1/f1/f noise and avalanche scaling in plastic deformation

We study the intermittency and noise of dislocation systems undergoing shear deformation. Simulations of a simple two-dimensional discrete dislocation dynamics model indicate that the deformation rate exhibits a power spectrum scaling of the type $1/f^{\alpha}$. The noise exponent is far away from a Lorentzian, with $\alpha \approx 1.5$. This result is directly related to the way the durations of avalanches of plastic deformation activity scale with their size.Comment: 6 pages, 5 figures, submitted to Phys. Rev.

Surface criticality in random field magnets

The boundary-induced scaling of three-dimensional random field Ising magnets is investigated close to the bulk critical point by exact combinatorial optimization methods. We measure several exponents describing surface criticality: $\beta_1$ for the surface layer magnetization and the surface excess exponents for the magnetization and the specific heat, $\beta_s$ and $\alpha_s$. The latter ones are related to the bulk phase transition by the same scaling laws as in pure systems, but only with the same violation of hyperscaling exponent $\theta$ as in the bulk. The boundary disorders faster than the bulk, and the experimental and theoretical implications are discussed.Comment: 6 pages, 9 figures, to appear in Phys. Rev.

The effect of thresholding on temporal avalanche statistics

We discuss intermittent time series consisting of discrete bursts or avalanches separated by waiting or silent times. The short time correlations can be understood to follow from the properties of individual avalanches, while longer time correlations often present in such signals reflect correlations between triggerings of different avalanches. As one possible source of the latter kind of correlations in experimental time series, we consider the effect of a finite detection threshold, due to e.g. experimental noise that needs to be removed. To this end, we study a simple toy model of an avalanche, a random walk returning to the origin or a Brownian bridge, in the presence and absence of superimposed delta-correlated noise. We discuss the properties after thresholding of artificial timeseries obtained by mixing toy avalanches and waiting times from a Poisson process. Most of the resulting scalings for individual avalanches and the composite timeseries can be understood via random walk theory, except for the waiting time distributions when strong additional noise is added. Then, to compare with a more complicated case we study the Manna sandpile model of self-organized criticality, where some further complications appear.Comment: 15 pages, 12 figures, submitted to J. Stat. Mech., special issue of the UPoN2008 conferenc

Roughness and multiscaling of planar crack fronts

We consider numerically the roughness of a planar crack front within the long-range elastic string model, with a tunable disorder correlation length $\xi$. The problem is shown to have two important length scales, $\xi$ and the Larkin length $L_c$. Multiscaling of the crack front is observed for scales below $\xi$, provided that the disorder is strong enough. The asymptotic scaling with a roughness exponent $\zeta \approx 0.39$ is recovered for scales larger than both $\xi$ and $L_c$. If $L_c > \xi$, these regimes are separated by a third regime characterized by the Larkin exponent $\zeta_L \approx 0.5$. We discuss the experimental implications of our results.Comment: 8 pages, two figure

Boundary lubrication with a liquid crystal monolayer

We study boundary lubrication characteristics of a liquid crystal (LC) monolayer sheared between two crystalline surfaces by nonequilibrium molecular dynamics simulations, using a simplified rigid bead-necklace model of the LC molecules. We consider LC monolayers confined by surfaces with three different atomic structures, subject to different shearing velocities, thus approximating a wide variety of materials and driving conditions. The time dependence of the friction force is studied and correlated with that of the orientational order exhibited by the LC molecules, arising from the competition between the effect of the structure of the confining surfaces and that of the imposed sliding direction. We show that the observed stick-slip events for low shear rates involve order-disorder transitions, and that the LC monolayer no longer has enough time to reorder at high shear rates, resulting in a smooth sliding regime. An irregular stick-slip phase between the regular stick-slip and smooth sliding is observed for intermediate shear rates regardless of the surface structure.Peer reviewe

Dislocation interactions mediated by grain boundaries

The dynamics of dislocation assemblies in deforming crystals indicate the emergence of collective phenomena, intermittent fluctuations and strain avalanches. In polycrystalline materials, the understanding of plastic deformation mechanisms depends on grasping the role of grain boundaries on dislocation motion. Here the interaction of dislocations and elastic, low angle grain boundaries is studied in the framework of a discrete dislocation representation. We allow grain boundaries to deform under the effect of dislocation stress fields and compare the effect of such a perturbation to the case of rigid grain boudaries. We are able to determine, both analytically and numerically, corrections to dislocation stress fields acting on neighboring grains, as mediated by grain boundary deformation. Finally, we discuss conclusions and consequences for the avalanche statistics, as observed in polycrystalline samples.Comment: 13 pages, 5 figure

Tuning the Correlation Decay in the Resistance Fluctuations of Multi-Species Networks

A new network model is proposed to describe the $1/f^\alpha$ resistance noise in disordered materials for a wide range of $\alpha$ values ($0< \alpha < 2$). More precisely, we have considered the resistance fluctuations of a thin resistor with granular structure in different stationary states: from nearly equilibrium up to far from equilibrium conditions. This system has been modelled as a network made by different species of resistors, distinguished by their resistances, temperature coefficients and by the energies associated with thermally activated processes of breaking and recovery. The correlation behavior of the resistance fluctuations is analyzed as a function of the temperature and applied current, in both the frequency and time domains. For the noise frequency exponent, the model provides $0< \alpha < 1$ at low currents, in the Ohmic regime, with $\alpha$ decreasing inversely with the temperature, and $1< \alpha <2$ at high currents, in the non-Ohmic regime. Since the threshold current associated with the onset of nonlinearity also depends on the temperature, the proposed model qualitatively accounts for the complicate behavior of $\alpha$ versus temperature and current observed in many experiments. Correspondingly, in the time domain, the auto-correlation function of the resistance fluctuations displays a variety of behaviors which are tuned by the external conditions.Comment: 26 pages, 16 figures, Submitted to JSTAT - Special issue SigmaPhi200

Spatial fluctuations in transient creep deformation

We study the spatial fluctuations of transient creep deformation of materials as a function of time, both by Digital Image Correlation (DIC) measurements of paper samples and by numerical simulations of a crystal plasticity or discrete dislocation dynamics model. This model has a jamming or yielding phase transition, around which power-law or Andrade creep is found. During primary creep, the relative strength of the strain rate fluctuations increases with time in both cases - the spatially averaged creep rate obeys the Andrade law $\epsilon_t \sim t^{-0.7}$, while the time dependence of the spatial fluctuations of the local creep rates is given by $\Delta \epsilon_t \sim t^{-0.5}$. A similar scaling for the fluctuations is found in the logarithmic creep regime that is typically observed for lower applied stresses. We review briefly some classical theories of Andrade creep from the point of view of such spatial fluctuations. We consider these phenomenological, time-dependent creep laws in terms of a description based on a non-equilibrium phase transition separating evolving and frozen states of the system when the externally applied load is varied. Such an interpretation is discussed further by the data collapse of the local deformations in the spirit of absorbing state/depinning phase transitions, as well as deformation-deformation correlations and the width of the cumulative strain distributions. The results are also compared with the order parameter fluctuations observed close to the depinning transition of the 2$d$ Linear Interface Model or the quenched Edwards-Wilkinson equation.Comment: 27 pages, 18 figure

Yielding and irreversible deformation below the microscale: Surface effects and non-mean-field plastic avalanches

Nanoindentation techniques recently developed to measure the mechanical response of crystals under external loading conditions reveal new phenomena upon decreasing sample size below the microscale. At small length scales, material resistance to irreversible deformation depends on sample morphology. Here we study the mechanisms of yield and plastic flow in inherently small crystals under uniaxial compression. Discrete structural rearrangements emerge as series of abrupt discontinuities in stress-strain curves. We obtain the theoretical dependence of the yield stress on system size and geometry and elucidate the statistical properties of plastic deformation at such scales. Our results show that the absence of dislocation storage leads to crucial effects on the statistics of plastic events, ultimately affecting the universal scaling behavior observed at larger scales.Comment: Supporting Videos available at http://dx.plos.org/10.1371/journal.pone.002041