RESUMEN

This work aims at reconsidering several interpretations coexisting in the recent literature concerning nonlinear susceptibilities in supercooled liquids. We present experimental results on glycerol and propylene carbonate, showing that the three independent cubic susceptibilities have very similar frequency and temperature dependences, for both their amplitudes and phases. This strongly suggests a unique physical mechanism responsible for the growth of these nonlinear susceptibilities. We show that the framework proposed by two of us [J.-P. Bouchaud and G. Biroli, Phys. Rev. B 72, 064204 (2005)PRBMDO1098-012110.1103/PhysRevB.72.064204], where the growth of nonlinear susceptibilities is intimately related to the growth of glassy domains, accounts for all the salient experimental features. We then review several complementary and/or alternative models and show that the notion of cooperatively rearranging glassy domains is a key (implicit or explicit) ingredient to all of them. This paves the way for future experiments, which should deepen our understanding of glasses.

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Glasses are ubiquitous in daily life and technology. However, the microscopic mechanisms generating this state of matter remain subject to debate: Glasses are considered either as merely hyperviscous liquids or as resulting from a genuine thermodynamic phase transition toward a rigid state. We show that third- and fifth-order susceptibilities provide a definite answer to this long-standing controversy. Performing the corresponding high-precision nonlinear dielectric experiments for supercooled glycerol and propylene carbonate, we find strong support for theories based on thermodynamic amorphous order. Moreover, when lowering temperature, we find that the growing transient domains are compact--that is, their fractal dimension d(f) = 3. The glass transition may thus represent a class of critical phenomena different from canonical second-order phase transitions for which d(f) < 3.

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We generalize the reaction-diffusion model A+B→0 in order to study the impact of an excess of A (or B) at the reaction front. We provide an exact solution of the model, which shows that the linear response breaks down: the average displacement of the reaction front grows as the square root of the imbalance. We argue that this model provides a highly simplified but generic framework to understand the square-root impact of large orders in financial markets.

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Motivated by empirical data, we develop a statistical description of the queue dynamics for large tick assets based on a two-dimensional Fokker-Planck (diffusion) equation. Our description explicitly includes state dependence, i.e., the fact that the drift and diffusion depend on the volume present on both sides of the spread. "Jump" events, corresponding to sudden changes of the best limit price, must also be included as birth-death terms in the Fokker-Planck equation. All quantities involved in the equation can be calibrated using high-frequency data on the best quotes. One of our central findings is that the dynamical process is approximately scale invariant, i.e., the only relevant variable is the ratio of the current volume in the queue to its average value. While the latter shows intraday seasonalities and strong variability across stocks and time periods, the dynamics of the rescaled volumes is universal. In terms of rescaled volumes, we found that the drift has a complex two-dimensional structure, which is a sum of a gradient contribution and a rotational contribution, both stable across stocks and time. This drift term is entirely responsible for the dynamical correlations between the ask queue and the bid queue.

RESUMEN

We have measured, as a function of the age t(a), the aging of the nonlinear dielectric susceptibility χ(3) of glycerol below the glass transition. Whereas the linear susceptibility can be accurately accounted for in terms of an age dependent relaxation time τ(α)(t(a)), this scaling breaks down for χ(3), suggesting an increase of the amplitude of χ(3). This is a strong indication that the number N(corr) of molecules involved in relaxation events increases with t(a). For T=0.96×T(g), we find that N(corr) increases by ~10% when t(a) varies from 1 to 100 ks. This sheds new light on the relation between length scales and time scales in glasses.

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We measure the thickness of the heavy water layer trapped under the stress corrosion fracture surface of silica using neutron reflectivity experiments. We show that the penetration depth is 65-85   Å, suggesting the presence of a damaged zone of ∼100   Šextending ahead of the crack tip during its propagation. This estimate of the size of the damaged zone is compatible with other recent results.

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The ac nonlinear dielectric response chi3(omega,T) of glycerol was measured close to its glass transition temperature T(g) to investigate the prediction that supercooled liquids respond in an increasingly nonlinear way as the dynamics slows down (as spin glasses do). We find that chi3(omega,T) indeed displays several nontrivial features. It is peaked as a function of the frequency omega and obeys scaling as a function of omega tau(T), with tau(T) the relaxation time of the liquid. The height of the peak, proportional to the number of dynamically correlated molecules N(corr)(T), increases as the system becomes glassy, and chi3 decays as a power law of omega over several decades beyond the peak. These findings confirm the collective nature of the glassy dynamics and provide the first direct estimate of the T dependence of N(corr).

RESUMEN

We use recently introduced three-point dynamic susceptibilities to obtain an experimental determination of the temperature evolution of the number of molecules Ncorr that are dynamically correlated during the structural relaxation of supercooled liquids. We first discuss in detail the physical content of three-point functions that relate the sensitivity of the averaged two-time dynamics to external control parameters (such as temperature or density), as well as their connection to the more standard four-point dynamic susceptibility associated with dynamical heterogeneities. We then demonstrate that these functions can be experimentally determined with good precision. We gather available data to obtain the temperature dependence of Ncorr for a large number of supercooled liquids over a wide range of relaxation time scales from the glass transition up to the onset of slow dynamics. We find that Ncorr systematically grows when approaching the glass transition. It does so in a modest manner close to the glass transition, which is consistent with an activation-based picture of the dynamics in glassforming materials. For higher temperatures, there appears to be a regime where Ncorr behaves as a power-law of the relaxation time. Finally, we find that the dynamic response to density, while being smaller than the dynamic response to temperature, behaves similarly, in agreement with theoretical expectations.

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We study theoretically and numerically a family of multipoint dynamic susceptibilities that quantify the strength and characteristic length scales of dynamic heterogeneities in glass-forming materials. We use general theoretical arguments (fluctuation-dissipation relations and symmetries of relevant dynamical field theories) to relate the sensitivity of averaged two-time correlators to temperature and density to spontaneous fluctuations of the local dynamics. Our theoretical results are then compared to molecular dynamics simulations of the Newtonian, Brownian, and Monte Carlo dynamics of two representative glass-forming liquids, a fragile binary Lennard-Jones mixture, and a model for the strong glass-former silica. We justify in detail the claim made by Berthier et al. [Science 310, 1797 (2005)] that the temperature dependence of correlation functions allows one to extract useful information on dynamic length scales in glassy systems. We also discuss some subtle issues associated with the choice of microscopic dynamics and of statistical ensemble through conserved quantities, which are found to play an important role in determining dynamic correlations.

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We study in detail the predictions of various theoretical approaches, in particular, mode-coupling theory (MCT) and kinetically constrained models (KCMs), concerning the time, temperature, and wave vector dependence of multipoint correlation functions that quantify the strength of both induced and spontaneous dynamical fluctuations. We also discuss the precise predictions of MCT concerning the statistical ensemble and microscopic dynamics dependence of these multipoint correlation functions. These predictions are compared to simulations of model fragile and strong glass-forming liquids. Overall, MCT fares quite well in the fragile case, in particular, explaining the observed crucial role of the statistical ensemble and microscopic dynamics, while MCT predictions do not seem to hold in the strong case. KCMs provide a simplified framework for understanding how these multipoint correlation functions may encode dynamic correlations in glassy materials. However, our analysis highlights important unresolved questions concerning the application of KCMs to supercooled liquids.

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Understanding glass formation is a challenge, because the existence of a true glass state, distinct from liquid and solid, remains elusive: Glasses are liquids that have become too viscous to flow. An old idea, as yet unproven experimentally, is that the dynamics becomes sluggish as the glass transition approaches, because increasingly larger regions of the material have to move simultaneously to allow flow. We introduce new multipoint dynamical susceptibilities to estimate quantitatively the size of these regions and provide direct experimental evidence that the glass formation of molecular liquids and colloidal suspensions is accompanied by growing dynamic correlation length scales.

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We report on an extensive study of the influence of spin anisotropy on spin glass aging dynamics. New temperature cycle experiments allow us to compare quantitatively the memory effect in four Heisenberg spin glasses with various degrees of random anisotropy and one Ising spin glass. The sharpness of the memory effect appears to decrease continuously with the spin anisotropy. Besides, the spin glass coherence length is determined by magnetic field change experiments for the first time in the Ising sample. For three representative samples, from Heisenberg to Ising spin glasses, we can consistently account for both sets of experiments (temperature cycle and magnetic field change) using a single expression for the growth of the coherence length with time.

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The relation between single particle and ensemble measurements is addressed for semiconductor CdSe nanocrystals. We record their fluorescence at the single molecule level and analyze their emission intermittency, which is governed by unusual random processes known as Lévy statistics. We report the observation of statistical aging and ergodicity breaking, both related to the occurrence of Lévy statistics. Our results show that the behavior of ensemble quantities, such as the total fluorescence of an ensemble of nanocrystals, can differ from the time-averaged individual quantities, and must be interpreted with care.

Asunto(s)

Compuestos de Cadmio/química , Nanotecnología/métodos , Compuestos de Selenio/química , Fluorescencia , Microscopía Fluorescente/métodos , Teoría Cuántica , Estadística como Asunto/métodos

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A general approach is presented for understanding the stress response function in anisotropic granular layers in two dimensions. The formalism accommodates both classical anisotropic elasticity theory and linear theories of anisotropic directed-force chain networks. Perhaps surprisingly, two-peak response functions can occur even for classical, anisotropic elastic materials, such as triangular networks of springs with different stiffnesses. In such cases, the peak widths grow linearly with the height of the layer, contrary to the diffusive spreading found in "stress-only" hyperbolic models. In principle, directed-force chain networks can exhibit the two-peak, diffusively spreading response function of hyperbolic models, but all models in a particular class studied here are found to be in the elliptic regime.

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We study a one-dimensional generalization of the exponential trap model using both numerical simulations and analytical approximations. We obtain the asymptotic shape of the average diffusion front in the subdiffusive phase. Our central result concerns the localization properties. We find the dynamical participation ratios to be finite, but different from their equilibrium counterparts. Therefore, the idea of a partial equilibrium within the limited region of space explored by the walk is not exact, even for long times where each site is visited a very large number of times. We discuss the physical origin of this discrepancy, and characterize the full distribution of dynamical weights. We also study two different two-time correlation functions, which exhibit different aging properties: one is "sub aging" whereas the other one shows "full aging," therefore, two diverging time scales appear in this model. We give intuitive arguments and simple analytical approximations that account for these differences, and obtain new predictions for the asymptotic (short-time and long-time) behavior of the scaling functions. Finally, we discuss the issue of multiple time scalings in this model.

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We investigate the behavior of the response function in the one-dimensional trap model using scaling arguments that we confirm by numerical simulations. We study the average position of the random walk at time t(w)+t, given that a small bias h is applied at time t(w). Several scaling regimes are found, depending on the relative values of t, t(w), and h. Comparison with the diffusive motion in the absence of bias allows us to show that the fluctuation-dissipation relation is valid even in the aging regime, at least for times such that linear response is obeyed. However, for sufficiently long times, the response always becomes nonlinear in h.

RESUMEN

We compute the dynamical structure factor S( q,tau) of an elastic medium where force dipoles appear at random in space and in time, due to "micro-collapses" of the structure. Various regimes are found, depending on the wave vector q and the collapse time theta. In an early time regime, the logarithm of the structure factor behaves as (q tau)(3/2), as predicted in (L. Cipelletti et al., Phys. Rev Lett. 84, 2275 (2000)) using heuristic arguments. However, in an intermediate-time regime we rather obtain a (q tau)(5/4) behaviour. Finally, the asymptotic long-time regime is found to behave as q(3/2)tau. We also give a plausible scenario for aging, in terms of a strain-dependent energy barrier for micro-collapses. The relaxation time is found to grow with the age t(w), quasi-exponentially at first, and then as t(w)(4/5) with logarithmic corrections.

RESUMEN

We investigate aging in glassy systems based on a simple model, where a point in configuration space performs thermally activated jumps between the minima of a random energy landscape. The model allows us to show explicitly a subaging behavior and multiple scaling regimes for the correlation function. Both the exponents characterizing the scaling of the different relaxation times with the waiting time and those characterizing the asymptotic decay of the scaling functions are obtained analytically by invoking a "partial equilibrium" concept.

RESUMEN

We have recently developed some simple continuum models of static granular media which display "fragile" behavior: They predict that the medium is unable to support certain types of infinitesimal load (which we call "incompatible" loads) without plastic rearrangement. We argue that a fragile description may be appropriate when the mechanical integrity of the medium arises adaptively, in response to a load, through an internal jamming process. We hypothesize that a network of force chains (or "granular skeleton") evolves until it can just support the applied load, at which point it comes to rest; it then remains intact so long as no incompatible load is applied. Our fragile models exhibits unusual mechanical responses involving hyperbolic equations for stress propagation along fixed characteristics through the material. These characteristics represent force chains; their arrangement expressly depends on the construction history. Thus, for example, we predict a large difference in the stress pattern beneath two conical piles of sand, one poured from a point source and one created by sieving. (c) 1999 American Institute of Physics.