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Register a new userSpatio-temporal scaling for out-of-equilibrium relaxation dynamics of an elastic manifold in random media: crossover between the Larkin regime and thermally activated regime
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We study relaxation dynamics of a three dimensional elastic manifold in random potential from a uniform initial condition by numerically solving the Langevin equation.We observe growth of roughness of the system up to larger wavelengths with time.We analyze structure factor in detail and find a compact scaling ansatz describing two distinct time regimes and crossover between them. We find short time regime corresponding to length scale smaller than the Larkin length $L_c$ is well described by the Larkin model which predicts a power law growth of domain size $L(t)$. Longer time behavior exhibits the random manifold regime with slower growth of $L(t)$.
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We study numerically the depinning transition of driven elastic interfaces in a random-periodic medium with localized periodic-correlation peaks in the direction of motion. The analysis of the moving interface geometry reveals the existence of several characteristic lengths separating different length-scale regimes of roughness. We determine the scaling behavior of these lengths as a function of the velocity, temperature, driving force, and transverse periodicity. A dynamical roughness diagram is thus obtained which contains, at small length scales, the critical and fast-flow regimes typical of the random-manifold (or domain wall) depinning, and at large length-scales, the critical and fast-flow regimes typical of the random-periodic (or charge-density wave) depinning. From the study of the equilibrium geometry we are also able to infer the roughness diagram in the creep regime, extending the depinning roughness diagram below threshold. Our results are relevant for understanding the geometry at depinning of arrays of elastically coupled thin manifolds in a disordered medium such as driven particle chains or vortex-line planar arrays. They also allow to properly control the effect of transverse periodic boundary conditions in large-scale simulations of driven disordered interfaces.
We study the high temperature regime within the glass phase of an elastic object with short ranged disorder. In that regime we argue that the scaling functions of any observable are described by a continuum model with a $delta$-correlated disorder and that they are universal up to only two parameters that can be explicitly computed. This is shown numerically on the roughness of directed polymer models and by dimensional and functional renormalization group arguments. We discuss experimental consequences such as non-monotonous behaviour with temperature.
The thermal rounding of the depinning transition of an elastic interface sliding on a washboard potential is studied through analytic arguments and very accurate numerical simulations. We confirm the standard view that well below the depinning threshold the average velocity can be calculated considering thermally activated nucleation of forward moving defects. However, we find that the straightforward extension of this analysis to near or above the depinning threshold does not fully describe the physics of the thermally assisted motion. In particular, we find that exactly at the depinning point the average velocity does not follow a pure power-law of the temperature as naively expected by the analogy with standard phase transitions but presents subtle logarithmic corrections. We explain the physical mechanisms behind these corrections and argue that they are non-peculiar collective effects which may also apply to the case of interfaces sliding on uncorrelated disordered landscapes.
In their seminal paper on scattering by an inhomogeneous solid, Debye and coworkers proposed a simple exponentially decaying function for the two-point correlation function of an idealized class of two-phase random media. Such {it Debye random media}, which have been shown to be realizable, are singularly distinct from all other models of two-phase media in that they are entirely defined by their one- and two-point correlation functions. To our knowledge, there has been no determination of other microstructural descriptors of Debye random media. In this paper, we generate Debye random media in two dimensions using an accelerated Yeong-Torquato construction algorithm. We then ascertain microstructural descriptors of the constructed media, including their surface correlation functions, pore-size distributions, lineal-path function, and chord-length probability density function. Accurate semi-analytic and empirical formulas for these descriptors are devised. We compare our results for Debye random media to those of other popular models (overlapping disks and equilibrium hard disks), and find that the former model possesses a wider spectrum of hole sizes, including a substantial fraction of large holes. Our algorithm can be applied to generate other models defined by their two-point correlation functions, and their other microstructural descriptors can be determined and analyzed by the procedures laid out here.
For the first time, the diffusion phase diagram in highly confined colloidal systems, predicted by Continuous Time Random Walk (CTRW), is experimentally obtained. Temporal and spatial fractional exponents, $alpha$ and $mu$, introduced within the framework of CTRW, are simultaneously measured by Pulse Field Gradient Nuclear Magnetic Resonance technique in samples of micro-beads dispersed in water. We find that $alpha$ depends on the disorder degree of the system. Conversely, $mu$ depends on both bead sizes and magnetic susceptibility differences within samples. Our findings fully match the CTRW predictions.
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