Using molecular dynamics simulations, we show that a simple model of a glassy material exhibits the shear localization phenomenon observed in many complex fluids. At low shear rates, the system separates into a fluidized shear band and an unsheared part. The two bands are characterized by a very different dynamics probed by a local intermediate scattering function. Furthermore, a stick-slip motion is observed at very small shear rates. Our results, which open the possibility of exploring complex rheological behavior using simulations, are compared to recent experiments on various soft glasses.

We have recently shown that in nonequilibrium spin systems at criticality the limit X-infinity of the fluctuation-dissipation ratio X(t,t(w)) for tt(w)1 can be measured using observables such as magnetization or energy [ Phys. Rev. E 68, 016116 (2003) ]. Pleimling argues in a Comment [preceding paper, Phys. Rev. 70, 018101 (2004) ] on our paper that for such observables correlation and response functions are dominated by one-time quantities dependent only on t, and are therefore not suitable for a determination of X-infinity. Using standard scaling forms of correlation and response functions, as used by Pleimling, we show that our data do have a genuine two-time dependence and allow X(t,t(w)) and X-infinity to be measured, so that Pleimling's criticisms are easily refuted. We also compare with predictions from renormalization-group calculations, which are consistent with our numerical observation of a fluctuation-dissipation plot for the magnetization that is very close to a straight line. A key point remains that coherent observables make measurements of X-infinity easier than the traditionally used incoherent ones, producing fluctuation-dissipation plots whose slope is close to X-infinity over a much larger range.

We study numerically the properties of local low-energy excitations in the two-dimensional Ising spin glass with Gaussian couplings. Given the ground state, we determine the lowest-lying connected cluster of flipped spins containing one given spin, either with a fixed volume, or with a volume constrained to lie in a certain range. Our aim is to understand corrections to the scaling predicted by the droplet picture of spin glasses and to resolve contradictory results reported in the literature for the stiffness exponent. We find no clear trace of corrections to scaling, and the obtained stiffness exponent is in relatively good agreement with standard domain-wall calculations.

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 T-c 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.

We show that the dynamics between inherent structures in glassforming systems can be understood in purely dynamical terms, without any reference to "topographic" features of the potential energy landscape. This "nontopographic" interpretation is based instead on the existence of dynamical heterogeneities and on their statistical properties. Our view is supported by the study of simple dynamically facilitated models of glassformers. These models also allow for the formulation of quantitative theoretical predictions which are successfully compared to published data obtained in numerical and experimental studies of local dynamics of supercooled liquids. (C) 2003 American Institute of Physics.