Mykyta V. Chubynsky

Diffusing diffusivity: a model for anomalous, yet Brownian, diffusion.

Wang et al. [Proc. Natl. Acad. Sci. U.S.A. 106, 15160 (2009)] have found that in several systems the linear time dependence of the mean-square displacement (MSD) of diffusing colloidal particles, typical of normal diffusion, is accompanied by a non-Gaussian displacement distribution G(x,t), with roughly exponential tails at short times, a situation they termed “anomalous yet Brownian” diffusion. The diversity of systems in which this is observed calls for a generic model. We present such a model where there is diffusivity memory but no direction memory in the particle trajectory, and we show that it leads to both a linear MSD and a non-Gaussian G(x,t) at short times. In our model, the diffusivity is undergoing a (perhaps biased) random walk, hence the expression “diffusing diffusivity”. G(x,t) is predicted to be exactly exponential at short times if the distribution of diffusivities is itself exponential, but an exponential remains a good fit for a variety of diffusivity distributions. Moreover, our generic model can be modified to produce subdiffusion.

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 modified 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 Barré 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.

Self-organized criticality in the intermediate phase of rigidity percolation.

Experimental results for covalent glasses have highlighted the existence of a 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 nonpercolating 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.

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 molecular dynamics in the simulations of a vacancy below 700 K.