Onset Temperature of Slow Dynamics in Glass Forming Liquids

The behaviour of a model glass forming liquid is analyzed for a range of densities, with a focus on the temperature interval where the liquid begins to display non-Arrhenius temperature dependence of relaxation times. Analyzing the dynamics along with properties of local potential energy minima sampled by the liquid, a crossover or onset temperature $T_s$ is identified below which the liquid manifests {\it slow dynamics}, and a change in the character of typical local potential energy minima.Comment: 16 pages, 5 figures, to appear in PhysChemCom

Consensus using Asynchronous Failure Detectors

The FLP result shows that crash-tolerant consensus is impossible to solve in asynchronous systems, and several solutions have been proposed for crash-tolerant consensus under alternative (stronger) models. One popular approach is to augment the asynchronous system with appropriate failure detectors, which provide (potentially unreliable) information about process crashes in the system, to circumvent the FLP impossibility. In this paper, we demonstrate the exact mechanism by which (sufficiently powerful) asynchronous failure detectors enable solving crash-tolerant consensus. Our approach, which borrows arguments from the FLP impossibility proof and the famous result from CHT, which shows that $\Omega$ is a weakest failure detector to solve consensus, also yields a natural proof to $\Omega$ as a weakest asynchronous failure detector to solve consensus. The use of I/O automata theory in our approach enables us to model execution in a more detailed fashion than CHT and also addresses the latent assumptions and assertions in the original result in CHT

Free volume distribution of nearly jammed hard sphere packings

We calculate the free volume distributions of nearly jammed packings of monodisperse and bidisperse hard sphere configurations. These distributions differ qualitatively from those of the fluid, displaying a power law tail at large free volumes, which constitutes a distinct signature of nearly jammed configurations, persisting for moderate degrees of decompression. We reproduce and explain the observed distribution by considering the pair correlation function within the first coordination shell for jammed hard sphere configurations. We analyze features of the equation of state near jamming, and discuss the significance of observed asphericities of the free volumes to the equation of state.Comment: J Chem Phys 2014 (in press

Short-time β\beta-relaxation in glass-forming liquids is cooperative in nature

Temporal relaxation of density fluctuations in supercooled liquids near the glass transition occurs in multiple steps. The short-time $\beta$-relaxation is generally attributed to spatially local processes involving the rattling motion of a particle in the transient cage formed by its neighbors. Using molecular dynamics simulations for three model glass-forming liquids, we show that the $\beta$-relaxation is actually cooperative in nature. Using finite-size scaling analysis, we extract a growing length-scale associated with $\beta$-relaxation from the observed dependence of the $\beta$-relaxation time on the system size. Remarkably, the temperature dependence of this length scale is found to be the same as that of the length scale that describes the spatial heterogeneity of local dynamics in the long-time $\alpha$-relaxation regime. These results show that the conventional interpretation of $\beta$-relaxation as a local process is too simplified and provide a clear connection between short-time dynamics and long-time structural relaxation in glass-forming liquids

Growing length and time scales in glass forming liquids

We study the growing time scales and length scales associated with dynamical slow down for a realistic glass former, using computer simulations. We perform finite size scaling to evaluate a length scale associated with dynamical heterogeneity which grows as temperature decreases. However, relaxation times which also grow with decreasing temperature, do not show the same kind of scaling behavior with system size as the dynamical heterogeneity, indicating that relaxation times are not solely determined by the length scale of dynamical heterogeneity. We show that relaxation times are instead determined, for all studied system sizes and temperatures, by configurational entropy, in accordance with the Adam-Gibbs relation, but in disagreement with theoretical expectations based on spin-glass models that configurational entropy is not relevant at temperatures substantially above the critical temperature of mode coupling theory. The temperature dependence of the heterogeneity length scale shows significant deviations from theoretical expectations, and the length scale one may extract from the system size dependence of the configurational entropy has much weaker temperature dependence compared to the heterogeneity length scale at all studied temperatures. Our results provide new insights into the dynamics of glass-forming liquids and pose serious challenges to existing theoretical descriptions

Oscillatory athermal quasi-static deformation of a model glass

We report computer simulations of oscillatory athermal quasi-static shear deformation of dense amorphous samples of a three dimensional model glass former. A dynamical transition is observed as the amplitude of the deformation is varied: for large values of the amplitude the system exhibits diffusive behavior and loss of memory of the initial conditions, whereas localization is observed for small amplitudes. Our results suggest that the same kind of transition found in driven colloidal systems is present in the case of amorphous solids (e.g. metallic glasses). The onset of the transition is shown to be related to the onset of energy dissipation. Shear banding is observed for large system sizes, without, however, affecting qualitative aspects of the transition

Density-temperature scaling of the fragility in a model glass-former

Dynamical quantities such as the diffusion coefficient and relaxation times for some glass-formers may depend on density and temperature through a specific combination, rather than independently, allowing the representation of data over ranges of density and temperature as a function of a single scaling variable. Such a scaling, referred to as density - temperature (DT) scaling, is exact for liquids with inverse power law (IPL) interactions but has also been found to be approximately valid in many non-IPL liquids. We have analyzed the consequences of DT scaling on the density dependence of the fragility in a model glass-former. We find the density dependence of kinetic fragility to be weak, and show that it can be understood in terms of DT scaling and deviations of DT scaling at low densities. We also show that the Adam-Gibbs relation exhibits DT scaling and the scaling exponent computed from the density dependence of the activation free energy in the Adam-Gibbs relation, is consistent with the exponent values obtained by other means

Breakdown of the Stokes-Einstein relation in two, three and four dimensions

The breakdown of the Stokes-Einstein (SE) relation between diffusivity and viscosity at low temperatures is considered to be one of the hallmarks of glassy dynamics in liquids. Theoretical analyses relate this breakdown with the presence of heterogeneous dynamics, and by extension, with the fragility of glass formers. We perform an investigation of the breakdown of the SE relation in 2, 3 and 4 dimensions, in order to understand these interrelations. Results from simulations of model glass formers show that the degree of the breakdown of the SE relation decreases with increasing spatial dimensionality. The breakdown itself can be rationalized via the difference between the activation free energies for diffusivity and viscosity (or relaxation times) in the Adam-Gibbs relation in three and four dimensions. The behavior in two dimensions also can be understood in terms of a generalized Adam-Gibbs relation that is observed in previous work. We calculate various measures of heterogeneity of dynamics and find that the degree of the SE breakdown and measures of heterogeneity of dynamics are generally well correlated but with some exceptions. The two dimensional systems we study show deviations from the pattern of behavior of the three and four dimensional systems both at high and low temperatures. The fragility of the studied liquids is found to increase with spatial dimensionality, contrary to the expectation based on the association of fragility with heterogeneous dynamics