Simple Model for Dynamic Heterogeneity in Glass-Forming Liquids.

Liquids near the glass transition exhibit dynamical heterogeneity, i.e., local relaxation rates fluctuate strongly over space and time. Here, we introduce a simple continuum model that allows for quantitative predictions for the correlators describing these fluctuations. We find remarkable agreement of the model predictions for the dynamic susceptibility χ_{4}(t) with numerical results for a binary hard-sphere liquid and for a Kob-Andersen Lennard-Jones mixture. Under this model, the lifetime τ_{ex} of the heterogeneities has little effect on the position t=t_{4}∼τ_{α} of the peak of χ_{4}(t), but it controls the decay of χ_{4}(t) after the peak, and we show how to estimate it from this decay.

Single-particle fluctuations dominate the long-time dynamic susceptibility in glass-forming liquids.

Liquids near the glass transition exhibit dynamical heterogeneity, i.e., correlated regions in the liquid relax at either a much faster rate or a much slower rate than the average. This collective phenomenon has been characterized by measurements of a dynamic susceptibility χ_{4}(t), which is sometimes interpreted in terms of the size of those relaxing regions and the intensity of the fluctuations. We show that the results of those measurements can be affected not only by the collective fluctuations in the relaxation rate, but also by density fluctuations in the initial state and by single-particle fluctuations. We also show that at very long times the average overlap C(t) probing the similarity between an initial and a final state separated by a time interval t decays as a power law C(t)∼t^{-d/2}. This is much slower than the stretched exponential behavior C(t)∼e^{-(t/τ)^{ß}} previously observed at times within one or two orders of magnitude of the α-relaxation time τ_{α}. We find that for times longer than 10-100τ_{α}, the dynamic susceptibility χ_{4}(t) is dominated by single-particle fluctuations, and that χ_{4}(t)≈C(t)∼t^{-d/2}. Finally, we introduce a method to extract the collective relaxation contribution to the dynamic susceptibility χ_{4}(t) by subtracting the effects of single-particle fluctuations and initial state density fluctuations. We apply this method to numerical simulations of two glass-forming models: a binary hard sphere system and a Kob-Andersen Lennard-Jones system. This allows us to extend the analysis of numerical data to timescales much longer than previously possible, and opens the door for further future progress in the study of dynamic heterogeneities, including the determination of the exchange time.

Cellular reprogramming dynamics follow a simple 1D reaction coordinate.

Cellular reprogramming, the conversion of one cell type to another, induces global changes in gene expression involving thousands of genes, and understanding how cells globally alter their gene expression profile during reprogramming is an ongoing problem. Here we reanalyze time-course data on cellular reprogramming from differentiated cell types to induced pluripotent stem cells (iPSCs) and show that gene expression dynamics during reprogramming follow a simple 1D reaction coordinate. This reaction coordinate is independent of both the time it takes to reach the iPSC state as well as the details of the experimental protocol used. Using Monte-Carlo simulations, we show that such a reaction coordinate emerges from epigenetic landscape models where cellular reprogramming is viewed as a 'barrier-crossing' process between cell fates. Overall, our analysis and model suggest that gene expression dynamics during reprogramming follow a canonical trajectory consistent with the idea of an 'optimal path' in gene expression space for reprogramming.

Universal scaling in the aging of the strong glass former SiO2.

We show that the aging dynamics of a strong glass former displays a strikingly simple scaling behavior, connecting the average dynamics with its fluctuations, namely, the dynamical heterogeneities. We perform molecular dynamics simulations of SiO2 with van Beest-Kramer-van Santen interactions, quenching the system from high to low temperature, and study the evolution of the system as a function of the waiting time tw measured from the instant of the quench. We find that both the aging behavior of the dynamic susceptibility χ4 and the aging behavior of the probability distribution P(fs,r) of the local incoherent intermediate scattering function fs,r can be described by simple scaling forms in terms of the global incoherent intermediate scattering function C. The scaling forms are the same that have been found to describe the aging of several fragile glass formers and that, in the case of P(fs,r), have been also predicted theoretically. A thorough study of the length scales involved highlights the importance of intermediate length scales. We also analyze directly the scaling dependence on particle type and on wavevector q and find that both the average and the fluctuations of the slow aging dynamics are controlled by a unique aging clock, which is not only independent of the wavevector q, but is also the same for O and Si atoms.

Slow and long-ranged dynamical heterogeneities in dissipative fluids.

A two-dimensional bidisperse granular fluid is shown to exhibit pronounced long-ranged dynamical heterogeneities as dynamical arrest is approached. Here we focus on the most direct approach to study these heterogeneities: we identify clusters of slow particles and determine their size, Nc, and their radius of gyration, RG. We show that , providing direct evidence that the most immobile particles arrange in fractal objects with a fractal dimension, df, that is observed to increase with packing fraction ϕ. The cluster size distribution obeys scaling, approaching an algebraic decay in the limit of structural arrest, i.e., ϕ→ϕc. Alternatively, dynamical heterogeneities are analyzed via the four-point structure factor S4(q,t) and the dynamical susceptibility χ4(t). S4(q,t) is shown to obey scaling in the full range of packing fractions, 0.6 ≤ϕ≤ 0.805, and to become increasingly long-ranged as ϕ→ϕc. Finite size scaling of χ4(t) provides a consistency check for the previously analyzed divergences of χ4(t) ∝ (ϕ-ϕc)(-γχ) and the correlation length ξ∝ (ϕ-ϕc)(-γξ). We check the robustness of our results with respect to our definition of mobility. The divergences and the scaling for ϕ→ϕc suggest a non-equilibrium glass transition which seems qualitatively independent of the coefficient of restitution.

Strong dynamical heterogeneity and universal scaling in driven granular fluids.

Large-scale simulations of two-dimensional bidisperse granular fluids allow us to determine spatial correlations of slow particles via the four-point structure factor S(4)(q,t). Both cases, elastic (ϵ=1) and inelastic (ϵ<1) collisions, are studied. As the fluid approaches structural arrest, i.e., for packing fractions in the range 0.6≤ϕ≤0.805, scaling is shown to hold: S(4)(q,t)/χ(4)(t)=s(qξ(t)). Both the dynamic susceptibility χ(4)(τ(α)) and the dynamic correlation length ξ(τ(α)) evaluated at the α relaxation time τ(α) can be fitted to a power law divergence at a critical packing fraction. The measured ξ(τ(α)) widely exceeds the largest one previously observed for three-dimensional (3d) hard sphere fluids. The number of particles in a slow cluster and the correlation length are related by a robust power law, χ(4)(τ(α))≈ξ(d-p)(τ(α)), with an exponent d-p≈1.6. This scaling is remarkably independent of ϵ, even though the strength of the dynamical heterogeneity at constant volume fraction depends strongly on ϵ.

Fluctuations in the time variable and dynamical heterogeneity in glass-forming systems.

We test a hypothesis for the origin of dynamical heterogeneity in slowly relaxing systems, namely that it emerges from soft (Goldstone) modes associated with a broken continuous symmetry under time reparametrizations. We do this by constructing coarse grained observables and decomposing the fluctuations of these observables into transverse components, which are associated with the postulated time-fluctuation soft modes, and a longitudinal component, which represents the rest of the fluctuations. Our test is performed on data obtained in simulations of four models of structural glasses. As the hypothesis predicts, we find that the time reparametrization fluctuations become increasingly dominant as temperature is lowered and timescales are increased. More specifically, the ratio between the strengths of the transverse fluctuations and the longitudinal fluctuations grows as a function of the dynamical susceptibility, χ(4), which represents the strength of the dynamical heterogeneity; and the correlation volumes for the transverse fluctuations are approximately proportional to those for the dynamical heterogeneity, while the correlation volumes for the longitudinal fluctuations remain small and approximately constant.

Mapping dynamical heterogeneity in structural glasses to correlated fluctuations of the time variables.

Dynamical heterogeneities--strong fluctuations near the glass transition--are believed to be crucial to explain much of the glass transition phenomenology. One hypothesis for their origin is that they emerge from soft (Goldstone) modes associated with a broken continuous symmetry under time reparametrizations. To test this hypothesis, we use numerical simulation data to construct coarse grained observables and decompose their fluctuations into two transverse components associated with the postulated soft modes and a longitudinal component unrelated to them. We find that as temperature is lowered and time scales are increased, the time reparametrization fluctuations become increasingly dominant, and that their correlation volumes grow together with those of the dynamical heterogeneities, while the correlation volumes for longitudinal fluctuations remain small.

Equilibrium and nonequilibrium fluctuations in a glass-forming liquid.

Glass-forming liquids display strong fluctuations-dynamical heterogeneities-near their glass transition. By numerically simulating a binary Weeks-Chandler-Andersen liquid and varying both temperature and time scale, we investigate the probability distributions of two kinds of local fluctuations in the nonequilibrium (aging) regime and in the equilibrium regime, and find them to be very similar in the two regimes and across temperatures. We also observe that, when appropriately rescaled, the integrated dynamic susceptibility is very weakly dependent on temperature and very similar in both regimes.

Growth of spatial correlations in the aging of a simple structural glass.

We present a detailed numerical study of dynamical heterogeneities in the aging regime of a simple binary Lennard-Jones glass former. For most waiting times t_{w} and final times t , both the dynamical susceptibility chi_{4}(t,t_{w}) and the dynamical correlation length xi_{4}(t,t_{w}) can be approximated as products of two factors: (i) a waiting-time-dependent scale that grows as a power of t_{w} , and (ii) a scaling function dependent on t,t_{w} only through the value of the intermediate scattering function C(t,t_{w}) . We find that chi_{4}(t,t_{w}) is determined only in part by the correlation volume.

Separation of time scales and reparametrization invariance for aging systems.

We show that the generating functional describing the slow dynamics of spin-glass systems is invariant under reparametrizations of the time. This result is general and applies for both infinite and short-range models. It follows simply from the assumption that a separation between short time scales and long time scales exists in the system, and from the constraints of causality and unitarity. Global-time reparametrization invariance suggests that the low action excitations in a spin-glass may be smoothly spatially varying time reparametrizations. These Goldstone modes may provide the basis for an analytic dynamical theory of short-range spin glasses.

Heterogeneous aging in spin glasses.

We introduce a set of theoretical ideas that form the basis for an analytical framework capable of describing nonequilibrium dynamics in glassy systems. We test the resulting scenario by comparing its predictions with numerical simulations of short-range spin glasses. Local fluctuations and responses are shown to be connected by a generalized local out-of-equilibrium fluctuation-dissipation relation. Scaling relationships are uncovered for the slow evolution of heterogeneities at all time scales.