AVAILABLE SLIDES:
- Axelle Amon (Université de Rennes) — Aftershocks as a time independant phenomenon [slides]
- Jérôme Crassous (Université de Rennes) — "Metastability of a periodic network of threads: what are the shapes of a knitted fabric ?" or "Packing of frictional fibers" [slides]
- Kilian Duplat (ILM, Université Lyon 1) — Correlation in OFC earthquakes model [slides]
- Yohann Faure (LPENS Lyon) — Interaction between slowly slipping and locked frictional interfaces [slides]
- Andrei Fedorenko (LPENS Lyon) — Surface criticality in disorder-driven quantum transitions [slides]
- Vincent Jeudy (LPS, Université Paris Saclay) — Internal structure dependent creep motion of domain walls driven by spin-transfer torques [slides]
- Tristan Jocteur (LIPhy, Grenoble-Alpes) — Yielding is an absorbing phase transition with vanishing critical fluctuations [slides]
- Romain Mari (LIPhy, Grenoble-Alpes) — Random organization model with long-ranged interactions [slides]
- Olivier Pierre-Louis (ILM, Université Lyon 1) — An invasion model for disordered 2D systems [slides]
- Antoine Sanner (ETH Zürich) — Effect of topological disorder on the toughness of spring networks [slides]
- Kay Wiese (LPENS Paris) — Hyperuniformity in the Manna Model, Conserved Directed Percolation and Depinning [slides]
Axelle Amon (Université de Rennes) — Aftershocks as a time independant phenomenon [slides]
Sequences of aftershocks following Omori's empirical law are observed after most major earthquakes, as well as in laboratory-scale fault-mimicking experiments. Nevertheless, the origin of this memory effect is still unclear. I will present an analytical framework for treating labquake and earthquake catalogs on an equal footing. Using this analysis method, we show that when memory is considered to be in deformation and not in time, all data collapse onto a single master curve, showing that the timescale is entirely fixed by the inverse of the strain rate.
Maximilien Bernard (LPENS Paris) — Anomalous scaling of heterogeneous interfaces: a new picture from sample to sample fluctuations
We study a discrete model of an heterogeneous elastic line with internal disorder, submitted to thermal fluctuations. The monomers are connected through random springs with independent and identically distributed elastic constants drawn from p(k) ~ k^{µ-1} for k->0. When µ>1, the scaling of the standard Edwards-Wilkinson model is recovered. When µ<1, the elastic line exhibits an anomalous scaling of the type observed in many growth models and experiments. Here we derive and use the exact expression for the exact probability distribution of the line shape at equilibrium, as well as the spectral properties of the matrix containing the random couplings,to fully characterize the sample-to-sample fluctuations. Our results lead to novel scaling predictions that partially disagree with previous works, but which are corroborated by numerical simulations. We also provide a novel interpretation of the anomalous scaling in terms of the abrupt jumps in the line's shape that dominate the average value of the observable.
Eric Bertin (LIPhy, Grenoble-Alpes) — Far-from-equilibrium complex landscape
Systems with a complex dynamics like glasses or models of biological evolution are often pictured in terms of complex landscapes, with a large number of possible collective states. We show on the example of a stochastic spin model with non-reciprocal and heterogeneous interactions how the complex landscape notion can be generalized far from equilibrium, where collective states may exhibit spontaneous oscillations, often hidden by the presence of disorder. We identify relevant observables, like the density of entropy production, to unveil the presence of oscillations, and we characterize the complex landscape of our model in terms of a configurational entropy, that counts the number of nonequilibrium collective states with a given entropy production density.
Mehdi Bouzid (3SR, Grenoble-Alpes) — Revealing elastic heterogeneities in colloidal gels
Adhesive particles dispersed in a suspension can self-assemble into a rigid percolating network called gel. They are ubiquitous in nature and in many industrial process raging from batteries, food stuff, to pharmaceutical products. Here we investigate the emergent elastic behavior of such colloidal gels formed from a continuous quench with a competitive interaction given by a short-range attraction and long-range repulsion. We show that the gelation is controlled by a rigidity percolation transition. We extract a characteristic correlation length scale that probe the size of the elastic and structural heterogeneities which diverge at the critical point. We demonstrate that independently of the nature of the interactions, the particle concentration as well as the path through which non-ergocity is attained (the preparation protocol) the elastic moduli and the vibrational properties of gels can be predicted by a mean field description in which bending modes of fractal clusters of about the size of the correlation length dominates under small deformation.
Nirvana Caballero (DQMP, Université de Genève) — Phase separation on surfaces in the presence of matter exchange
We introduce a field theory to explore how surface compositions interact with their bulk environments. We demonstrate that the rate of matter exchange significantly influences the emergence of complex, patterned compositions on the surface. Our analytical and numerical findings indicate that coarsening processes are arrested, resulting in domains with defined characteristic length scales. These suggest that the varied lipid composition observed in cellular membranes can be explained by simple physical interactions, offering a fundamental physical perspective on biological phenomena.
Jérôme Crassous (Université de Rennes) — "Metastability of a periodic network of threads: what are the shapes of a knitted fabric ?" or "Packing of frictional fibers" [slides]
Knitted fabrics are metamaterials with remarkable mechanical properties, such as extreme deformability and multiple history-dependent rest shapes. This letter shows that those properties may stem from a continuous set of metastable states for a mechanically relaxed fabric, evidenced through experiments, numerical simulations and analytical developments. Those states arise from the frictional contact forces acting in the braid zone where the threads interlace and follow a line in the configuration space accurately described by a 2D-elastica model. The friction coefficient sets a terminal point along this line, and the continuous set of relaxed states is obtained by varying the braid inclination while contact forces remain on the friction cone
Adèle Douin (ILM, Université Lyon 1) — Negative avalanches and anomalous dilation in a granular fault
When slowly shearing a granular system, we expect a slow accumulation of mechanical energy and a global dilation, interrupted by sudden avalanche-like events of energy release and a contraction of the structure. However, in the case of a compressed medium, we report a much richer behavior of the avalanches, including all four possible combinations between sudden contraction or sudden dilation with abrupt energy release or abrupt energy accumulation. Modifications in the stress network, captured by photoelasticity, explain the four scenarios, particularly the totally counterintuitive one of sudden energy accumulation and dilation, that usually liberates a large amount of acoustic energy. Decoding it in the context of earthquakes: a large quake may not result in a relaxation of the fault, but in a more charged configuration.
Kilian Duplat (ILM, Université Lyon 1) — Correlation in OFC earthquakes model [slides]
During the evolution of OFC systems, a transient regime occurs during which patches, defined as domains of sites with similar energy states, may emerge. These patches evolve over time, eventually propagating towards the system's center. The system then enter the stationnary state where avalanche size distribution can be evaluated. The formation and behavior of these patches are influenced by system size and dissipation. Through snapshots and correlation functions, the progression of patches is observed, with larger systems exhibiting longer invasion times. To determine the end of the transient regime, it is necessary to identify when the patches reach the center of the system. We introduce a method to evaluate the transient regime by mesuring the correlation length at the center of the system. Additionnaly, we study the evolution of the correlation length as function of the dissipation and system size.
Yohann Faure (LPENS Lyon) — Interaction between slowly slipping and locked frictional interfaces [slides]
What happens at the interface between two solid bodies in contact when they start sliding? This problem has important implications to various fields such as engineering, where the challenge is to control friction, or earthquake dynamics, where prediction of earthquakes occurrence and magnitude is crucial. A frictional interface is composed of an ensemble of discrete contacts that resist to shear. Sliding motion is mediated by the propagation of an interfacial rupture, breaking the micro-contacts, that has been shown to be a true shear crack [1]. Seismic faults are known to release the stress accumulated during tectonic movement through these interfacial rapid ruptures, giving rise to earthquakes, or via slow slip events, called aseismic slip [2]. In this talk, we present model laboratory experiments in which we study the interaction mechanisms between a slowly slipping region of a frictional interface and neighboring locked regions that are destabilized by rapid interfacial ruptures, i.e., earthquakes [3]. We emulate slow-slip regions by introducing a granular material patch along a portion of the frictional interface. By measuring the response of the fault to shear and performing interfacial slip measurements, we show that the slow-slip region acts as a nucleation center for seismic rupture, thereby increasing the frequency of earthquakes. The slow-slip region destabilizes into a rapid rupture, following the same rules as a pure crack in a homogeneous solid. These findings are important for unraveling the role of slow slip in the seismic cycle of a fault.
[1] I. Svetlizky and J. Fineberg, "Classical shear cracks drive the onset of dry frictional motion", Nature 509, 205 (2014).
[2] Z. Peng and J. Gomberg, "An integrated perspective of the continuum between earthquakes and slow-slip phenomena", Nature Geoscience 3, 599 (2010).
[3] Y. Faure and E. Bayart, "Experimental evidence of seismic ruptures initiated by aseismic slip", arXiv:2312.17511 (2023).
Andrei Fedorenko (LPENS Lyon) — Surface criticality in disorder-driven quantum transitions [slides]
The effects of surfaces on phase transitions have received much attention during last several decades. In semi-infinite classical spin systems one distinguishes three boundary universality classes: the ordinary, the extraordinary, and the special. For the ordinary transition the bulk and the boundary order simultaneously, while at the extraordinary transition the bulk orders in the presence of already ordered boundary. The special transition corresponds to a multicritical point where the lines of the ordinary, the extraordinary, and the surface transitions meet. Much less is known about the effects of surfaces on quantum phase transitions, especially those that cannot be studied by mapping onto (d+1)-dimensional classical systems. These include disorder-driven phase transitions such as Anderson localization and recently discovered non-Anderson transitions between nodal semimetals and diffusive metals. In my talk, I will give a brief overview of the recent progress in understanding surface criticality in these disorder-driven quantum transitions.
Nina Javerzat (LIPhy, Grenoble-Alpes) — Conformal invariance of the 2d rigidity transition
Rigidity percolation is a simple and generic framework to understand the solidification of amorphous matter, by focusing on the subnetworks responsible for the overall solidity --the rigid clusters. I will present the recent finding that, although amorphous matter does not display any structural long-range order, an important symmetry emerges at the onset of rigidity percolation: conformal invariance. I will first explain how one can show that percolation clusters are statistically invariant under conformal transformations using a numerical method. I will then present an alternative and powerful way of treating conformal symmetry in 2d, the so-called Schramm-Loewner evolution. I will show how exploiting conformal invariance via this framework allows to make new universal predictions on central-force rigidity percolation, and how these results could be extended to other types of rigidity transitions.
Based on Phys. Rev. Lett. 130, 268201 (2023) and Phys. Rev. Lett. 132, 018201(2024).
Vincent Jeudy (LPS, Université Paris Saclay) — Internal structure dependent creep motion of domain walls driven by spin-transfer torques [slides]
We will discuss the thermally-activated creep motion of domain walls driven by spin-polarized current in a thin (Ga,Mn)(As,P) film with perpendicular anisotropy. In particular, we will focus on the respective contributions to domain wall motion of the adiabatic and non-adiabatic components of spin-transfer torques (STT) exerted by the spin-polarized current on the domain wall magnetization. The non-adiabatic STT is found to compensate linearly an external magnetic field, with a slope compatible with a steady domain wall internal structure. Close to the compensation between field and non-adiabatic STT, the contribution of adiabatic STT is strongly enhanced. We show that the adiabatic STT may both increase or reduce domain wall velocity, which we associate to variations of creep pinning energy barrier with domain wall internal structure. Far from compensation, the effects of adiabatic STT become negligible and so field and current driven domain wall motion present common universal behaviors described by the quenched Edwards Wilkinson universality class.
Yonglun Jiang (Laboratoire Charles Coulomb, Université de Montpellier) — Space/time coupling between plastic activities in steady state flow of disordered solids
We study the space and time correlation between plastic activities in the shear flow of a 2-dimensional glassy system. We visualize the detailed flow dynamics through a 3-dimensional space/time diagram. In the diagram, we find a coexistence of large empty volume with no plastic activities and scattered localized regions with heavy traffics of plastic activities. The observation is a clear demonstration of the intrinsic dynamical heterogeneity and the existence of correlation between plastic activities. We further quantify the space/time coupling through several different ways and find strong correlation at short distance and short time. Such a coupling explains the gradual growth of plastically deform regions in the system during the flow. We finally compare with systems such as earthquakes, and emphasize the striking similarities between them even through they are across such a wide range of length scales.
Tristan Jocteur (LIPhy, Grenoble-Alpes) — Yielding is an absorbing phase transition with vanishing critical fluctuations [slides]
The yielding transition in athermal complex fluids can be interpreted as an absorbing phase transition between an elastic, absorbing state with high mesoscopic degeneracy and a flowing, active state. We characterize quantitatively this phase transition in an elastoplastic model under fixed applied shear stress, using a finite-size scaling analysis. We find vanishing critical fluctuations of the order parameter (i.e., the shear rate), and relate this property to the convex character of the phase transition. Exponent values strongly differ from that of Conserved Directed Percolation, the expected universality class for systems with infinitely many absorbing states. This discrepancy is traced back to the long-range character of elastic interactions and to zero modes of the elastic propagator, both resulting from mechanical equilibrium. We show explicitly that the CDP class is recovered when both properties are relaxed. We locate yielding within a family of models akin to fixed-energy sandpile models, only with long-range redistribution kernels with zero-modes that result from mechanical equilibrium. For redistribution kernels with sufficiently fast decay, this family of models belong to a short-range universality class distinct from the Conserved Directed Percolation class, which is induced by zero modes.
Dheeraj Kumar (PMMH, ESPCI Paris) — Memory effects in mesoscopic elasto-plastic models of amorphous solids
Experiments and atomic scale simulations have shown that amorphous solids under oscillatory shear, despite responding plastically, can settle in reversible steady states visiting the same sequence of particle configurations from one driving cycle to the next [1]. Such non-trivial periodic responses have also been termed as limit cycles. In an earlier work [2], we had captured these limit cycles using a lattice-based elastoplastic model (EPM) and studied the yielding transition as a function of preparation protocol of the sample. Here we report the memory behaviour of the same EPM. We show that our model, after prior oscillatory training, holds memory of initial shear direction and training amplitude. We demonstrate simple read-out protocols to reveal these memories. We also show that the memory of shear direction emerges from the development of polarization in the mechanical fields during training. These mechanical fields also hold memory of training amplitude. In line with non-interacting models, such as the Preisach model [3], we show that plastic events that reveal memory of training amplitude or shear direction are (almost) always a subset of those experienced in the limit cycle. Finally, we manipulate training sequences in oscillatory shear to encode memory of multiple training amplitudes and highlight expectations from return point memory.
[1] N. C. Keim, J. D. Paulsen, Z. Zeravcic, S. Sastry, & S. R. Nagel, "Memory formation in matter", Reviews of Modern Physics, 91, 035002 (2019).
[2] D. Kumar, S. Patinet, C. E. Maloney, I. Regev, D. Vandembroucq, & M. Mungan, "Mapping out the glassy landscape of a mesoscopic elastoplastic model", The Journal of Chemical Physics, 157, (2022).
[3] F. Preisach, "Über die magnetische Nachwirkung", Zeitschrift für physik, 94, 277 (1935).
Romain Mari (LIPhy, Grenoble-Alpes) — Random organization model with long-ranged interactions [slides]
Viscous suspensions under cyclic shearing of small amplitude display an intriguing phenomenon called random organization: after a finite number of cycles, suspended particles follow reversible trajectories that, when analyzed stroboscopically in time, can be interpreted as absorbing states. For larger shearing amplitudes, such reversible trajectories are never reached, and the stroboscopic dynamics show particles diffusion. These two phases are separated by a continuous transition at a critical shearing amplitude, which has been argued to belong to the conserved directed percolation class (CDP). Oddly enough, CDP usually gathers systems with short-ranged interactions, whereas in suspensions particles interact via contact but also long-ranged hydrodynamic interactions, causing passive regions to be affected by nearby active ones. Using numerical simulations of a minimal model for random organization with long-ranged interactions, we show how varying the algebraic decay affects the universality class of random organization. Our results beg the question of the possible generalizations of the CDP class to systems with long-ranged interactions.
Laureano Ortellado (LIPhy, Grenobles-Alpes) — Validating Local Symmetry Principle in Mixed Fractures I+III with X-ray Tomography
When a brittle material is fractured through uniaxial tensile stress, the crack propagates planar and perpendicular to the loading direction [1]. However, when out-of-plane shear stress is applied under such conditions (mixed mode I+III), the crack front breaks down into facets that twist relative to the parent planar crack [2]. Unfortunately, linear fracture mechanics fails to describe the physical mechanism that leads to crack fragmentation in mixed-mode I+III crack propagation necessitating the development of ad hoc criteria [3]. One widely accepted criterion is the principle of local symmetry, in which the fracture propagates in the shear-free direction, yet its validation is hindered by experimental uncertainties [4]. In this study, we develop a setup capable of generating controlled mix-mode fractures in a hydrogel. Then, we subsequently obtain a 3D tomographic image of the crack as it grows. Additionally, we employ finite element analysis to infer fracture mechanics parameters that otherwise will be inaccessible by experimental methods. These results are then compared with a novel conceptual fracture model developed herein, aiming to elucidate the complex behavior exhibited by mixed mode I+III cracks front in brittle materials.
[1] T.L. Anderson, "Fracture Mechanics: Fundamentals and Applications" CRC press, Boca Raton (2017).
[2] D.D. Pollard, P. Segall, P.T. Delaney, "Formation and interpretation of dilatant echelon cracks", Geological Society of America Bulletin 93, 1291 (1982).
[3] J. Fineberg, M. Marder, "Instability in dynamic fracture", Physics Reports 313, 1 (1999).
[4] K. Pham, K. Ravi-Chandar, "Further examination of the criterion for crack initiation under mixed-mode i+ iii loading", International Journal of Fracture 189, 121 (2014).
Olivier Pierre-Louis (ILM, Université Lyon 1) — An invasion model for disordered 2D systems [slides]
We propose a model where domains grow up to their convex hulls and merge when they overlap. This model can be seen as a continuum and isotropic counterpart of bootstrap percolation models. Starting with randomly deposited overlapping disks on a plane, we find a discontinuous transition that occurs via macroscopic avalanches. The disk concentration threshold is found to decrease as the system size is increased. Domain size distributions exhibit power-law tails for finite disk concentrations. This model is applied (i) to the de-adhesion of graphene caused by intercalation of nanoparticles, and (ii) to the dynamics of atomic steps during the dissolution of calcite. We also discuss the relevance of this model for the study of imbibition processes in disordered two-dimenional systems.
[1] D. Martin-Calle and O. Pierre-Louis, Phys. Rev. E 108, 044108 (2023).
Antoine Sanner (ETH Zürich) — Effect of topological disorder on the toughness of spring networks [slides]
On a coarse-grained level, polymer gels and architected materials correspond to a network of (nonlinear) springs. Here, we investigate how topological disorder affects crack propagation in spring network simulations. In particular, we quantify the the fracture energy, or toughness, that corresponds to the energy dissipated per unit crack advance. Our simulations on two dimensional networks show that the heterogeneity introduced by randomly removing springs pins and deflects the crack, leading to an increase in fracture energy. In contrast, in three dimensional networks, the fracture energy decreases when randomly removing springs. The reason is that in two dimensions, the crack-tip is a point that gets arrested by the strongest heterogeneity it encounters, while in three dimensions the crack tip is a line that interacts simultaneously with strong and weak spots.
Jérôme Weiss (ISTerre, Grenoble-Alpes) — Earthquakes interactions explained by thermally activated friction and stress redistributions
Earthquakes and faults are often considered as a paradigm of “crackling noise”, i.e. slowly driven complex systems responding through intermittent events characterized by scale-free statistics such as a power law distribution of seismic moments (the GR law), space/time correlations expressed e.g. by a slow decaying rate of aftershocks (the Omori's law) associated to scale free (sub)diffusion. Understanding the physical origin of these scaling laws is also obviously of primary importance in terms of natural hazards forecasting. Since the pioneering work of Burridge and Knopoff in 1967, spring-slider-blocks models, incorporating (only) simple static friction and elastic interactions, have been proposed to simulate fault mechanics and earthquakes. The seminal 1D models were later extended to 2D using cellular automata, with a simplified (short-range) version of elastic stress redistribution[Olami et al., 1992]. If these models are able to simulate events power-law distributed in slip sizes, they do not incorporate a genuine timescale, so are unable to simulate aftershocks and the associated space and time clustering. More recently, these spring-slider-blocks models were augmented from deterministic rheologies incorporating a timescale, such as viscous-elastic or rate-and-state rheologies, in order to simulate these complex space/time properties. Here we follow a different, stochastic approach, by introducing thermal activation of local sliding: sliding of a block can be triggered even if the force acting on that block is below its local (athermal) threshold, with a probability depending on the local force gap, while such thermal activation can possibly trigger an athermal avalanche – an earthquake – from elastic forces redistribution. Such a very simple model, including only basic static friction, elastic interactions and thermal activation, allows reproducing an Omori decay of aftershock triggering, an increasing aftershock productivity with increasing mainshock magnitude, and a spatial clustering of earthquakes. If the agreement between this model and earthquake phenomenology is, by many ways, striking, we also discuss possible future developments.
Kay Wiese (LPENS Paris) — Hyperuniformity in the Manna Model, Conserved Directed Percolation and Depinning [slides]
We use an exact mapping of the Manna model, or equivalently conserved directed percolation, onto disordered elastic manifolds at depinning to show that particle-density fluctuations in these two models are hyperuniform. The structure factor of the particle density behaves for small q as S(q)~|q|^\sigma$ with \sigma={4-d-2\zeta}, where \zeta is the roughness exponent at depinning. In dimension d=1, \sigma=1/2, while for all dimensions 0.6> \sigma >= 0. Our results fit well known simulations in the literature, except in d=1, where we perform our own simulations to confirm our findings.
