Hierarchical models of rigidity percolation

We introduce models of generic rigidity percolation in two dimensions on hierarchical networks, and solve them exactly by means of a renormalization transformation. We then study how the possibility for the network to self organize in order to avoid stressed bonds may change the phase diagram. In contrast to what happens on random graphs and in some recent numerical studies at zero temperature, we do not find a true intermediate phase separating the usual rigid and floppy ones.Comment: 20 pages, 8 figures. Figures improved, references added, small modifications. Accepted in Phys. Rev.

Bouncing off the walls : the influence of gas-kinetic and van der Waals effects in drop impact

A model is developed for liquid drop impact on a solid surface that captures the thin film gas flow beneath the drop, even when the film’s thickness is below the mean free path in the gas so that gas kinetic effects (GKE) are important. Simulation results agree with experiments, with the impact speed threshold between bouncing and wetting reproduced to within 5 least 50 mapped and provides experimentally verifiable predictions. There are two principal modes of contact leading to wetting and both are associated with a van der Waals driven instability of the film

Activated sampling in complex materials at finite temperature: the properly-obeying-probability activation-relaxation technique

While the dynamics of many complex systems is dominated by activated events, there are very few simulation methods that take advantage of this fact. Most of these procedures are restricted to relatively simple systems or, as with the activation-relaxation technique (ART), sample the conformation space efficiently at the cost of a correct thermodynamical description. We present here an extension of ART, the properly-obeying-probability ART (POP-ART), that obeys detailed balance and samples correctly the thermodynamic ensemble. Testing POP-ART on two model systems, a vacancy and an interstitial in crystalline silicon, we show that this method recovers the proper thermodynamical weights associated with the various accessible states and is significantly faster than MD in the diffusion of a vacancy below 700 K.Comment: 10 pages, 3 figure

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

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