J.-P. Bouchaud

Direct experimental evidence of a growing length scale accompanying the glass transition

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.

Relation between bid–ask spread, impact and volatility in order-driven markets

We show that the cost of market orders and the profit of infinitesimal market-making or -taking strategies can be expressed in terms of directly observable quantities, namely the spread and the lag-dependent impact function. Imposing that any market taking or liquidity providing strategies is at best marginally profitable, we obtain a linear relation between the bid–ask spread and the instantaneous impact of market orders, in good agreement with our empirical observations on electronic markets. We then use this relation to justify a strong, and hitherto unnoticed, empirical correlation between the spread and the volatility per trade, with R 2s exceeding 0.9. This correlation suggests both that the main determinant of the bid–ask spread is adverse selection, and that most of the volatility comes from trade impact. We argue that the role of the time-horizon appearing in the definition of costs is crucial and that long-range correlations in the order flow, overlooked in previous studies, must be carefully factored in. We find that the spread is significantly larger on the NYSE, a liquid market with specialists, where monopoly rents appear to be present.

Can crack front waves explain the roughness of cracks

We review recent theoretical progress on the dynamics of brittle crack fronts and its relationship to the roughness of fracture surfaces. We discuss the possibility that the small scale roughness of cracks, which is characterized by a roughness exponent ≃0.5, could be caused by the generation, during local instabilities by depinning, of diffusively broadened corrugation waves, which have recently been observed to propagate elastically along moving crack fronts. We find that the theory agrees plausibly with the orders of magnitude observed. Various consequences and limitations, as well as alternative explanations, are discussed. We argue that another mechanism, possibly related to damage cavity coalescence, is needed to account for the observed large scale roughness of cracks that is characterized by a roughness exponent ≃0.8.

Dynamics of Ranking Processes in Complex Systems

The world is addicted to ranking: everything, from the reputation of scientists, journals, and universities to purchasing decisions is driven by measured or perceived differences between them. Here, we analyze empirical data capturing real time ranking in a number of systems, helping to identify the universal characteristics of ranking dynamics. We develop a continuum theory that not only predicts the stability of the ranking process, but shows that a noise-induced phase transition is at the heart of the observed differences in ranking regimes. The key parameters of the continuum theory can be explicitly measured from data, allowing us to predict and experimentally document the existence of three phases that govern ranking stability.

Statistical models for company growth

We study Suttons ‘microcanonical’ model for the internal organization of firms, that leads to non-trivial scaling properties for the statistics of growth rates. We show that the growth rates are asymptotically Gaussian in this model, whereas empirical results suggest that the kurtosis of the distribution increases with size. We also obtain the conditional distribution of the number and size of sub-sectors in Suttons model. We formulate and solve an alternative model, based on the assumption that the sector sizes follow a power-law distribution. We find in this new model both anomalous scaling of the variance of growth rates and non-Gaussian asymptotic distributions. We give some testable predictions of the two models that would differentiate them further. We also discuss why the growth rate statistics at the country level and at the company level should be identical.

Evidence of Deep Water Penetration in Silica during Stress Corrosion Fracture

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 65-85u2009u200au200aÅ, suggesting the presence of a damaged zone of ∼100u2009u200au200aÅ extending ahead of the crack tip during its propagation. This estimate of the size of the damaged zone is compatible with other recent results.

Evidence of growing spatial correlations during the aging of glassy glycerol.

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.

Damage of silicate glasses during stress corrosion

We show that water penetrates into the silicate glass matrix during stress corrosion fracture by probing what is stored under the fracture surface using neutron reflection. The concentration profile determined for two different values of the external loading exhibits a region close to the fracture surface where the water content is fairly elevated, suggesting a high amount of damage.

Nonlinear Susceptibility Experiments in a Supercooled Liquid: Evidence of Growing Spatial Correlations Close to Tg

We give an overview of our recent works in which the a.c. nonlinear dielectric response of an archetypical glassformer (glycerol) was measured close to its glass transition temperature T g . The purpose was to investigate the prediction that the nonlinear susceptibility is directly related to the number of dynamically correlated molecules N { corr} (T). We explain that two nonlinear susceptibilities are available, namely χ3 (3) and χ3 (1), which correspond respectively to the nonlinear cubic response at the third harmonics and at the first harmonics. We describe how to measure these nonlinear responses, even if they yield signals much smaller than that of the linear response. We show that both (vert {chi }_{3}^{(3)}(omega,T)vert) and (vert {chi }_{3}^{(1)}(omega,T)vert) are peaked as a function of the angular frequency ω and mainly obeys critical scaling as a function of ωτα(T), where τα(T) is the relaxation time of the liquid. Both χ3 (3) and χ3 (1) decay with the same power-law of ω beyond the peak. The height of the peak increases as the temperature approaches T g : This yields an accurate determination of the temperature dependence of N { corr} (T), once the contribution of saturation of dipoles is disentangled from that of dynamical glassy correlations.