to a simple model for which we provide an approximate expression for the number of energy basins as a function of the rigidity. This allows to understand certains features of the glass transition, like the jump in the specific heat or the reversible window observed in chalcogenide glasses.Comment: 1 text+3 eps figure

Self-Organization and the Physics of Glassy Networks

Network glasses are the physical prototype for many self-organized systems, ranging from proteins to computer science. Conventional theories of gases, liquids, and crystals do not account for the strongly material-selective character of the glass-forming tendency, the phase diagrams of glasses, or their optimizable properties. A new topological theory, only 25 years old, has succeeded where conventional theories have failed. It shows that (probably all slowly quenched) glasses, including network glasses, are the result of the combined effects of a few simple mechanisms. These glass-forming mechanisms are topological in nature, and have already been identified for several important glasses, including chalcogenide alloys, silicates (window glass, computer chips), and proteins.Comment: One PDF file contains 10 figures and tex

Effect of fatigue loading on structure and functional behaviour of fascicles from energy-storing tendons

Tendons can broadly be categorized according to their function: those that act purely to position the limb and those that have an additional function as energy stores. Energy-storing tendons undergo many cycles of large deformations during locomotion, and so must be able to extend and recoil efficiently, rapidly and repeatedly. Our previous work has shown rotation in response to applied strain in fascicles from energy-storing tendons, indicating the presence of helical substructures which may provide greater elasticity and recovery. In the current study, we assessed how preconditioning and fatigue loading affect the ability of fascicles from the energy-storing equine superficial digital flexor tendon to extend and recoil. We hypothesized that preconditioned samples would exhibit changes in microstructural strain response, but would retain their ability to recover. We further hypothesized that fatigue loading would result in sample damage, causing further alterations in extension mechanisms and a significant reduction in sample recovery. The results broadly support these hypotheses: preconditioned samples showed some alterations in microstructural strain response, but were able to recover following the removal of load. However, fatigue loaded samples showed visual evidence of damage and exhibited further alterations in extension mechanisms, characterized by decreased rotation in response to applied strain. This was accompanied by increased hysteresis and decreased recovery. These results suggest that fatigue loading results in a compromised helix substructure, reducing the ability of energy-storing tendons to recoil. A decreased ability to recoil may lead to an impaired response to further loading, potentially increasing the likelihood of injury