Disordered elastic systems and one-dimensional interfaces
TL;DR: In this paper, the authors introduce the generic framework of disordered elastic systems (DES), giving a short "recipe" of a DES modeling and presenting the quantities of interest in order to probe the static and dynamical disorder-induced properties of such systems.
Abstract: We briefly introduce the generic framework of disordered elastic systems (DES), giving a short ‘recipe’ of a DES modeling and presenting the quantities of interest in order to probe the static and dynamical disorder-induced properties of such systems. We then focus on a particular low-dimensional DES, namely the one-dimensional interface in short-ranged elasticity and short-ranged quenched disorder. Illustrating different elements given in the introductory sections, we discuss specifically the consequences of the interplay between a finite temperature T > 0 and a finite interface width ξ > 0 on the static geometrical fluctuations at different lengthscales, and the implications on the quasistatic dynamics.
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470 citations
TL;DR: In this article, the authors review the physical insight provided by elastoplastic models into practical issues such as strain localization, creep and steady-state rheology, but also the fundamental questions that they address with respect to criticality at the yielding point and the statistics of avalanches of plastic events.
Abstract: The deformation and flow of disordered solids, such as metallic glasses and concentrated emulsions, involves swift localized rearrangements of particles that induce a long-range deformation field. To describe these heterogeneous processes, elastoplastic models handle the material as a collection of 'mesoscopic' blocks alternating between an elastic behavior and plastic relaxation, when they are too loaded. Plastic relaxation events redistribute stresses in the system in a very anisotropic way. We review not only the physical insight provided by these models into practical issues such as strain localization, creep and steady-state rheology, but also the fundamental questions that they address with respect to criticality at the yielding point and the statistics of avalanches of plastic events. Furthermore, we discuss connections with concurrent mean-field approaches and with related problems such as the plasticity of crystals and the depinning of an elastic line.
246 citations
TL;DR: In this paper, structural and electronic features associated with the concomitant Peierls-charge density wave (CDW) instabilities observed in most one-dimensional (1D) inorganic and organic electronic conductors are reviewed.
83 citations
TL;DR: In this article, the authors focus on piezoresponse force microscopy measurements of individual ferroelectric domain walls, allowing their static configuration and dynamic response to be accessed with nanoscale resolution over multiple orders of length scale and velocity.
56 citations
Cites background from "Disordered elastic systems and one-..."
...(a) Interface velocity v as a function of the driving force F , adapted from [29]....
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...In the case of more general disorder, it may also be necessary to consider all the n-th order moments of the probability distribution function (PDF) of relative displacements ∆u(r), which reflect the characteristic scaling properties of the system [29]:...
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...(d) The roughness B(r) of the interface grows with the length scale r, adapted from [29]....
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...(a) Relative displacement ∆u(r) for r = z2 − z1 of a one-dimensional interface from its flat, elastically optimal configuration under the influence of weak collective pinning in a disorder potential, adapted from [29] (b) Random bond disorder preserves the symmetry of the double-well potential, while locally changing its depth....
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TL;DR: Ferrero et al. as mentioned in this paper presented the Consejo Nacional de Investigaciones Cientificas y Tecnicas (CICTE), which is the National Council of Energia Atomica.
47 citations
References
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TL;DR: In this article, the roughness exponent of driven elastic strings at the depinning threshold in $1+1$ dimensions for different functional forms of the (short-range) elastic energy is computed.
Abstract: Within a recently developed framework of dynamical Monte Carlo algorithms, we compute the roughness exponent $\ensuremath{\zeta}$ of driven elastic strings at the depinning threshold in $1+1$ dimensions for different functional forms of the (short-range) elastic energy. A purely harmonic elastic energy leads to an unphysical value for $\ensuremath{\zeta}$. We include supplementary terms in the elastic energy of at least quartic order in the local extension. We then find a roughness exponent of $\ensuremath{\zeta}\ensuremath{\simeq}0.63$, which coincides with the one obtained for different cellular automaton models of directed percolation depinning. We discuss the implications of our analysis for higher-dimensional elastic manifolds in disordered media.
74 citations
TL;DR: In this article, exact identities for a family of models including (a) a domain wall in a random field Ising model (RFIM), and (b) the random anisotropy model in the no-vortex approximation were derived.
Abstract: Exact identities are derived for a family of models including (a) a domain wall in a random field Ising model (RFIM), and (b) the random anisotropyXY model in the no-vortex approximation. In particular, the second moment of thermal fluctuations is not affected by frozen randomness. It is checked in a one-dimensional model that higher moments are on the contrary strongly enhanced. Thus, thermal fluctuations are strongly non-Gaussian. This reflects excursions between remote potential wells in the phase space. It is shown exactly that the Imry-Ma argument yields a correct evaluation of the field-induced fluctuations for the one-dimensional model.
72 citations
"Disordered elastic systems and one-..." refers background in this paper
...This very particular form of elasticity is central for the mappings to other statistical physics problems and for the statistical tilt symmetry (STS), a fundamental property for 1D interfaces in presence of disorder [46, 47, 48]....
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TL;DR: In this article, the steady state of driven elastic strings in disordered media below the depinning threshold was studied and the dynamic phase diagram was derived from the transition pathways between metastable states.
Abstract: We study the steady state of driven elastic strings in disordered media below the depinning threshold. In the low-temperature limit, for a fixed sample, the steady state is dominated by a single configuration, which we determine exactly from the transition pathways between metastable states. We obtain the dynamical phase diagram in this limit. At variance with a thermodynamic phase transition, the depinning transition is not associated with a divergent length scale of the steady state below threshold, but only of the transient dynamics. We discuss the distribution of barrier heights, and check the validity of the dynamic phase diagram at small but finite temperatures using Langevin simulations. The phase diagram continues to hold for broken statistical tilt symmetry. We point out the relevance of our results for experiments of creep motion in elastic interfaces.
72 citations
"Disordered elastic systems and one-..." refers background or methods in this paper
...07, d = 1 and in numerical studies [22]....
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...Numerically there are in particular very efficient algorithm in 1D in order to address the dynamics and the static of the 1D interface, starting from a Langevin equation both at zero [40] and at small but finite temperature [41, 22]....
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TL;DR: The distribution of local fluctuations of the crack front velocity are related to the observed avalanche size distribution and space-time correlations of the local velocities show a simple diffusion growth behavior.
Abstract: We have studied the propagation of a crack front along the heterogeneous weak plane of a transparent poly(methyl methacrylate) (PMMA) block using two different loading conditions: imposed constant velocity and creep relaxation. We have focused on the intermittent local dynamics of the fracture front for a wide range of average crack front propagation velocities spanning over four decades. We computed the local velocity fluctuations along the fracture front. Two regimes are emphasized: a depinning regime of high velocity clusters defined as avalanches and a pinning regime of very low-velocity creeping lines. The scaling properties of the avalanches and pinning lines (size and spatial extent) are found to be independent of the loading conditions and of the average crack front velocity. The distribution of local fluctuations of the crack front velocity are related to the observed avalanche size distribution. Space-time correlations of the local velocities show a simple diffusion growth behavior.
67 citations
"Disordered elastic systems and one-..." refers background in this paper
...the imaging of the imbibition line of a fluid on a disordered substrate [26], of a crack front along an heterogeneous weak plane [27] by ultra-fast CCD camera, or of avalanches in ferromagnetic thin films [5]....
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TL;DR: It is argued that the power-law distribution of large thermally active excitation is a consequence of the continuous statistical tilt'' symmetry of the directed polymer, the breaking of which gives rise to the large active excitations in a manner analogous to the appearance of Goldstone modes in pure systems with a broken continuous symmetry.
Abstract: A systematic analysis of large-scale fluctuations in the low-temperature pinned phase of a directed polymer in a random potential is described. These fluctuations come from rare regions with nearly degenerate ground states.'' The probability distribution of their sizes is found to have a power-law tail. The rare regions in the tail dominate much of the physics. The analysis presented here takes advantage of the mapping to the noisy Burgers' equation. It complements a phenomenological description of glassy phases based on a scaling picture of droplet excitations and a recent variational approach with broken replica symmetry.'' It is argued that the power-law distribution of large thermally active excitations is a consequence of the continuous statistical tilt'' symmetry of the directed polymer, the breaking of which gives rise to the large active excitations in a manner analogous to the appearance of Goldstone modes in pure systems with a broken continuous symmetry.
65 citations
"Disordered elastic systems and one-..." refers background in this paper
...This very particular form of elasticity is central for the mappings to other statistical physics problems and for the statistical tilt symmetry (STS), a fundamental property for 1D interfaces in presence of disorder [46, 47, 48]....
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