Search PubMed⌕ Search

Biomedical subjects

Juan P Garrahan

Publications and source records attributed to Juan P Garrahan.

At least 19 recordsLinked to original sources
PubMed2006

Space-time thermodynamics and subsystem observables in a kinetically constrained model of glassy materials.

In a recent article [M. Merolle et al., Proc. Natl. Acad. Sci. U.S.A. 102, 10837 (2005)], it was argued that dynamic heterogeneity in d-dimensional glass formers is a manifestation of an order-disorder phenomenon in the d+1 dimensions of space time. By considering a dynamical analog of the free energy, evidence was found for phase coexistence between active and inactive regions of space time, and it was suggested that this phenomenon underlies the glass transition. Here we develop these ideas further by investigating in detail the one-dimensional Fredrickson-Andersen (FA) model, in which the active and inactive phases originate in the reducibility of the dynamics. We illustrate the phase coexistence by considering the distributions of mesoscopic space-time observables. We show how the analogy with phase coexistence can be strengthened by breaking microscopic reversibility in the FA model, leading to a nonequilibrium theory in the directed percolation universality class.

Journal Article↗
PubMed2006

Activated aging dynamics and negative fluctuation-dissipation ratios.

In glassy materials, aging proceeds at large times via thermal activation. We show that this can lead to negative dynamical response functions and novel and well-defined violations of the fluctuation-dissipation theorem, in particular, negative fluctuation-dissipation ratios. Our analysis is based on detailed theoretical and numerical results for the activated aging regime of simple kinetically constrained models. The results are relevant to a variety of physical situations, such as aging in glass formers, thermally activated domain growth, and granular compaction.

Journal Article↗
PubMed2005

Heterogeneity and growing length scales in the dynamics of kinetically constrained lattice gases in two dimensions.

We study dynamical heterogeneity and growing dynamical length scales in two kinetically constrained models, namely, the one- and two-vacancy assisted triangular lattice gases. One of the models is a strong glassformer and the other is a fragile glassformer. Both exhibit heterogeneous dynamics with broadly distributed time scales as seen in the distribution of persistence times. We show that the Stokes-Einstein relation is violated, to a greater degree in the fragile glassformer, and show how this violation is related to dynamic heterogeneity. We extract dynamical length scales from structure factors of mobile particles and show, quantitatively, the growth of this length scale as density increases. We comment on how the scaling of lengths and times in these models relates to that in facilitated spin models of glasses.

Journal Article↗
PubMed2005

Caging and mosaic length scales in plaquette spin models of glasses.

We consider two systems of Ising spins with plaquette interactions. They are simple models of glasses which have dual representations as kinetically constrained systems. These models allow an explicit analysis using the mosaic, or entropic droplet, approach of the random first-order transition theory of the glass transition. We show that the low-temperature states of these systems resemble glassy mosaic states, despite the fact that excitations are localized and that there are no static singularities. By means of finite-size thermodynamics we study a generalized caging effect whereby the system is frozen on short length scales, but free at larger length scales. We find that the freezing length scales obtained from statics coincide with those relevant to dynamic correlations, as expected in the mosaic view. The simple nucleation arguments of the mosaic approach, however, do not give the correct relation between freezing lengths and relaxation times, as they do not capture the transition states for relaxation. We discuss how these results make a connection between the mosaic and the dynamic facilitation views of glass formers.

Journal Article↗
PubMed2005

Dynamical exchanges in facilitated models of supercooled liquids.

We investigate statistics of dynamical exchange events in coarse-grained models of supercooled liquids in spatial dimensions d=1, 2, and 3. The models, based upon the concept of dynamical facilitation, capture generic features of statistics of exchange times and persistence times. Here, distributions for both times are related and calculated for cases of strong and fragile glass formers over a range of temperatures. Exchange-time distributions are shown to be particularly sensitive to the model parameters and dimensions, and exhibit more structured and richer behavior than persistence-time distributions. Mean exchange times are shown to be Arrhenius, regardless of models and spatial dimensions. Specifically, tx approximately c-2, with c being the excitation concentration. Different dynamical exchange processes are identified and characterized from the underlying trajectories. We discuss experimental possibilities to test some of our theoretical findings.

Journal Article↗
PubMed2005

Space-time thermodynamics of the glass transition.

We consider the probability distribution for fluctuations in dynamical action and similar quantities related to dynamic heterogeneity. We argue that the so-called "glass transition" is a manifestation of low action tails in these distributions where the entropy of trajectory space is subextensive in time. These low action tails are a consequence of dynamic heterogeneity and an indication of phase coexistence in trajectory space. The glass transition, where the system falls out of equilibrium, is then an order-disorder phenomenon in space-time occurring at a temperature T(g), which is a weak function of measurement time. We illustrate our perspective ideas with facilitated lattice models and note how these ideas apply more generally.

Journal Article↗
PubMed2005

Thermodynamics of coarse-grained models of supercooled liquids.

In recent papers, we have argued that kinetically constrained coarse-grained models can be applied to understand dynamic properties of glass-forming materials, and we have used this approach in various applications that appear to validate this view. In one such paper [J. P. Garrahan and D. Chandler, Proc. Natl. Acad. Sci. U.S.A. 100, 9710 (2003)], among other things we argued that this approach also explains why the heat-capacity discontinuity at the glass transition is generally larger for fragile materials than for strong materials. In the preceding article, Biroli, Bouchaud, and Tarjus have objected to our explanation on this point, arguing that the class of models we apply is inconsistent with both the absolute size and the temperature dependence of the experimental specific heat. Their argument, however, neglects parameters associated with the coarse graining. Accounting for these parameters, we show here that our treatment of dynamics is not inconsistent with heat-capacity discontinuities.

Comment↗
PubMed2005

Static and dynamic length scales in a simple glassy plaquette model.

We study static and dynamic spatial correlations in a two-dimensional spin model with four-body plaquette interactions and standard Glauber dynamics by means of analytic arguments and Monte Carlo simulations. We study in detail the dynamical behavior which becomes glassy at low temperatures, due to the emergence of effective kinetic constraints in a dual representation where spins are mapped to plaquette variables. We study the interplay between nontrivial static correlations of the spins and the dynamic "four-point" correlations usually studied in the context of supercooled liquids. We show that slow dynamics is spatially heterogeneous due to the presence of diverging length scales and scaling, as is also found in kinetically constrained models. This analogy is illustrated by a comparative study of a froth model where the kinetic constraints are imposed.

Journal Article↗
PubMed2005

Glassy behavior in an exactly solved spin system with a ferromagnetic transition.

We show that applying simple dynamical rules to Baxter's eight-vertex model leads to a system which resembles a glass-forming liquid. There are analogies with liquid, supercooled liquid, glassy, and crystalline states. The disordered phases exhibit strong dynamical heterogeneity at low temperatures, which may be described in terms of an emergent mobility field. Their dynamics are well described by a simple model with trivial thermodynamics, but an emergent kinetic constraint. We show that the (second order) thermodynamic transition to the ordered phase may be interpreted in terms of confinement of the excitations in the mobility field. We also describe the aging of disordered states toward the ordered phase, in terms of simple rate equations.

Journal Article↗
PubMed2005

Numerical study of a fragile three-dimensional kinetically constrained model.

We numerically study the three-dimensional generalization of the kinetically constrained east model, the north-or-east-or-front (NEF) model. We characterize the equilibrium behavior of the NEF model in detail, measuring the temperature dependence of several quantities: alpha-relaxation time, distributions of relaxation times, dynamic susceptibility, dynamic correlation length, and four-point susceptibility. We show that the NEF model describes quantitatively experimental observations over an exceptionally wide range of time scales. We illustrate this by fitting experimental data obtained both in the mildly supercooled regime by optical Kerr effect and close to the glass transition by dielectric spectroscopy.

Journal Article↗
PubMed2005

Renormalization group study of a kinetically constrained model for strong glasses.

We derive a dynamic field theory for a kinetically constrained model, based on the Fredrickson-Andersen model, which we expect to describe the properties of an Arrhenius (strong) supercooled liquid at the coarse-grained level. We study this field theory using the renormalization group. For mesoscopic length and time scales, and for space dimension d>/=2 , the behavior of the model is governed by a zero-temperature dynamical critical point in the directed percolation universality class. We argue that in d=1 its behavior is that of compact directed percolation. We perform detailed numerical simulations of the corresponding Fredrickson-Andersen model on the lattice in various dimensions, and find reasonable quantitative agreement with the field theory predictions.

Journal Article↗
PubMed2004

Facilitated spin models in one dimension: a real-space renormalization group study.

We use a real-space renormalization group (RSRG) to study the low-temperature dynamics of kinetically constrained Ising chains (KCICs). We consider the cases of the Fredrickson-Andersen (FA) model, the East model, and the partially asymmetric KCIC. We show that the RSRG allows one to obtain in a unified manner the dynamical properties of these models near their zero-temperature critical points. These properties include the dynamic exponent, the growth of dynamical length scales, and the behavior of the excitation density near criticality. For the partially asymmetric chain, the RG predicts a crossover, on sufficiently large length and time scales, from East-like to FA-like behavior. Our results agree with the known results for KCICs obtained by other methods.

Journal Article↗
PubMed2004

Excitation lines and the breakdown of Stokes-Einstein relations in supercooled liquids.

By applying the concept of dynamical facilitation and analyzing the excitation lines that result from this facilitation, we investigate the origin of decoupling of transport coefficients in supercooled liquids. We illustrate our approach with two classes of models. One depicts diffusion in a strong glass former, and the other in a fragile glass former. At low temperatures, both models exhibit violation of the Stokes-Einstein relation, D approximately tau(-1), where D is the self-diffusion constant and tau is the structural relaxation time. In the strong case, the violation is sensitive to dimensionality d, going as D approximately tau(-2/3) for d=1 and as D approximately tau(-0.95) for d=3. In the fragile case, however, we argue that dimensionality dependence is weak, and show that for d=1, D approximately tau(-0.73). This scaling for the fragile case compares favorably with the results of a recent experimental study for a three-dimensional fragile glass former.

Journal Article↗
PubMed2004

Dynamic criticality in glass-forming liquids.

We propose that the dynamics of supercooled liquids and the formation of glasses can be understood from the existence of a zero-temperature dynamical critical point. To support our proposal, we derive a dynamic field theory for a generic kinetically constrained model, which we expect to describe the dynamics of a supercooled liquid. We study this field theory using the renormalization group (RG). Its long time behavior is dominated by a zero-temperature critical point, which for d>2 belongs to the directed percolation universality class. Molecular dynamics simulations seem to confirm the existence of dynamic scaling behavior consistent with the RG predictions.

Journal Article↗
PubMed2003

Real space origin of temperature crossovers in supercooled liquids.

We show that the various crossovers between dynamical regimes observed in experiments and simulations of supercooled liquids can be explained in simple terms from the existence and statistical properties of dynamical heterogeneities. We confirm that dynamic heterogeneity is responsible for the slowing down of glass formers at temperatures well above the dynamic singularity Tc predicted by mode-coupling theory. Our results imply that activated processes govern the long-time dynamics even in the temperature regime where they are neglected by mode-coupling theory. We show that alternative interpretations based on topographic properties of the potential energy landscape are inefficient ways of describing simple physical features which are naturally accounted for within our approach. We show in particular that the reported links between mode coupling and landscape singularities do not exist.

Journal Article↗
PubMed2003

Coarse-grained microscopic model of glass formers.

We introduce a coarse-grained model for atomic glass formers. Its elements are physically motivated local microscopic dynamical rules parameterized by observables. Results of the model are established and used to interpret the measured behaviors of supercooled fluids approaching glass transitions. The model predicts the presence of a crossover from hierarchical super-Arrhenius dynamics at short length scales to diffusive Arrhenius dynamics at large length scales. This prediction distinguishes our model from other theories of glass formers and can be tested by experiment.

Journal Article↗
PubMed2003

Fluctuation-dissipation relations in the nonequilibrium critical dynamics of Ising models.

We investigate the relation between two-time multispin correlation and response functions in the nonequilibrium critical dynamics of Ising models in d=1 and d=2 spatial dimensions. In these nonequilibrium situations, the fluctuation-dissipation theorem (FDT) is not satisfied. We find FDT "violations" qualitatively similar to those reported in various glassy materials, but quantitatively dependent on the chosen observable, in contrast to the results obtained in infinite-range glass models. Nevertheless, all FDT violations can be understood by considering separately the contributions from large wave vectors, which are at quasiequilibrium and obey the FDT, and from small wave vectors where a generalized FDT holds with a nontrivial fluctuation-dissipation ratio X infinity. In d=1, we get X(infinity)=1/2 for spin observables, which measure the orientation of domains, while X(infinity)=0 for observables that are sensitive to the domain-wall motion. Numerical simulations in d=2 reveal a unique X infinity approximately equal 0.34 for all observables. Measurement protocols for X infinity are discussed in detail. Our results suggest that the definition of an effective temperature T(eff)=T/X(infinity) for large length scales is generically possible in nonequilibrium critical dynamics.

Journal Article↗