Avalanches in Breakdown and Fracture Processes

We investigate the breakdown of disordered networks under the action of an increasing external---mechanical or electrical---force. We perform a mean-field analysis and estimate scaling exponents for the approach to the instability. By simulating two-dimensional models of electric breakdown and fracture we observe that the breakdown is preceded by avalanche events. The avalanches can be described by scaling laws, and the estimated values of the exponents are consistent with those found in mean-field theory. The breakdown point is characterized by a discontinuity in the macroscopic properties of the material, such as conductivity or elasticity, indicative of a first order transition. The scaling laws suggest an analogy with the behavior expected in spinodal nucleation.Comment: 15 pages, 12 figures, submitted to Phys. Rev. E, corrected typo in authors name, no changes to the pape

Ageing and Relaxation in Glass Forming Systems

We propose that there exists a generic class of glass forming systems that have competing states (of crystalline order or not) which are locally close in energy to the ground state (which is typically unique). Upon cooling, such systems exhibit patches (or clusters) of these competing states which become locally stable in the sense of having a relatively high local shear modulus. It is in between these clusters where ageing, relaxation and plasticity under strain can take place. We demonstrate explicitly that relaxation events that lead to ageing occur where the local shear modulus is low (even negative), and result in an increase in the size of local patches of relative order. We examine the ageing events closely from two points of view. On the one hand we show that they are very localized in real space, taking place outside the patches of relative order, and from the other point of view we show that they represent transitions from one local minimum in the potential surface to another. This picture offers a direct relation between structure and dynamics, ascribing the slowing down in glass forming systems to the reduction in relative volume of the amorphous material which is liquid-like. While we agree with the well known Adam-Gibbs proposition that the slowing down is due to an entropic squeeze (a dramatic decrease in the number of available configurations), we do not agree with the Adam-Gibbs (or the Volger-Fulcher) formulae that predict an infinite relaxation time at a finite temperature. Rather, we propose that generically there should be no singular crisis at any finite temperature: the relaxation time and the associated correlation length (average cluster size) increase at most super-exponentially when the temperature is lowered

Structure of binary polymer blends: Multiple time step hybrid Monte Carlo simulations and self-consistent integral-equation theory

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