arXiv subjects

Elisabeth Agoritsas

Publications and source records attributed to Elisabeth Agoritsas.

At least 19 recordsLinked to original sources

arXiv2024

Memory formation in dense persistent active matter

Protocol-dependent states in structural glasses can encode a disordered, yet retrievable memory. While training such materials is typically done via a global drive, such as external shear, in dense active matter the driving is instead local and spatio-temporally correlated. Here we focus on the impact of such spatial correlation on memory formation. We investigate the mechanical response of a dense amorphous packing of athermal particles, subject to an oscillatory quasistatic driving with a tunable spatial correlation, akin to the instantaneous driving pattern in active matter. We find that the capacity to encode memory can be rendered comparable upon a proper rescaling on the spatial correlation, whereas the efficiency in memory formation increases with motion cooperativity.

cond-mat.soft↗

arXiv2024

Loss of memory of an elastic line on its way to limit cycles

Under an oscillating mechanical drive, an amorphous material progressively forgets its initial configuration and might eventually converge to a limit cycle. Beyond quasistatic drivings, how structurally disordered systems lose or record such memory remains theoretically challenging. Here we investigate these issues in a minimal model system -- with quenched disorder and memory encoded in a spatial pattern -- where the oscillating protocol can formally be replaced by finite positive-velocity driving. We consider an elastic line driven at zero temperature in a fixed disordered landscape, with bi-periodic boundary conditions and tunable system size. This setting allows us to control the area swept by the line at each cycle in a given disorder realisation, as would the amplitude of an oscillating drive. We find that the line converges to disorder-dependent limit cycles, jointly for its geometrical \emph{and} velocity profiles. Moreover, the way it forgets its initial condition is strongly coupled to the nature of the velocity dynamics it displays depending on system size. We conclude on the implications of these results for the response of amorphous materials under \emph{non}-quasistatic oscillating protocols.

cond-mat.stat-mech↗

arXiv2023

Ductile-to-brittle transition and yielding in soft amorphous materials: perspectives and open questions

Soft amorphous materials are viscoelastic solids ubiquitously found around us, from clays and cementitious pastes to emulsions and physical gels encountered in food or biomedical engineering. Under an external deformation, these materials undergo a noteworthy transition from a solid to a liquid state that reshapes the material microstructure. This yielding transition was the main theme of a workshop held from January 9 to 13, 2023 at the Lorentz Center in Leiden. The manuscript presented here offers a critical perspective on the subject, synthesizing insights from the various brainstorming sessions and informal discussions that unfolded during this week of vibrant exchange of ideas. The result of these exchanges takes the form of a series of open questions that represent outstanding experimental, numerical, and theoretical challenges to be tackled in the near future.

cond-mat.soft↗

arXiv2023

Explaining the effects of non-convergent sampling in the training of Energy-Based Models

In this paper, we quantify the impact of using non-convergent Markov chains to train Energy-Based models (EBMs). In particular, we show analytically that EBMs trained with non-persistent short runs to estimate the gradient can perfectly reproduce a set of empirical statistics of the data, not at the level of the equilibrium measure, but through a precise dynamical process. Our results provide a first-principles explanation for the observations of recent works proposing the strategy of using short runs starting from random initial conditions as an efficient way to generate high-quality samples in EBMs, and lay the groundwork for using EBMs as diffusion models. After explaining this effect in generic EBMs, we analyze two solvable models in which the effect of the non-convergent sampling in the trained parameters can be described in detail. Finally, we test these predictions numerically on a ConvNet EBM and a Boltzmann machine.

cs.LG↗

arXiv2022

Microscopic interplay of temperature and disorder of a one-dimensional elastic interface

Elastic interfaces display scale-invariant geometrical fluctuations at sufficiently large lengthscales. Their asymptotic static roughness then follows a power-law behavior, whose associated exponent provides a robust signature of the universality class to which they belong. The associated prefactor has instead a non-universal amplitude fixed by the microscopic interplay between thermal fluctuations and disorder, usually hidden below experimental resolution. Here we compute numerically the roughness of a one-dimensional elastic interface subject to both thermal fluctuations and a quenched disorder with a finite correlation length. We evidence the existence of a novel power-law regime at short lengthscales. We determine the corresponding exponent $ζ_\textrm{dis}$ and find compelling numerical evidence that, contrarily to available analytic predictions, one has $ζ_\textrm{dis} < 1$. We discuss the consequences on the temperature dependence of the roughness and the connection with the asymptotic random-manifold regime at large lengthscales. We also discuss the implications of our findings for other systems such as the Kardar-Parisi-Zhang equation and the Burgers turbulence.

cond-mat.dis-nn↗

arXiv2022

Mean-field description for the architecture of low-energy excitations in glasses

In amorphous materials, groups of particles can rearrange locally into a new stable configuration. Such elementary excitations are key as they determine the response to external stresses, as well as to thermal and quantum fluctuations. Yet, understanding what controls their geometry remains a challenge. Here we build a scaling description of the geometry and energy of low-energy excitations in terms of the distance to an instability, as predicted for instance at the dynamical transition in mean field approaches of supercooled liquids. We successfully test our predictions in ultrastable computer glasses, with a gapped and ungapped (regular) spectrum. Overall, our approach explains why excitations become less extended, with a higher energy and displacement scale upon cooling.

cond-mat.soft↗

arXiv2021

Supersymmetries in non-equilibrium Langevin dynamics

Stochastic phenomena are often described by Langevin equations, which serve as a mesoscopic model for microscopic dynamics. It is known since the work of Parisi and Sourlas that reversible (or equilibrium) dynamics present supersymmetries (SUSYs). These are revealed when the path-integral action is written as a function not only of the physical fields, but also of Grassmann fields representing a Jacobian arising from the noise distribution. SUSYs leave the action invariant upon a transformation of the fields that mixes the physical and the Grassmann ones. We show that, contrarily to the common belief, it is possible to extend the known reversible construction to the case of arbitrary irreversible dynamics, for overdamped Langevin equations with additive white noise - provided their steady state is known. The construction is based on the fact that the Grassmann representation of the functional determinant is not unique, and can be chosen so as to present a generalization of the Parisi-Sourlas SUSY. Our approach is valid both for Martin-Siggia-Rose-Janssen-de Dominicis and for Onsager-Machlup actions. We show how such SUSYs are related to time-reversal symmetries and allow one to derive modified fluctuation-dissipation relations valid in non-equilibrium. We give as a concrete example the results for the Kardar-Parisi-Zhang equation.

cond-mat.stat-mech↗

arXiv2021

A direct link between active matter and sheared granular systems

The similarity in mechanical properties of dense active matter and sheared amorphous solids has been noted in recent years without a rigorous examination of the underlying mechanism. We develop a mean-field model that predicts that their critical behavior should be equivalent in infinite dimensions, up to a rescaling factor that depends on the correlation length of the applied field. We test these predictions in 2d using a new numerical protocol, termed `athermal quasi-static random displacement', and find that these mean-field predictions are surprisingly accurate in low dimensions. We identify a general class of perturbations that smoothly interpolate between the uncorrelated localized forces that occur in the high-persistence limit of dense active matter, and system-spanning correlated displacements that occur under applied shear. These results suggest a universal framework for predicting flow, deformation, and failure in active and sheared disordered materials.

cond-mat.soft↗

arXiv2021

A numerical study of the statistics of roughness parameters for fluctuating interfaces

Self-affine rough interfaces are ubiquitous in experimental systems, and display characteristic scaling properties as a signature of the nature of disorder in their supporting medium, i.e. of the statistical features of its heterogeneities. Different methods have been used to extract roughness information from such self-affine structures, and in particular their scaling exponents and associated prefactors. Notably, for an experimental characterization of roughness features, it is of paramount importance to properly assess sample-to-sample fluctuations of roughness parameters. Here, by performing scaling analysis based on displacement correlation functions in real and reciprocal space, we compute statistical properties of the roughness parameters. As an ideal, artifact-free reference case study and particularly targeting finite-size systems, we consider three cases of numerically simulated one-dimensional interfaces: (i) elastic lines under thermal fluctuations and free of disorder, (ii) directed polymers in equilibrium with a disordered energy landscape, and (iii) elastic lines in the critical depinning state when the external applied driving force equals the depinning force set by disorder. Our results shows that sample-to-sample fluctuations are rather large when measuring the roughness exponent. These fluctuations are also relevant for roughness amplitudes. Therefore a minimum of independent interface realizations (at least a few tens in our numerical simulations) should be used to guarantee sufficient statistical averaging, an issue often overlooked in experimental reports.

cond-mat.dis-nn↗

arXiv2021

Field-dependent roughness of moving domain walls in a Pt/Co/Pt magnetic thin film

The creep motion of domain walls driven by external fields in magnetic thin films is described by universal features related to the underlying depinning transition. One key parameter in this description is the roughness exponent characterizing the growth of fluctuations of the domain wall position with its longitudinal length scale. The roughness amplitude, which gives information about the scale of fluctuations, however, has received less attention. Albeit their relevance, experimental reports of the roughness parameters, both exponent and amplitude, are scarce. We report here experimental values of the roughness parameters for different magnetic field intensities in the creep regime at room temperature for a Pt/Co/Pt thin film. The mean value of the roughness exponent is $ζ= 0.74$, and we show that it can be rationalized as an effective value in terms of the known universal values corresponding to the depinning and thermal cases. In addition, it is shown that the roughness amplitude presents a significant increase with decreasing field. These results contribute to the description of domain wall motion in disordered thin magnetic systems.

cond-mat.dis-nn↗

arXiv2020

Mean-field dynamics of infinite-dimensional particle systems: global shear versus random local forcing

In infinite dimension, many-body systems of pairwise interacting particles provide exact analytical benchmarks for features of amorphous materials, such as the stress-strain curve of glasses under quasistatic shear. Here, instead of a global shear, we consider an alternative driving protocol as recently introduced in Ref. [1], which consists of randomly assigning a constant local displacement on each particle, with a finite spatial correlation length. We show that, in the infinite-dimension limit, the mean-field dynamics under such a random forcing is strictly equivalent to that under global shear, upon a simple rescaling of the accumulated strain. Moreover, the scaling factor is essentially given by the variance of the relative local displacements on interacting pairs of particles, which encodes the presence of a finite spatial correlation. In this framework, global shear is simply a special case of a much broader family of local forcing, that can be explored by tuning its spatial correlations. We discuss specifically the implications on the quasistatic driving of glasses -- initially prepared at a replica-symmetric equilibrium -- and how the corresponding 'stress-strain'-like curves and the elastic moduli can be rescaled onto their quasistatic-shear counterparts. These results hint at a unifying framework for establishing rigourous analogies, at the mean-field level, between different driven disordered systems.

cond-mat.dis-nn↗

arXiv2020

Thermal origin of quasi-localised excitations in glasses

Key aspects of glasses are controlled by the presence of excitations in which a group of particles can rearrange. Surprisingly, recent observations indicate that their density is dramatically reduced and their size decreases as the temperature of the supercooled liquid is lowered. Some theories predict these excitations to cause a gap in the spectrum of quasi-localised modes of the Hessian that grows upon cooling, while others predict a pseudo-gap ${D_L(ω)} \sim ω^α$. To unify these views and observations, we generate glassy configurations of controlled gap magnitude $ω_c$ at temperature ${T=0}$, using so-called `breathing' particles, and study how such gapped states respond to thermal fluctuations. We find that \textit{(i)}~the gap always fills up at finite $T$ with ${D_L(ω) \approx A_4(T) \, ω^4}$ and ${A_4 \sim \exp(-E_a / T)}$ at low $T$, \textit{(ii)}~$E_a$ rapidly grows with $ω_c$, in reasonable agreement with a simple scaling prediction ${E_a\sim ω_c^4}$ and \textit{(iii)}~at larger $ω_c$ excitations involve fewer particles, as we rationalise, and eventually become string-like. We propose an interpretation of mean-field theories of the glass transition, in which the modes beyond the gap act as an excitation reservoir, from which a pseudo-gap distribution is populated with its magnitude rapidly decreasing at lower $T$. We discuss how this picture unifies the rarefaction as well as the decreasing size of excitations upon cooling, together with a string-like relaxation occurring near the glass transition.

cond-mat.soft↗

arXiv2020

From bulk descriptions to emergent interfaces: connecting the Ginzburg-Landau and elastic line models

Controlling interfaces is highly relevant from a technological point of view. However, their rich and complex behavior makes them very difficult to describe theoretically, and hence to predict. In this work, we establish a procedure to connect two levels of descriptions of interfaces: for a bulk description, we consider a two-dimensional Ginzburg-Landau model evolving with a Langevin equation, and boundary conditions imposing the formation of a rectilinear domain wall. At this level of description no assumptions need to be done over the interface, but analytical calculations are almost impossible to handle. On a different level of description, we consider a one-dimensional elastic line model evolving according to the Edwards-Wilkinson equation, which only allows one to study continuous and univalued interfaces, but which was up to now one of the most successful tools to treat interfaces analytically. To establish the connection between the bulk description and the interface description, we propose a simple method that applies both to clean and disordered systems. We probe the connection by numerical simulations at both levels, and our simulations, in addition to making contact with experiments, allow us to test and provide insight to develop new analytical approaches to treat interfaces.

cond-mat.dis-nn↗

arXiv2019

Out-of-equilibrium dynamical equations of infinite-dimensional particle systems. II. The anisotropic case under shear strain

As an extension of the isotropic setting presented in the companion paper [J. Phys. A 52, 144002 (2019)], we consider the Langevin dynamics of a many-body system of pairwise interacting particles in $d$ dimensions, submitted to an external shear strain. We show that the anisotropy introduced by the shear strain can be simply addressed by moving into the co-shearing frame, leading to simple dynamical mean field equations in the limit ${d\to\infty}$. The dynamics is then controlled by a single one-dimensional effective stochastic process which depends on three distinct strain-dependent kernels - self-consistently determined by the process itself - encoding the effective restoring force, friction and noise terms due to the particle interactions. From there one can compute dynamical observables such as particle mean-square displacements and shear stress fluctuations, and eventually aim at providing an exact ${d \to \infty}$ benchmark for liquid and glass rheology. As an application of our results, we derive dynamically the 'state-following' equations that describe the static response of a glass to a finite shear strain until it yields.

cond-mat.dis-nn↗

arXiv2019

Out-of-equilibrium dynamical equations of infinite-dimensional particle systems. I. The isotropic case

We consider the Langevin dynamics of a many-body system of interacting particles in $d$ dimensions, in a very general setting suitable to model several out-of-equilibrium situations, such as liquid and glass rheology, active self-propelled particles, and glassy aging dynamics. The pair interaction potential is generic, and can be chosen to model colloids, atomic liquids, and granular materials. In the limit ${d\to\infty}$, we show that the dynamics can be exactly reduced to a single one-dimensional effective stochastic equation, with an effective thermal bath described by kernels that have to be determined self-consistently. We present two complementary derivations, via a dynamical cavity method and via a path-integral approach. From the effective stochastic equation, one can compute dynamical observables such as pressure, shear stress, particle mean-square displacement, and the associated response function. As an application of our results, we derive dynamically the `state-following' equations that describe the response of a glass to quasistatic perturbations, thus bypassing the use of replicas. The article is written in a modular way, that allows the reader to skip the details of the derivations and focus on the physical setting and the main results.

cond-mat.dis-nn↗

arXiv2018

Out-of-equilibrium dynamical mean-field equations for the perceptron model

Perceptrons are the building blocks of many theoretical approaches to a wide range of complex systems, ranging from neural networks and deep learning machines, to constraint satisfaction problems, glasses and ecosystems. Despite their applicability and importance, a detailed study of their Langevin dynamics has never been performed yet. Here we derive the mean-field dynamical equations that describe the continuous random perceptron in the thermodynamic limit, in a very general setting with arbitrary noise and friction kernels, not necessarily related by equilibrium relations. We derive the equations in two ways: via a dynamical cavity method, and via a path-integral approach in its supersymmetric formulation. The end point of both approaches is the reduction of the dynamics of the system to an effective stochastic process for a representative dynamical variable. Because the perceptron is formally very close to a system of interacting particles in a high dimensional space, the methods we develop here can be transferred to the study of liquid and glasses in high dimensions. Potentially interesting applications are thus the study of the glass transition in active matter, the study of the dynamics around the jamming transition, and the calculation of rheological properties in driven systems.

cond-mat.dis-nn↗

arXiv2017

Nontrivial rheological exponents in sheared yield stress fluids

In this work we discuss possible physical origins for non-trivial exponents in the athermal rheology of soft materials at low but finite driving rates. A key ingredient in our scenario is the presence of a self-consistent mechanical noise that stems from the spatial superposition of long-range elastic responses to localized plastically deforming regions. We study analytically a mean-field model, in which this mechanical noise is accounted for by a stress diffusion term coupled to the plastic activity. Within this description we show how a dependence of the shear modulus and/or the local relaxation time on the shear rate introduces corrections to the usual mean-field prediction, concerning the Herschel-Bulkley-type rheological response of exponent 1/2. This feature of the mean-field picture is then shown to be robust with respect to structural disorder and partial relaxation of the local stress. We test this prediction numerically on a mesoscopic lattice model that implements explicitly the long-range elastic response to localized shear transformations, and we conclude on how our scenario might be tested in rheological experiments.

cond-mat.soft↗

arXiv2017

Nonlinear Rheology in a Model Biological Tissue

Mechanical signaling plays a key role in biological processes like embryo development and cancer growth. One prominent way to probe mechanical properties of tissues is to study their response to externally applied forces. Using a particle-based model featuring random apoptosis and environment-dependent division rates, we evidence a crossover from linear flow to a shear-thinning regime with increasing shear rate. To rationalize this non-linear flow we derive a theoretical mean-field scenario that accounts for the interplay of mechanical and active noise in local stresses. These noises are respectively generated by the elastic response of the cell matrix to cell rearrangements and by the internal activity.

cond-mat.soft↗