Elisabeth Agoritsas

Bio: Elisabeth Agoritsas is an academic researcher from École Polytechnique Fédérale de Lausanne. The author has contributed to research in topics: Langevin dynamics & Particle system. The author has an hindex of 14, co-authored 37 publications receiving 453 citations. Previous affiliations of Elisabeth Agoritsas include University of Grenoble & University of Paris.

On the relevance of disorder in athermal amorphous materials under shear

Abstract: We show that, at least at a mean-field level, the effect of structural disorder in sheared amorphous media is very dissimilar depending on the thermal or athermal nature of their underlying dynamics. We first introduce a toy model, including explicitly two types of noise (thermal versus athermal). Within this interpretation framework, we argue that mean-field athermal dynamics can be accounted for by the so-called Hebraud-Lequeux (HL) model, in which the mechanical noise stems explicitly from the plastic activity in the sheared medium. Then, we show that the inclusion of structural disorder, by means of a distribution of yield energy barriers, has no qualitative effect in the HL model, while such a disorder is known to be one of the key ingredients leading kinematically to a finite macroscopic yield stress in other mean-field descriptions, such as the Soft-Glassy-Rheology model. We conclude that the statistical mechanisms at play in the emergence of a macroscopic yield stress, and a complex stationary dynamics at low shear rate, are different in thermal and athermal amorphous systems.

Nonlinear Rheology in a Model Biological Tissue.

Abstract: The rheological response of dense active matter is a topic of fundamental importance for many processes in nature such as the mechanics of biological tissues. 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 an increasing shear rate. To rationalize this nonlinear 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.

Disordered elastic systems and one-dimensional interfaces

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.

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

Abstract: 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 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.

A direct link between active matter and sheared granular systems.

Abstract: 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-as measured by their avalanche statistics-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 two dimensions using a numerical protocol, termed "athermal quasistatic random displacement," and find that these mean-field predictions are surprisingly accurate in low dimensions. We identify a general class of perturbations that smoothly interpolates 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.

Shape Fluctuations and Random Matrices

Abstract: We study a certain random groeth model in two dimensions closely related to the one-dimensional totally asymmetric exclusion process. The results show that the shape fluctuations, appropriately scaled, converges in distribution to the Tracy-Widom largest eigenvalue distribution for the Gaussian Unitary Ensemble.