Sloped terrains tend to creep downward over time, even when their slope is below the nominal angle of repose. This behavior can result from periodic variations in environmental conditions, such as daily or seasonal fluctuations in temperature and humidity. We study this process by considering a model of an athermal yield stress material under an applied stress lower than the critical yield stress value σ_c. Normally, in such a situation the material does not flow at all. However, under cyclic temporal variation of system parameters a finite amount of irreversible deformation can remain after each cycle, and a long term steady-state flow of the whole system can be induced. In our model, we cycle the strength of internal elastic interactions to mimic the effect of cyclic variation of environmental conditions in the real soils. We find that the amount of deformation per cycle increases if σ_c is approached from below, and it decreases and even vanishes at a novel critical stress σ_0<σ_c when this, in turn, is reached from above. Interestingly, σ_0 plays a role similar to the endurance limit in the context of fatigue damage propagation. Despite the model's simplicity, our results offer a fresh perspective on subcritical landform evolution, with implications for the creep of hill slopes over long periods and the precursors to runaway landslides.

Yield stress materials deform irreversibly at a finite strain-rate if loaded with a fixed stress σ larger than some critical yield stress σc. When σ < σc deformation is absent, except for transient or thermally activated processes. However, the cyclic temporal variation of system parameters can induce a persistent irreversible deformation under sub-critical athermal conditions. We characterize this phenomenon using well established models in the fields of the yielding and depinning transitions. We find that the amount of deformation per cycle increases if σc is approached from below, and it decreases and even vanishes at a novel critical stress σ0 < σc when this is reached from above. Interestingly, σ0 plays a role similar to the fatigue limit in the context of fatigue damage propagation. Our study is inspired by the literature on soft Earth geophysics where soil creep mechanisms have been correlated with cyclic changes of environmental conditions, such as daily or seasonal fluctuations in temperature and humidity, which in turn promote fluctuations in the systems internal mechanical properties. We believe our findings can motivate an interdisciplinary perspective on the study of sub-critical landform evolution, as the creep of hill slopes over long periods of time.

We numerically investigate the statistics of avalanches in glassy systems of active particles with finite persistence, with and without an externally applied shear. In departing from the infinite-persistence limit and exploring the interplay of internal activity and external driving, we uncover when and why active and passive systems display similar avalanche statistics and where these analogies fail. We find that power-law distributed stress drops emerge only when activity builds long enough correlations, controlled by the persistence length, with exponents that vary from the purely strain-driven case, to the purely activity-driven case, in a smooth fashion. The local structure and scaling of avalanches of plastic rearrangements remains universal across both limit cases, supporting an interpretation of activity as increasing the typical size of the regions involved in a given avalanche. Our results bridge quasistatic shear strain and finite-persistence active yielding, showing that avalanches driven by self-propulsion retain the characteristic fingerprints of long-range stress propagation.

Drawing inspiration from honeybee swarms' nest-site selection process, we assess the ability of a kilobot robot swarm to replicate this captivating example of collective decision making. Honeybees locate the optimal site for their new nest by aggregating information about potential locations and exchanging it through their waggle dance. The complexity and elegance of solving this problem rely on two key abilities of scout honeybees: self-discovery and imitation, symbolizing and , respectively. We employ a mathematical model to represent this nest-site selection problem and program our kilobots to follow its rules. Our experiments demonstrate that the kilobot swarm can collectively reach consensus decisions in a decentralized manner, akin to honeybees. However, the strength of this consensus depends not only on the interplay between independence and interdependence but also on critical factors such as swarm density and the motion of kilobots. These factors enable the formation of a percolated communication network, through which each robot can receive information beyond its immediate vicinity. By shedding light on this crucial layer of complexity—the crowding and mobility conditions during the decision making—we emphasize the significance of factors typically overlooked but essential to living systems and life itself. Published by the American Physical Society 2024

We perform a comprehensive analysis of a collective decision-making model inspired by honeybee behavior. This model integrates individual exploration for option discovery and social interactions for information sharing, while also considering option qualities. Our assessment of the decision process outcome employs standard consensus metrics and investigates its correlation with convergence time, revealing common trade-offs between speed and accuracy. Furthermore, we show the model's compliance with Weber's law of relative stimulus perception, aligning with previous analysis of collective decision problems. Our study also identifies nonequilibrium critical behavior in specific limits of the model, where the highest values of consensus are achieved. This result highlights the intriguing relationship between optimal performance, critically, and the fluctuations caused by finite-size effects, often seen in biological systems. Our findings are especially relevant for finite adaptive systems, as they provide insights into navigating decision-making scenarios with similar options more effectively.

We model the isotropic depinning transition of a domain-wall using a two dimensional Ginzburg-Landau scalar field instead of a directed elastic string in a random media. An exact algorithm accurately targets both the critical depinning field and the critical configuration for each sample. For random bond disorder of weak strength $\Delta$, the critical field scales as $\Delta^{4/3}$ in agreement with the predictions for the quenched Edwards-Wilkinson elastic model. However, critical configurations display overhangs beyond a characteristic length $l_{\tt 0} \sim \Delta^{-\alpha}$, with $\alpha\approx 2.2$, indicating a finite-size crossover. At the large scales, overhangs recover the orientational symmetry which is broken by directed elastic interfaces. We obtain quenched Edwards-Wilkinson exponents below $l_{\tt 0}$ and invasion percolation depinning exponents above $l_{\tt 0}$. A full picture of domain wall isotropic depinning in two dimensions is hence proposed.

We examine the structural relaxation of glassy materials at finite temperatures, considering the effect of activated rearrangements and long-range elastic interactions. Our three-dimensional mesoscopic relaxation model shows how the displacements induced by localized relaxation events can result in faster-than-exponential relaxation. Thermal activation allows for local rearrangements, which generate elastic responses and possibly cascades of new relaxation events. To study the interplay between this elastically-dominated and thermally-dominated dynamics, we introduce tracer particles that follow the displacement field induced by the local relaxation events and also incorporate Brownian motion. Our results reveal that the dynamic exponents and shape parameter of the dynamical structure factor depend on this competition and display a crossover from faster-than-exponential to exponential relaxation as temperature increases, consistent with recent observations in metallic glasses. Additionally, we find the distribution of waiting times between activations to be broadly distributed at low temperatures, providing a measure of dynamical heterogeneities characteristic for to glassy dynamics.

The behavior of shear-oscillated amorphous materials is studied using a coarse-grained model. Samples are prepared at different degrees of annealing and then subjected to athermal and quasi-static oscillatory deformations at various fixed amplitudes. The steady-state reached after several oscillations is fully determined by the initial preparation and the oscillation amplitude, as seen from stroboscopic stress and energy measurements. Under small oscillations, poorly annealed materials display shear-annealing, while ultra-stabilized materials are insensitive to them. Yet, beyond a critical oscillation amplitude, both kinds of materials display a discontinuous transition to the same mixed state composed of a fluid shear-band embedded in a marginal solid. Quantitative relations between uniform shear and the steady-state reached with this protocol are established. The transient regime characterizing the growth and the motion of the shear band is also studied.

L. J. Albornoz, 2, 3 E. E. Ferrero, A. B. Kolton, 4 V. Jeudy, S. Bustingorry, and J. Curiale 3, ∗ Instituto de Nanociencia y Nanotecnoloǵıa, CNEA–CONICET, Centro Atómico Bariloche, Av. E. Bustillo 9500 (R8402AGP), San Carlos de Bariloche, Rı́o Negro, Argentina. Université Paris-Saclay, CNRS, Laboratoire de Physique des Solides, 91405, Orsay, France. Instituto Balseiro, Universidad Nacional de Cuyo–CNEA, Centro Atómico Bariloche, Av. E. Bustillo 9500 (R8402AGP) San Carlos de Bariloche, Rı́o Negro, Argentina. Centro Atómico Bariloche, Comisión Nacional de Enerǵıa Atómica (CNEA), Consejo Nacional de Investigaciones Cient́ıficas y Técnicas (CONICET), Av. E. Bustillo 9500 (R8402AGP) San Carlos de Bariloche, Rı́o Negro, Argentina. (Dated: July 19, 2021)

The strain load Δγthat triggers consecutive avalanches is a key observable in the slow deformation of amorphous solids. Its temporally averaged value ⟨Δγ⟩ displays a non-trivial system-size dependence that constitutes one of the distinguishing features of the yielding transition. Details of this dependence are not yet fully understood. We address this problem by means of theoretical analysis and simulations of elastoplastic models for amorphous solids. An accurate determination of the size dependence of ⟨Δγ⟩ leads to a precise evaluation of the steady-state distribution of local distances to instabilityx. We find that the usually assumed formP(x) ∼xθ(withθbeing the so-called pseudo-gap exponent) is not accurate at lowxand that in generalP(x) tends to a system-size-dependentfinitelimit asx→ 0. We work out the consequences of this finite-size dependence standing on exact results for random-walks and disclosing an alternative interpretation of the mechanical noise felt by a reference site. We test our predictions in two- and three-dimensional elastoplastic models, showing the crucial influence of the saturation ofP(x) at smallxon the size dependence of ⟨Δγ⟩ and related scalings.

We analyze the effect of temperature on the yielding transition of amorphous solids using different coarse-grained model approaches. On one hand we use an elasto-plastic model, with temperature introduced in the form of an Arrhenius activation law over energy barriers. On the other hand, we implement a Hamiltonian model with a relaxational dynamics, where temperature is introduced in the form of a Langevin stochastic force. In both cases, temperature transforms the sharp transition of the athermal case in a smooth crossover. We show that this thermally smoothed transition follows a simple scaling form that can be fully explained using a one-particle system driven in a potential under the combined action of a mechanical and a thermal noise, the stochastically-driven Prandtl-Tomlinson model. Our work harmonizes the results of simple models for amorphous solids with the phenomenological $\sim T^{2/3}$ law proposed by Johnson and Samwer [Phys. Rev. Lett. 95, 195501 (2005)] in the framework of experimental metallic glasses yield observations, and extend it to a generic case. Finally, our results strengthen the interpretation of the yielding transition as an effective mean-field phenomenon.

The thermally activated creep motion of an elastic interface weakly driven on a disordered landscape is one of the best examples of glassy universal dynamics. Its understanding has evolved over the past 30 years thanks to a fruitful interplay among elegant scaling arguments, sophisticated analytical calculations, efficient optimization algorithms, and creative experiments. In this article, starting from the pioneer arguments, we review the main theoretical and experimental results that lead to the current physical picture of the creep regime. In particular, we discuss recent works unveiling the collective nature of such ultraslow motion in terms of elementary activated events. We show that these events control the mean velocity of the interface and cluster into "creep avalanches" statistically similar to the deterministic avalanches observed at the depinning critical threshold. The associated spatiotemporal patterns of activated events have been recently observed in experiments with magnetic domain walls. The emergent physical picture is expected to be relevant for a large family of disordered systems presenting thermally activated dynamics.

Chen Liu, Ezequiel E. Ferrero, Eduardo A. Jagla, Kirsten Martens, Alberto Rosso, and Laurent Talon Laboratoire de Physique de l’Ecole Normale Supérieure, Paris, France Instituto de Nanociencia y Nanotecnoloǵıa, CNEA–CONICET, Centro Atómico Bariloche, (R8402AGP) San Carlos de Bariloche, Rı́o Negro, Argentina. Centro Atómico Bariloche, Instituto Balseiro, Comisión Nacional de Enerǵıa Atómica, CNEA, CONICET, UNCUYO, Av. E. Bustillo 9500 R8402AGP S. C. de Bariloche, Rı́o Negro, Argentina Univ. Grenoble Alpes, CNRS, LIPhy, 38000 Grenoble, France LPTMS, CNRS, Univ. Paris-Sud, Université Paris-Saclay, 91405 Orsay, France FAST, CNRS, Univ. Paris-Sud, Université Paris-Saclay, 91405 Orsay, France (Dated: January 1, 2021)

Recent atomistic simulations have identified novel rheological properties on amorphous materials under quasi-static oscillatory shear. Using a coarse-grained model based on the evolution of a continuum strain field, we characterize these properties in the stationary limit, reached after several oscillations. We built a `phase diagram' depending on two control parameters: the strain amplitude $\gamma_{\max}$ and the degree of annealing $E_{\text{init}}$. At small amplitudes, poorly annealed materials display {\em shear annealing} behavior, appearing better and better annealed as $\gamma_{\max}$ is increased. Ultra-stable materials are instead insensitive to those oscillations. Above a critical strain amplitude $\gamma_c$, that increases with annealing level, the melting of the material in a localized band of finite width is observed. Inside the band, the material flows, outside the band there is a marginal solid independent of the initial degree of annealing. Such a `phase transition' at $\gamma_c$ between a solid and a mixed phase is discontinuous. The transient dynamics before reaching the steady state is also studied.

We analyze the behavior of different elastoplastic models approaching the yielding transition. We propose two kind of rules for the local yielding events: yielding occurs above the local threshold either at a constant rate or with a rate that increases as the square root of the stress excess. We establish a family of static universal critical exponents which do not depend on this dynamic detail of the model rules: in particular, the exponents for the avalanche size distribution $P(S)\sim S^{-\tau_S}f(S/L^{d_f})$ and the exponents describing the density of sites at the verge of yielding, which we find to be of the form $P(x)\simeq P(0) + x^\theta$ with $P(0)\sim L^{-a}$ controlling the extremal statistics. On the other hand, we discuss exponents that are sensitive to the local yielding rule details. We find that, apart form the dynamical exponent $z$ controlling the duration of avalanches, also the flowcurve's (inverse) Herschel-Bulkley exponent $\beta$ ($\dot\gamma\sim(\sigma-\sigma_c)^\beta$) enters in this category, and is seen to differ in $\frac12$ between the two yielding rate cases. We give analytical support to this numerical observation by calculating the exponent variation in the Hebraud-Lequeux model and finding an identical shift. We further discuss an alternative mean-field approximation to yielding only based on the so-called Hurst exponent of the accumulated mechanical noise signal, which gives good predictions for the exponents extracted from simulations of fully spatial models.

We analyze the behavior of different elastoplastic models approaching the yielding transition. We propose two kinds of rules for the local yielding events: yielding occurs above the local threshold either at a constant rate or with a rate that increases as the square root of the stress excess. We establish a family of "static" universal critical exponents which do not depend on this dynamic detail of the model rules: in particular, the exponents for the avalanche size distribution P(S) ∼S-τSf(S/Ldf) and the exponents describing the density of sites at the verge of yielding, which we find to be of the form P(x) ≃P(0) + xθ with P(0) ∼L-a controlling the extremal statistics. On the other hand, we discuss "dynamical" exponents that are sensitive to the local yielding rule. We find that, apart form the dynamical exponent z controlling the duration of avalanches, also the flowcurve's (inverse) Herschel-Bulkley exponent β ([small gamma, Greek, dot above]∼ (σ-σc)β) enters in this category, and is seen to differ in ½ between the two yielding rate cases. We give analytical support to this numerical observation by calculating the exponent variation in the Hébraud-Lequeux model and finding an identical shift. We further discuss an alternative mean-field approximation to yielding only based on the so-called Hurst exponent of the accumulated mechanical noise signal, which gives good predictions for the exponents extracted from simulations of fully spatial models.

The origin of the brittle-to-ductile transition, experimentally observed in amorphous silica nanofibers as the sample size is reduced, is still debated. Here we investigate the issue by extensive molecular dynamics simulations at low and room temperatures for a broad range of sample sizes, with open and periodic boundary conditions. Our results show that small sample-size enhanced ductility is primarily due to diffuse damage accumulation, that for larger samples leads to brittle catastrophic failure. Surface effects such as boundary fluidization contribute to ductility at room temperature by promoting necking, but are not the main driver of the transition. Our results suggest that the experimentally observed size-induced ductility of silica nanofibers is a manifestation of finite-size criticality, as expected in general for quasi-brittle disordered networks.

Magnetic domain wall motion is at the heart of new magneto-electronic technologies and hence the need for a deeper understanding of domain wall dynamics in magnetic systems. In this context, numerical simulations using simple models can capture the main ingredients responsible for the complex observed domain wall behavior. We present a scalar-field model for the magnetization dynamics of quasi-two-dimensional systems with a perpendicular easy axis of magnetization which allows a direct comparison with typical experimental protocols, used in polar magneto-optical Kerr effect microscopy experiments. We show that the thermally activated creep and depinning regimes of domain wall motion can be reached, and the effect of different quenched disorder implementations can be assessed with the model. In particular, we show that the depinning field increases with the mean grain size of a Voronoi tessellation model for the disorder.